aboutsummaryrefslogtreecommitdiffstats
path: root/doc/design/outfile.ps
blob: bab36946b86eae61eb1acc8c0123306d28559c45 (plain) (blame)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
5206
5207
5208
5209
5210
5211
5212
5213
5214
5215
5216
5217
5218
5219
5220
5221
5222
5223
5224
5225
5226
5227
5228
5229
5230
5231
5232
5233
5234
5235
5236
5237
5238
5239
5240
5241
5242
5243
5244
5245
5246
5247
5248
5249
5250
5251
5252
5253
5254
5255
5256
5257
5258
5259
5260
5261
5262
5263
5264
5265
5266
5267
5268
5269
5270
5271
5272
5273
5274
5275
5276
5277
5278
5279
5280
5281
5282
5283
5284
5285
5286
5287
5288
5289
5290
5291
5292
5293
5294
5295
5296
5297
5298
5299
5300
5301
5302
5303
5304
5305
5306
5307
5308
5309
5310
5311
5312
5313
5314
5315
5316
5317
5318
5319
5320
5321
5322
5323
5324
5325
5326
5327
5328
5329
5330
5331
5332
5333
5334
5335
5336
5337
5338
5339
5340
5341
5342
5343
5344
5345
5346
5347
5348
5349
5350
5351
5352
5353
5354
5355
5356
5357
5358
5359
5360
5361
5362
5363
5364
5365
5366
5367
5368
5369
5370
5371
5372
5373
5374
5375
5376
5377
5378
5379
5380
5381
5382
5383
5384
5385
5386
5387
5388
5389
5390
5391
5392
5393
5394
5395
5396
5397
5398
5399
5400
5401
5402
5403
5404
5405
5406
5407
5408
5409
5410
5411
5412
5413
5414
5415
5416
5417
5418
5419
5420
5421
5422
5423
5424
5425
5426
5427
5428
5429
5430
5431
5432
5433
5434
5435
5436
5437
5438
5439
5440
5441
5442
5443
5444
5445
5446
5447
5448
5449
5450
5451
5452
5453
5454
5455
5456
5457
5458
5459
5460
5461
5462
5463
5464
5465
5466
5467
5468
5469
5470
5471
5472
5473
5474
5475
5476
5477
5478
5479
5480
5481
5482
5483
5484
5485
5486
5487
5488
5489
5490
5491
5492
5493
5494
5495
5496
5497
5498
5499
5500
5501
5502
5503
5504
5505
5506
5507
5508
5509
5510
5511
5512
5513
5514
5515
5516
5517
5518
5519
5520
5521
5522
5523
5524
5525
5526
5527
5528
5529
5530
5531
5532
5533
5534
5535
5536
5537
5538
5539
5540
5541
5542
5543
5544
5545
5546
5547
5548
5549
5550
5551
5552
5553
5554
5555
5556
5557
5558
5559
5560
5561
5562
5563
5564
5565
5566
5567
5568
5569
5570
5571
5572
5573
5574
5575
5576
5577
5578
5579
5580
5581
5582
5583
5584
5585
5586
5587
5588
5589
5590
5591
5592
5593
5594
5595
5596
5597
5598
5599
5600
5601
5602
5603
5604
5605
5606
5607
5608
5609
5610
5611
5612
5613
5614
5615
5616
5617
5618
5619
5620
5621
5622
5623
5624
5625
5626
5627
5628
5629
5630
5631
5632
5633
5634
5635
5636
5637
5638
5639
5640
5641
5642
5643
5644
5645
5646
5647
5648
5649
5650
5651
5652
5653
5654
5655
5656
5657
5658
5659
5660
5661
5662
5663
5664
5665
5666
5667
5668
5669
5670
5671
5672
5673
5674
5675
5676
5677
5678
5679
5680
5681
5682
5683
5684
5685
5686
5687
5688
5689
5690
5691
5692
5693
5694
5695
5696
5697
5698
5699
5700
5701
5702
5703
5704
5705
5706
5707
5708
5709
5710
5711
5712
5713
5714
5715
5716
5717
5718
5719
5720
5721
5722
5723
5724
5725
5726
5727
5728
5729
5730
5731
5732
5733
5734
5735
5736
5737
5738
5739
5740
5741
5742
5743
5744
5745
5746
5747
5748
5749
5750
5751
5752
5753
5754
5755
5756
5757
5758
5759
5760
5761
5762
5763
5764
5765
5766
5767
5768
5769
5770
5771
5772
5773
5774
5775
5776
5777
5778
5779
5780
5781
5782
5783
5784
5785
5786
5787
5788
5789
5790
5791
5792
5793
5794
5795
5796
5797
5798
5799
5800
5801
5802
5803
5804
5805
5806
5807
5808
5809
5810
5811
5812
5813
5814
5815
5816
5817
5818
5819
5820
5821
5822
5823
5824
5825
5826
5827
5828
5829
5830
5831
5832
5833
5834
5835
5836
5837
5838
5839
5840
5841
5842
5843
5844
5845
5846
5847
5848
5849
5850
5851
5852
5853
5854
5855
5856
5857
5858
5859
5860
5861
5862
5863
5864
5865
5866
5867
5868
5869
5870
5871
5872
5873
5874
5875
5876
5877
5878
5879
5880
5881
5882
5883
5884
5885
5886
5887
5888
5889
5890
5891
5892
5893
5894
5895
5896
5897
5898
5899
5900
5901
5902
5903
5904
5905
5906
5907
5908
5909
5910
5911
5912
5913
5914
5915
5916
5917
5918
5919
5920
5921
5922
5923
5924
5925
5926
5927
5928
5929
5930
5931
5932
5933
5934
5935
5936
5937
5938
5939
5940
5941
5942
5943
5944
5945
5946
5947
5948
5949
5950
5951
5952
5953
5954
5955
5956
5957
5958
5959
5960
5961
5962
5963
5964
5965
5966
5967
5968
5969
5970
5971
5972
5973
5974
5975
5976
5977
5978
5979
5980
5981
5982
5983
5984
5985
5986
5987
5988
5989
5990
5991
5992
5993
5994
5995
5996
5997
5998
5999
6000
6001
6002
6003
6004
6005
6006
6007
6008
6009
6010
6011
6012
6013
6014
6015
6016
6017
6018
6019
6020
6021
6022
6023
6024
6025
6026
6027
6028
6029
6030
6031
6032
6033
6034
6035
6036
6037
6038
6039
6040
6041
6042
6043
6044
6045
6046
6047
6048
6049
6050
6051
6052
6053
6054
6055
6056
6057
6058
6059
6060
6061
6062
6063
6064
6065
6066
6067
6068
6069
6070
6071
6072
6073
6074
6075
6076
6077
6078
6079
6080
6081
6082
6083
6084
6085
6086
6087
6088
6089
6090
6091
6092
6093
6094
6095
6096
6097
6098
6099
6100
6101
6102
6103
6104
6105
6106
6107
6108
6109
6110
6111
6112
6113
6114
6115
6116
6117
6118
6119
6120
6121
6122
6123
6124
6125
6126
6127
6128
6129
6130
6131
6132
6133
6134
6135
6136
6137
6138
6139
6140
6141
6142
6143
6144
6145
6146
6147
6148
6149
6150
6151
6152
6153
6154
6155
6156
6157
6158
6159
6160
6161
6162
6163
6164
6165
6166
6167
6168
6169
6170
6171
6172
6173
6174
6175
6176
6177
6178
6179
6180
6181
6182
6183
6184
6185
6186
6187
6188
6189
6190
6191
6192
6193
6194
6195
6196
6197
6198
6199
6200
6201
6202
6203
6204
6205
6206
6207
6208
6209
6210
6211
6212
6213
6214
6215
6216
6217
6218
6219
6220
6221
6222
6223
6224
6225
6226
6227
6228
6229
6230
6231
6232
6233
6234
6235
6236
6237
6238
6239
6240
6241
6242
6243
6244
6245
6246
6247
6248
6249
6250
6251
6252
6253
6254
6255
6256
6257
6258
6259
6260
6261
6262
6263
6264
6265
6266
6267
6268
6269
6270
6271
6272
6273
6274
6275
6276
6277
6278
6279
6280
6281
6282
6283
6284
6285
6286
6287
6288
6289
6290
6291
6292
6293
6294
6295
6296
6297
6298
6299
6300
6301
6302
6303
6304
6305
6306
6307
6308
6309
6310
6311
6312
6313
6314
6315
6316
6317
6318
6319
6320
6321
6322
6323
6324
6325
6326
6327
6328
6329
6330
6331
6332
6333
6334
6335
6336
6337
6338
6339
6340
6341
6342
6343
6344
6345
6346
6347
6348
6349
6350
6351
6352
6353
6354
6355
6356
6357
6358
6359
6360
6361
6362
6363
6364
6365
6366
6367
6368
6369
6370
6371
6372
6373
6374
6375
6376
6377
6378
6379
6380
6381
6382
6383
6384
6385
6386
6387
6388
6389
6390
6391
6392
6393
6394
6395
6396
6397
6398
6399
6400
6401
6402
6403
6404
6405
6406
6407
6408
6409
6410
6411
6412
6413
6414
6415
6416
6417
6418
6419
6420
6421
6422
6423
6424
6425
6426
6427
6428
6429
6430
6431
6432
6433
6434
6435
6436
6437
6438
6439
6440
6441
6442
6443
6444
6445
6446
6447
6448
6449
6450
6451
6452
6453
6454
6455
6456
6457
6458
6459
6460
6461
6462
6463
6464
6465
6466
6467
6468
6469
6470
6471
6472
6473
6474
6475
6476
6477
6478
6479
6480
6481
6482
6483
6484
6485
6486
6487
6488
6489
6490
6491
6492
6493
6494
6495
6496
6497
6498
6499
6500
6501
6502
6503
6504
6505
6506
6507
6508
6509
6510
6511
6512
6513
6514
6515
6516
6517
6518
6519
6520
6521
6522
6523
6524
6525
6526
6527
6528
6529
6530
6531
6532
6533
6534
6535
6536
6537
6538
6539
6540
6541
6542
6543
6544
6545
6546
6547
6548
6549
6550
6551
6552
6553
6554
6555
6556
6557
6558
6559
6560
6561
6562
6563
6564
6565
6566
6567
6568
6569
6570
6571
6572
6573
6574
6575
6576
6577
6578
6579
6580
6581
6582
6583
6584
6585
6586
6587
6588
6589
6590
6591
6592
6593
6594
6595
6596
6597
6598
6599
6600
6601
6602
6603
6604
6605
6606
6607
6608
6609
6610
6611
6612
6613
6614
6615
6616
6617
6618
6619
6620
6621
6622
6623
6624
6625
6626
6627
6628
6629
6630
6631
6632
6633
6634
6635
6636
6637
6638
6639
6640
6641
6642
6643
6644
6645
6646
6647
6648
6649
6650
6651
6652
6653
6654
6655
6656
6657
6658
6659
6660
6661
6662
6663
6664
6665
6666
6667
6668
6669
6670
6671
6672
6673
6674
6675
6676
6677
6678
6679
6680
6681
6682
6683
6684
6685
6686
6687
6688
6689
6690
6691
6692
6693
6694
6695
6696
6697
6698
6699
6700
6701
6702
6703
6704
6705
6706
6707
6708
6709
6710
6711
6712
6713
6714
6715
6716
6717
6718
6719
6720
6721
6722
6723
6724
6725
6726
6727
6728
6729
6730
6731
6732
6733
6734
6735
6736
6737
6738
6739
6740
6741
6742
6743
6744
6745
6746
6747
6748
6749
6750
6751
6752
6753
6754
6755
6756
6757
6758
6759
6760
6761
6762
6763
6764
6765
6766
6767
6768
6769
6770
6771
6772
6773
6774
6775
6776
6777
6778
6779
6780
6781
6782
6783
6784
6785
6786
6787
6788
6789
6790
6791
6792
6793
6794
6795
6796
6797
6798
6799
6800
6801
6802
6803
6804
6805
6806
6807
6808
6809
6810
6811
6812
6813
6814
6815
6816
6817
6818
6819
6820
6821
6822
6823
6824
6825
6826
6827
6828
6829
6830
6831
6832
6833
6834
6835
6836
6837
6838
6839
6840
6841
6842
6843
6844
6845
6846
6847
6848
6849
6850
6851
6852
6853
6854
6855
6856
6857
6858
6859
6860
6861
6862
6863
6864
6865
6866
6867
6868
6869
6870
6871
6872
6873
6874
6875
6876
6877
6878
6879
6880
6881
6882
6883
6884
6885
6886
6887
6888
6889
6890
6891
6892
6893
6894
6895
6896
6897
6898
6899
6900
6901
6902
6903
6904
6905
6906
6907
6908
6909
6910
6911
6912
6913
6914
6915
6916
6917
6918
6919
6920
6921
6922
6923
6924
6925
6926
6927
6928
6929
6930
6931
6932
6933
6934
6935
6936
6937
6938
6939
6940
6941
6942
6943
6944
6945
6946
6947
6948
6949
6950
6951
6952
6953
6954
6955
6956
6957
6958
6959
6960
6961
6962
6963
6964
6965
6966
6967
6968
6969
6970
6971
6972
6973
6974
6975
6976
6977
6978
6979
6980
6981
6982
6983
6984
6985
6986
6987
6988
6989
6990
6991
6992
6993
6994
6995
6996
6997
6998
6999
7000
7001
7002
7003
7004
7005
7006
7007
7008
7009
7010
7011
7012
7013
7014
7015
7016
7017
7018
7019
7020
7021
7022
7023
7024
7025
7026
7027
7028
7029
7030
7031
7032
7033
7034
7035
7036
7037
7038
7039
7040
7041
7042
7043
7044
7045
7046
7047
7048
7049
7050
7051
7052
7053
7054
7055
7056
7057
7058
7059
7060
7061
7062
7063
7064
7065
7066
7067
7068
7069
7070
7071
7072
7073
7074
7075
7076
7077
7078
7079
7080
7081
7082
7083
7084
7085
7086
7087
7088
7089
7090
7091
7092
7093
7094
7095
7096
7097
7098
7099
7100
7101
7102
7103
7104
7105
7106
7107
7108
7109
7110
7111
7112
7113
7114
7115
7116
7117
7118
7119
7120
7121
7122
7123
7124
7125
7126
7127
7128
7129
7130
7131
7132
7133
7134
7135
7136
7137
7138
7139
7140
7141
7142
7143
7144
7145
7146
7147
7148
7149
7150
7151
7152
7153
7154
7155
7156
7157
7158
7159
7160
7161
7162
7163
7164
7165
7166
7167
7168
7169
7170
7171
7172
7173
7174
7175
7176
7177
7178
7179
7180
7181
7182
7183
7184
7185
7186
7187
7188
7189
7190
7191
7192
7193
7194
7195
7196
7197
7198
7199
7200
7201
7202
7203
7204
7205
7206
7207
7208
7209
7210
7211
7212
7213
7214
7215
7216
7217
7218
7219
7220
7221
7222
7223
7224
7225
7226
7227
7228
7229
7230
7231
7232
7233
7234
7235
7236
7237
7238
7239
7240
7241
7242
7243
7244
7245
7246
7247
7248
7249
7250
7251
7252
7253
7254
7255
7256
7257
7258
7259
7260
7261
7262
7263
7264
7265
7266
7267
7268
7269
7270
7271
7272
7273
7274
7275
7276
7277
7278
7279
7280
7281
7282
7283
7284
7285
7286
7287
7288
7289
7290
7291
7292
7293
7294
7295
7296
7297
7298
7299
7300
7301
7302
7303
7304
7305
7306
7307
7308
7309
7310
7311
7312
7313
7314
7315
7316
7317
7318
7319
7320
7321
7322
7323
7324
7325
7326
7327
7328
7329
7330
7331
7332
7333
7334
7335
7336
7337
7338
7339
7340
7341
7342
7343
7344
7345
7346
7347
7348
7349
7350
7351
7352
7353
7354
7355
7356
7357
7358
7359
7360
7361
7362
7363
7364
7365
7366
7367
7368
7369
7370
7371
7372
7373
7374
7375
7376
7377
7378
7379
7380
7381
7382
7383
7384
7385
7386
7387
7388
7389
7390
7391
7392
7393
7394
7395
7396
7397
7398
7399
7400
7401
7402
7403
7404
7405
7406
7407
7408
7409
7410
7411
7412
7413
7414
7415
7416
7417
7418
7419
7420
7421
7422
7423
7424
7425
7426
7427
7428
7429
7430
7431
7432
7433
7434
7435
7436
7437
7438
7439
7440
7441
7442
7443
7444
7445
7446
7447
7448
7449
7450
7451
7452
7453
7454
7455
7456
7457
7458
7459
7460
7461
7462
7463
7464
7465
7466
7467
7468
7469
7470
7471
7472
7473
7474
7475
7476
7477
7478
7479
7480
7481
7482
7483
7484
7485
7486
7487
7488
7489
7490
7491
7492
7493
7494
7495
7496
7497
7498
7499
7500
7501
7502
7503
7504
7505
7506
7507
7508
7509
7510
7511
7512
7513
7514
7515
7516
7517
7518
7519
7520
7521
7522
7523
7524
7525
7526
7527
7528
7529
7530
7531
7532
7533
7534
7535
7536
7537
7538
7539
7540
7541
7542
7543
7544
7545
7546
7547
7548
7549
7550
7551
7552
7553
7554
7555
7556
7557
7558
7559
7560
7561
7562
7563
7564
7565
7566
7567
7568
7569
7570
7571
7572
7573
7574
7575
7576
7577
7578
7579
7580
7581
7582
7583
7584
7585
7586
7587
7588
7589
7590
7591
7592
7593
7594
7595
7596
7597
7598
7599
7600
7601
7602
7603
7604
7605
7606
7607
7608
7609
7610
7611
7612
7613
7614
7615
7616
7617
7618
7619
7620
7621
7622
7623
7624
7625
7626
7627
7628
7629
7630
7631
7632
7633
7634
7635
7636
7637
7638
7639
7640
7641
7642
7643
7644
7645
7646
7647
7648
7649
7650
7651
7652
7653
7654
7655
7656
7657
7658
7659
7660
7661
7662
7663
7664
7665
7666
7667
7668
7669
7670
7671
7672
7673
7674
7675
7676
7677
7678
7679
7680
7681
7682
7683
7684
7685
7686
7687
7688
7689
7690
7691
7692
7693
7694
7695
7696
7697
7698
7699
7700
7701
7702
7703
7704
7705
7706
7707
7708
7709
7710
7711
7712
7713
7714
7715
7716
7717
7718
7719
7720
7721
7722
7723
7724
7725
7726
7727
7728
7729
7730
7731
7732
7733
7734
7735
7736
7737
7738
7739
7740
7741
7742
7743
7744
7745
7746
7747
7748
7749
7750
7751
7752
7753
7754
7755
7756
7757
7758
7759
7760
7761
7762
7763
7764
7765
7766
7767
7768
7769
7770
7771
7772
7773
7774
7775
7776
7777
7778
7779
7780
7781
7782
7783
7784
7785
7786
7787
7788
7789
7790
7791
7792
7793
7794
7795
7796
7797
7798
7799
7800
7801
7802
7803
7804
7805
7806
7807
7808
7809
7810
7811
7812
7813
7814
7815
7816
7817
7818
7819
7820
7821
7822
7823
7824
7825
7826
7827
7828
7829
7830
7831
7832
7833
7834
7835
7836
7837
7838
7839
7840
7841
7842
7843
7844
7845
7846
7847
7848
7849
7850
7851
7852
7853
7854
7855
7856
7857
7858
7859
7860
7861
7862
7863
7864
7865
7866
7867
7868
7869
7870
7871
7872
7873
7874
7875
7876
7877
7878
7879
7880
7881
7882
7883
7884
7885
7886
7887
7888
7889
7890
7891
7892
7893
7894
7895
7896
7897
7898
7899
7900
7901
7902
7903
7904
7905
7906
7907
7908
7909
7910
7911
7912
7913
7914
7915
7916
7917
7918
7919
7920
7921
7922
7923
7924
7925
7926
7927
7928
7929
7930
7931
7932
7933
7934
7935
7936
7937
7938
7939
7940
7941
7942
7943
7944
7945
7946
7947
7948
7949
7950
7951
7952
7953
7954
7955
7956
7957
7958
7959
7960
7961
7962
7963
7964
7965
7966
7967
7968
7969
7970
7971
7972
7973
7974
7975
7976
7977
7978
7979
7980
7981
7982
7983
7984
7985
7986
7987
7988
7989
7990
7991
7992
7993
7994
7995
7996
7997
7998
7999
8000
8001
8002
8003
8004
8005
8006
8007
8008
8009
8010
8011
8012
8013
8014
8015
8016
8017
8018
8019
8020
8021
8022
8023
8024
8025
8026
8027
8028
8029
8030
8031
8032
8033
8034
8035
8036
8037
8038
8039
8040
8041
8042
8043
8044
8045
8046
8047
8048
8049
8050
8051
8052
8053
8054
8055
8056
8057
8058
8059
8060
8061
8062
8063
8064
8065
8066
8067
8068
8069
8070
8071
8072
8073
8074
8075
8076
8077
8078
8079
8080
8081
8082
8083
8084
8085
8086
8087
8088
8089
8090
8091
8092
8093
8094
8095
8096
8097
8098
8099
8100
8101
8102
8103
8104
8105
8106
8107
8108
8109
8110
8111
8112
8113
8114
8115
8116
8117
8118
8119
8120
8121
8122
8123
8124
8125
8126
8127
8128
8129
8130
8131
8132
8133
8134
8135
8136
8137
8138
8139
8140
8141
8142
8143
8144
8145
8146
8147
8148
8149
8150
8151
8152
8153
8154
8155
8156
8157
8158
8159
8160
8161
8162
8163
8164
8165
8166
8167
8168
8169
8170
8171
8172
8173
8174
8175
8176
8177
8178
8179
8180
8181
8182
8183
8184
8185
8186
8187
8188
8189
8190
8191
8192
8193
8194
8195
8196
8197
8198
8199
8200
8201
8202
8203
8204
8205
8206
8207
8208
8209
8210
8211
8212
8213
8214
8215
8216
8217
8218
8219
8220
8221
8222
8223
8224
8225
8226
8227
8228
8229
8230
8231
8232
8233
8234
8235
8236
8237
8238
8239
8240
8241
8242
8243
8244
8245
8246
8247
8248
8249
8250
8251
8252
8253
8254
8255
8256
8257
8258
8259
8260
8261
8262
8263
8264
8265
8266
8267
8268
8269
8270
8271
8272
8273
8274
8275
8276
8277
8278
8279
8280
8281
8282
8283
8284
8285
8286
8287
8288
8289
8290
8291
8292
8293
8294
8295
8296
8297
8298
8299
8300
8301
8302
8303
8304
8305
8306
8307
8308
8309
8310
8311
8312
8313
8314
8315
8316
8317
8318
8319
8320
8321
8322
8323
8324
8325
8326
8327
8328
8329
8330
8331
8332
8333
8334
8335
8336
8337
8338
8339
8340
8341
8342
8343
8344
8345
8346
8347
8348
8349
8350
8351
8352
8353
8354
8355
8356
8357
8358
8359
8360
8361
8362
8363
8364
8365
8366
8367
8368
8369
8370
8371
8372
8373
8374
8375
8376
8377
8378
8379
8380
8381
8382
8383
8384
8385
8386
8387
8388
8389
8390
8391
8392
8393
8394
8395
8396
8397
8398
8399
8400
8401
8402
8403
8404
8405
8406
8407
8408
8409
8410
8411
8412
8413
8414
8415
8416
8417
8418
8419
8420
8421
8422
8423
8424
8425
8426
8427
8428
8429
8430
8431
8432
8433
8434
8435
8436
8437
8438
8439
8440
8441
8442
8443
8444
8445
8446
8447
8448
8449
8450
8451
8452
8453
8454
8455
8456
8457
8458
8459
8460
8461
8462
8463
8464
8465
8466
8467
8468
8469
8470
8471
8472
8473
8474
8475
8476
8477
8478
8479
8480
8481
8482
8483
8484
8485
8486
8487
8488
8489
8490
8491
8492
8493
8494
8495
8496
8497
8498
8499
8500
8501
8502
8503
8504
8505
8506
8507
8508
8509
8510
8511
8512
8513
8514
8515
8516
8517
8518
8519
8520
8521
8522
8523
8524
8525
8526
8527
8528
8529
8530
8531
8532
8533
8534
8535
8536
8537
8538
8539
8540
8541
8542
8543
8544
8545
8546
8547
8548
8549
8550
8551
8552
8553
8554
8555
8556
8557
8558
8559
8560
8561
8562
8563
8564
8565
8566
8567
8568
8569
8570
8571
8572
8573
8574
8575
8576
8577
8578
8579
8580
8581
8582
8583
8584
8585
8586
8587
8588
8589
8590
8591
8592
8593
8594
8595
8596
8597
8598
8599
8600
8601
8602
8603
8604
8605
8606
8607
8608
8609
8610
8611
8612
8613
8614
8615
8616
8617
8618
8619
8620
8621
8622
8623
8624
8625
8626
8627
8628
8629
8630
8631
8632
8633
8634
8635
8636
8637
8638
8639
8640
8641
8642
8643
8644
8645
8646
8647
8648
8649
8650
8651
8652
8653
8654
8655
8656
8657
8658
8659
8660
8661
8662
8663
8664
8665
8666
8667
8668
8669
8670
8671
8672
8673
8674
8675
8676
8677
8678
8679
8680
8681
8682
8683
8684
8685
8686
8687
8688
8689
8690
8691
8692
8693
8694
8695
8696
8697
8698
8699
8700
8701
8702
8703
8704
8705
8706
8707
8708
8709
8710
8711
8712
8713
8714
8715
8716
8717
8718
8719
8720
8721
8722
8723
8724
8725
8726
8727
8728
8729
8730
8731
8732
8733
8734
8735
8736
8737
8738
8739
8740
8741
8742
8743
8744
8745
8746
8747
8748
8749
8750
8751
8752
8753
8754
8755
8756
8757
8758
8759
8760
8761
8762
8763
8764
8765
8766
8767
8768
8769
8770
8771
8772
8773
8774
8775
8776
8777
8778
8779
8780
8781
8782
8783
8784
8785
8786
8787
8788
8789
8790
8791
8792
8793
8794
8795
8796
8797
8798
8799
8800
8801
8802
8803
8804
8805
8806
8807
8808
8809
8810
8811
8812
8813
8814
8815
8816
8817
8818
8819
8820
8821
8822
8823
8824
8825
8826
8827
8828
8829
8830
8831
8832
8833
8834
8835
8836
8837
8838
8839
8840
8841
8842
8843
8844
8845
8846
8847
8848
8849
8850
8851
8852
8853
8854
8855
8856
8857
8858
8859
8860
8861
8862
8863
8864
8865
8866
8867
8868
8869
8870
8871
8872
8873
8874
8875
8876
8877
8878
8879
8880
8881
8882
8883
8884
8885
8886
8887
8888
8889
8890
8891
8892
8893
8894
8895
8896
8897
8898
8899
8900
8901
8902
8903
8904
8905
8906
8907
8908
8909
8910
8911
8912
8913
8914
8915
8916
8917
8918
8919
8920
8921
8922
8923
8924
8925
8926
8927
8928
8929
8930
8931
8932
8933
8934
8935
8936
8937
8938
8939
8940
8941
8942
8943
8944
8945
8946
8947
8948
8949
8950
8951
8952
8953
8954
8955
8956
8957
8958
8959
8960
8961
8962
8963
8964
8965
8966
8967
8968
8969
8970
8971
8972
8973
8974
8975
8976
8977
8978
8979
8980
8981
8982
8983
8984
8985
8986
8987
8988
8989
8990
8991
8992
8993
8994
8995
8996
8997
8998
8999
9000
9001
9002
9003
9004
9005
9006
9007
9008
9009
9010
9011
9012
9013
9014
9015
9016
9017
9018
9019
9020
9021
9022
9023
9024
9025
9026
9027
9028
9029
9030
9031
9032
9033
9034
9035
9036
9037
9038
9039
9040
9041
9042
9043
9044
9045
9046
9047
9048
9049
9050
9051
9052
9053
9054
9055
9056
9057
9058
9059
9060
9061
9062
9063
9064
9065
9066
9067
9068
9069
9070
9071
9072
9073
9074
9075
9076
9077
9078
9079
9080
9081
9082
9083
9084
9085
9086
9087
9088
9089
9090
9091
9092
9093
9094
9095
9096
9097
9098
9099
9100
9101
9102
9103
9104
9105
9106
9107
9108
9109
9110
9111
9112
9113
9114
9115
9116
9117
9118
9119
9120
9121
9122
9123
9124
9125
9126
9127
9128
9129
9130
9131
9132
9133
9134
9135
9136
9137
9138
9139
9140
9141
9142
9143
9144
9145
9146
9147
9148
9149
9150
9151
9152
9153
9154
9155
9156
9157
9158
9159
9160
9161
9162
9163
9164
9165
9166
9167
9168
9169
9170
9171
9172
9173
9174
9175
9176
9177
9178
9179
9180
9181
9182
9183
9184
9185
9186
9187
9188
9189
9190
9191
9192
9193
9194
9195
9196
9197
9198
9199
9200
9201
9202
9203
9204
9205
9206
9207
9208
9209
9210
9211
9212
9213
9214
9215
9216
9217
9218
9219
9220
9221
9222
9223
9224
9225
9226
9227
9228
9229
9230
9231
9232
9233
9234
9235
9236
9237
9238
9239
9240
9241
9242
9243
9244
9245
9246
9247
9248
9249
9250
9251
9252
9253
9254
9255
9256
9257
9258
9259
9260
9261
9262
9263
9264
9265
9266
9267
9268
9269
9270
9271
9272
9273
9274
9275
9276
9277
9278
9279
9280
9281
9282
9283
9284
9285
9286
9287
9288
9289
9290
9291
9292
9293
9294
9295
9296
9297
9298
9299
9300
9301
9302
9303
9304
9305
9306
9307
9308
9309
9310
9311
9312
9313
9314
9315
9316
9317
9318
9319
9320
9321
9322
9323
9324
9325
9326
9327
9328
9329
9330
9331
9332
9333
9334
9335
9336
9337
9338
9339
9340
9341
9342
9343
9344
9345
9346
9347
9348
9349
9350
9351
9352
9353
9354
9355
9356
9357
9358
9359
9360
9361
9362
9363
9364
9365
9366
9367
9368
9369
9370
9371
9372
9373
9374
9375
9376
9377
9378
9379
9380
9381
9382
9383
9384
9385
9386
9387
9388
9389
9390
9391
9392
9393
9394
9395
9396
9397
9398
9399
9400
9401
9402
9403
9404
9405
9406
9407
9408
9409
9410
9411
9412
9413
9414
9415
9416
9417
9418
9419
9420
9421
9422
9423
9424
9425
9426
9427
9428
9429
9430
9431
9432
9433
9434
9435
9436
9437
9438
9439
9440
9441
9442
9443
9444
9445
9446
9447
9448
9449
9450
9451
9452
9453
9454
9455
9456
9457
9458
9459
9460
9461
9462
9463
9464
9465
9466
9467
9468
9469
9470
9471
9472
9473
9474
9475
9476
9477
9478
9479
9480
9481
9482
9483
9484
9485
9486
9487
9488
9489
9490
9491
9492
9493
9494
9495
9496
9497
9498
9499
9500
9501
9502
9503
9504
9505
9506
9507
9508
9509
9510
9511
9512
9513
9514
9515
9516
9517
9518
9519
9520
9521
9522
9523
9524
9525
9526
9527
9528
9529
9530
9531
9532
9533
9534
9535
9536
9537
9538
9539
9540
9541
9542
9543
9544
9545
9546
9547
9548
9549
9550
9551
9552
9553
9554
9555
9556
9557
9558
9559
9560
9561
9562
9563
9564
9565
9566
9567
9568
9569
9570
9571
9572
9573
9574
9575
9576
9577
9578
9579
9580
9581
9582
9583
9584
9585
9586
9587
9588
9589
9590
9591
9592
9593
9594
9595
9596
9597
9598
9599
9600
9601
9602
9603
9604
9605
9606
9607
9608
9609
9610
9611
9612
9613
9614
9615
9616
9617
9618
9619
9620
9621
9622
9623
9624
9625
9626
9627
9628
9629
9630
9631
9632
9633
9634
9635
9636
9637
9638
9639
9640
9641
9642
9643
9644
9645
9646
9647
9648
9649
9650
9651
9652
9653
9654
9655
9656
9657
9658
9659
9660
9661
9662
9663
9664
9665
9666
9667
9668
9669
9670
9671
9672
9673
9674
9675
9676
9677
9678
9679
9680
9681
9682
9683
9684
9685
9686
9687
9688
9689
9690
9691
9692
9693
9694
9695
9696
9697
9698
9699
9700
9701
9702
9703
9704
9705
9706
9707
9708
9709
9710
9711
9712
9713
9714
9715
9716
9717
9718
9719
9720
9721
9722
9723
9724
9725
9726
9727
9728
9729
9730
9731
9732
9733
9734
9735
9736
9737
9738
9739
9740
9741
9742
9743
9744
9745
9746
9747
9748
9749
9750
9751
9752
9753
9754
9755
9756
9757
9758
9759
9760
9761
9762
9763
9764
9765
9766
9767
9768
9769
9770
9771
9772
9773
9774
9775
9776
9777
9778
9779
9780
9781
9782
9783
9784
9785
9786
9787
9788
9789
9790
9791
9792
9793
9794
9795
9796
9797
9798
9799
9800
9801
9802
9803
9804
9805
9806
9807
9808
9809
9810
9811
9812
9813
9814
9815
9816
9817
9818
9819
9820
9821
9822
9823
9824
9825
9826
9827
9828
9829
9830
9831
9832
9833
9834
9835
9836
9837
9838
9839
9840
9841
9842
9843
9844
9845
9846
9847
9848
9849
9850
9851
9852
9853
9854
9855
9856
9857
9858
9859
9860
9861
9862
9863
9864
9865
9866
9867
9868
9869
9870
9871
9872
9873
9874
9875
9876
9877
9878
9879
9880
9881
9882
9883
9884
9885
9886
9887
9888
9889
9890
9891
9892
9893
9894
9895
9896
9897
9898
9899
9900
9901
9902
9903
9904
9905
9906
9907
9908
9909
9910
9911
9912
9913
9914
9915
9916
9917
9918
9919
9920
9921
9922
9923
9924
9925
9926
9927
9928
9929
9930
9931
9932
9933
9934
9935
9936
9937
9938
9939
9940
9941
9942
9943
9944
9945
9946
9947
9948
9949
9950
9951
9952
9953
9954
9955
9956
9957
9958
9959
9960
9961
9962
9963
9964
9965
9966
9967
9968
9969
9970
9971
9972
9973
9974
9975
9976
9977
9978
9979
9980
9981
9982
9983
9984
9985
9986
9987
9988
9989
9990
9991
9992
9993
9994
9995
9996
9997
9998
9999
10000
10001
10002
10003
10004
10005
10006
10007
10008
10009
10010
10011
10012
10013
10014
10015
10016
10017
10018
10019
10020
10021
10022
10023
10024
10025
10026
10027
10028
10029
10030
10031
10032
10033
10034
10035
10036
10037
10038
10039
10040
10041
10042
10043
10044
10045
10046
10047
10048
10049
10050
10051
10052
10053
10054
10055
10056
10057
10058
10059
10060
10061
10062
10063
10064
10065
10066
10067
10068
10069
10070
10071
10072
10073
10074
10075
10076
10077
10078
10079
10080
10081
10082
10083
10084
10085
10086
10087
10088
10089
10090
10091
10092
10093
10094
10095
10096
10097
10098
10099
10100
10101
10102
10103
10104
10105
10106
10107
10108
10109
10110
10111
10112
10113
10114
10115
10116
10117
10118
10119
10120
10121
10122
10123
10124
10125
10126
10127
10128
10129
10130
10131
10132
10133
10134
10135
10136
10137
10138
10139
10140
10141
10142
10143
10144
10145
10146
10147
10148
10149
10150
10151
10152
10153
10154
10155
10156
10157
10158
10159
10160
10161
10162
10163
10164
10165
10166
10167
10168
10169
10170
10171
10172
10173
10174
10175
10176
10177
10178
10179
10180
10181
10182
10183
10184
10185
10186
10187
10188
10189
10190
10191
10192
10193
10194
10195
10196
10197
10198
10199
10200
10201
10202
10203
10204
10205
10206
10207
10208
10209
10210
10211
10212
10213
10214
10215
10216
10217
10218
10219
10220
10221
10222
10223
10224
10225
10226
10227
10228
10229
10230
10231
10232
10233
10234
10235
10236
10237
10238
10239
10240
10241
10242
10243
10244
10245
10246
10247
10248
10249
10250
10251
10252
10253
10254
10255
10256
10257
10258
10259
10260
10261
10262
10263
10264
10265
10266
10267
10268
10269
10270
10271
10272
10273
10274
10275
10276
10277
10278
10279
10280
10281
10282
10283
10284
10285
10286
10287
10288
10289
10290
10291
10292
10293
10294
10295
10296
10297
10298
10299
10300
10301
10302
10303
10304
10305
10306
10307
10308
10309
10310
10311
10312
10313
10314
10315
10316
10317
10318
10319
10320
10321
10322
10323
10324
10325
10326
10327
10328
10329
10330
10331
10332
10333
10334
10335
10336
10337
10338
10339
10340
10341
10342
10343
10344
10345
10346
10347
10348
10349
10350
10351
10352
10353
10354
10355
10356
10357
10358
10359
10360
10361
10362
10363
10364
10365
10366
10367
10368
10369
10370
10371
10372
10373
10374
10375
10376
10377
10378
10379
10380
10381
10382
10383
10384
10385
10386
10387
10388
10389
10390
10391
10392
10393
10394
10395
10396
10397
10398
10399
10400
10401
10402
10403
10404
10405
10406
10407
10408
10409
10410
10411
10412
10413
10414
10415
10416
10417
10418
10419
10420
10421
10422
10423
10424
10425
10426
10427
10428
10429
10430
10431
10432
10433
10434
10435
10436
10437
10438
10439
10440
10441
10442
10443
10444
10445
10446
10447
10448
10449
10450
10451
10452
10453
10454
10455
10456
10457
10458
10459
10460
10461
10462
10463
10464
10465
10466
10467
10468
10469
10470
10471
10472
10473
10474
10475
10476
10477
10478
10479
10480
10481
10482
10483
10484
10485
10486
10487
10488
10489
10490
10491
10492
10493
10494
10495
10496
10497
10498
10499
10500
10501
10502
10503
10504
10505
10506
10507
10508
10509
10510
10511
10512
10513
10514
10515
10516
10517
10518
10519
10520
10521
10522
10523
10524
10525
10526
10527
10528
10529
10530
10531
10532
10533
10534
10535
10536
10537
10538
10539
10540
10541
10542
10543
10544
10545
10546
10547
10548
10549
10550
10551
10552
10553
10554
10555
10556
10557
10558
10559
10560
10561
10562
10563
10564
10565
10566
10567
10568
10569
10570
10571
10572
10573
10574
10575
10576
10577
10578
10579
10580
10581
10582
10583
10584
10585
10586
10587
10588
10589
10590
10591
10592
10593
10594
10595
10596
10597
10598
10599
10600
10601
10602
10603
10604
10605
10606
10607
10608
10609
10610
10611
10612
10613
10614
10615
10616
10617
10618
10619
10620
10621
10622
10623
10624
10625
10626
10627
10628
10629
10630
10631
10632
10633
10634
10635
10636
10637
10638
10639
10640
10641
10642
10643
10644
10645
10646
10647
10648
10649
10650
10651
10652
10653
10654
10655
10656
10657
10658
10659
10660
10661
10662
10663
10664
10665
10666
10667
10668
10669
10670
10671
10672
10673
10674
10675
10676
10677
10678
10679
10680
10681
10682
10683
10684
10685
10686
10687
10688
10689
10690
10691
10692
10693
10694
10695
10696
10697
10698
10699
10700
10701
10702
10703
10704
10705
10706
10707
10708
10709
10710
10711
10712
10713
10714
10715
10716
10717
10718
10719
10720
10721
10722
10723
10724
10725
10726
10727
10728
10729
10730
10731
10732
10733
10734
10735
10736
10737
10738
10739
10740
10741
10742
10743
10744
10745
10746
10747
10748
10749
10750
10751
10752
10753
10754
10755
10756
10757
10758
10759
10760
10761
10762
10763
10764
10765
10766
10767
10768
10769
10770
10771
10772
10773
10774
10775
10776
10777
10778
10779
10780
10781
10782
10783
10784
10785
10786
10787
10788
10789
10790
10791
10792
10793
10794
10795
10796
10797
10798
10799
10800
10801
10802
10803
10804
10805
10806
10807
10808
10809
10810
10811
10812
10813
10814
10815
10816
10817
10818
10819
10820
10821
10822
10823
10824
10825
10826
10827
10828
10829
10830
10831
10832
10833
10834
10835
10836
10837
10838
10839
10840
10841
10842
10843
10844
10845
10846
10847
10848
10849
10850
10851
10852
10853
10854
10855
10856
10857
10858
10859
10860
10861
10862
10863
10864
10865
10866
10867
10868
10869
10870
10871
10872
10873
10874
10875
10876
10877
10878
10879
10880
10881
10882
10883
10884
10885
10886
10887
10888
10889
10890
10891
10892
10893
10894
10895
10896
10897
10898
10899
10900
10901
10902
10903
10904
10905
10906
10907
10908
10909
10910
10911
10912
10913
10914
10915
10916
10917
10918
10919
10920
10921
10922
10923
10924
10925
10926
10927
10928
10929
10930
10931
10932
10933
10934
10935
10936
10937
10938
10939
10940
10941
10942
10943
10944
10945
10946
10947
10948
10949
10950
10951
10952
10953
10954
10955
10956
10957
10958
10959
10960
10961
10962
10963
10964
10965
10966
10967
10968
10969
10970
10971
10972
10973
10974
10975
10976
10977
10978
10979
10980
10981
10982
10983
10984
10985
10986
10987
10988
10989
10990
10991
10992
10993
10994
10995
10996
10997
10998
10999
11000
11001
11002
11003
11004
11005
11006
11007
11008
11009
11010
11011
11012
11013
11014
11015
11016
11017
11018
11019
11020
11021
11022
11023
11024
11025
11026
11027
11028
11029
11030
11031
11032
11033
11034
11035
11036
11037
11038
11039
11040
11041
11042
11043
11044
11045
11046
11047
11048
11049
11050
11051
11052
11053
11054
11055
11056
11057
11058
11059
11060
11061
11062
11063
11064
11065
11066
11067
11068
11069
11070
11071
11072
11073
11074
11075
11076
11077
11078
11079
11080
11081
11082
11083
11084
11085
11086
11087
11088
11089
11090
11091
11092
11093
11094
11095
11096
11097
11098
11099
11100
11101
11102
11103
11104
11105
11106
11107
11108
11109
11110
11111
11112
11113
11114
11115
11116
11117
11118
11119
11120
11121
11122
11123
11124
11125
11126
11127
11128
11129
11130
11131
11132
11133
11134
11135
11136
11137
11138
11139
11140
11141
11142
11143
11144
11145
11146
11147
11148
11149
11150
11151
11152
11153
11154
11155
11156
11157
11158
11159
11160
11161
11162
11163
11164
11165
11166
11167
11168
11169
11170
11171
11172
11173
11174
11175
11176
11177
11178
11179
11180
11181
11182
11183
11184
11185
11186
11187
11188
11189
11190
11191
11192
11193
11194
11195
11196
11197
11198
11199
11200
11201
11202
11203
11204
11205
11206
11207
11208
11209
11210
11211
11212
11213
11214
11215
11216
11217
11218
11219
11220
11221
11222
11223
11224
11225
11226
11227
11228
11229
11230
11231
11232
11233
11234
11235
11236
11237
11238
11239
11240
11241
11242
11243
11244
11245
11246
11247
11248
11249
11250
11251
11252
11253
11254
11255
11256
11257
11258
11259
11260
11261
11262
11263
11264
11265
11266
11267
11268
11269
11270
11271
11272
11273
11274
11275
11276
11277
11278
11279
11280
11281
11282
11283
11284
11285
11286
11287
11288
11289
11290
11291
11292
11293
11294
11295
11296
11297
11298
11299
11300
11301
11302
11303
11304
11305
11306
11307
11308
11309
11310
11311
11312
11313
11314
11315
11316
11317
11318
11319
11320
11321
11322
11323
11324
11325
11326
11327
11328
11329
11330
11331
11332
11333
11334
11335
11336
11337
11338
11339
11340
11341
11342
11343
11344
11345
11346
11347
11348
11349
11350
11351
11352
11353
11354
11355
11356
11357
11358
11359
11360
11361
11362
11363
11364
11365
11366
11367
11368
11369
11370
11371
11372
11373
11374
11375
11376
11377
11378
11379
11380
11381
11382
11383
11384
11385
11386
11387
11388
11389
11390
11391
11392
11393
11394
11395
11396
11397
11398
11399
11400
11401
11402
11403
11404
11405
11406
11407
11408
11409
11410
11411
11412
11413
11414
11415
11416
11417
11418
11419
11420
11421
11422
11423
11424
11425
11426
11427
11428
11429
11430
11431
11432
11433
11434
11435
11436
11437
11438
11439
11440
11441
11442
11443
11444
11445
11446
11447
11448
11449
11450
11451
11452
11453
11454
11455
11456
11457
11458
11459
11460
11461
11462
11463
11464
11465
11466
11467
11468
11469
11470
11471
11472
11473
11474
11475
11476
11477
11478
11479
11480
11481
11482
11483
11484
11485
11486
11487
11488
11489
11490
11491
11492
11493
11494
11495
11496
11497
11498
11499
11500
11501
11502
11503
11504
11505
11506
11507
11508
11509
11510
11511
11512
11513
11514
11515
11516
11517
11518
11519
11520
11521
11522
11523
11524
11525
11526
11527
11528
11529
11530
11531
11532
11533
11534
11535
11536
11537
11538
11539
11540
11541
11542
11543
11544
11545
11546
11547
11548
11549
11550
11551
11552
11553
11554
11555
11556
11557
11558
11559
11560
11561
11562
11563
11564
11565
11566
11567
11568
11569
11570
11571
11572
11573
11574
11575
11576
11577
11578
11579
11580
11581
11582
11583
11584
11585
11586
11587
11588
11589
11590
11591
11592
11593
11594
11595
11596
11597
11598
11599
11600
11601
11602
11603
11604
11605
11606
11607
11608
11609
11610
11611
11612
11613
11614
11615
11616
11617
11618
11619
11620
11621
11622
11623
11624
11625
11626
11627
11628
11629
11630
11631
11632
11633
11634
11635
11636
11637
11638
11639
11640
11641
11642
11643
11644
11645
11646
11647
11648
11649
11650
11651
11652
11653
11654
11655
11656
11657
11658
11659
11660
11661
11662
11663
11664
11665
11666
11667
11668
11669
11670
11671
11672
11673
11674
11675
11676
11677
11678
11679
11680
11681
11682
11683
11684
11685
11686
11687
11688
11689
11690
11691
11692
11693
11694
11695
11696
11697
11698
11699
11700
11701
11702
11703
11704
11705
11706
11707
11708
11709
11710
11711
11712
11713
11714
11715
11716
11717
11718
11719
11720
11721
11722
11723
11724
11725
11726
11727
11728
11729
11730
11731
11732
11733
11734
11735
11736
11737
11738
11739
11740
11741
11742
11743
11744
11745
11746
11747
11748
11749
11750
11751
11752
11753
11754
11755
11756
11757
11758
11759
11760
11761
11762
11763
11764
11765
11766
11767
11768
11769
11770
11771
11772
11773
11774
11775
11776
11777
11778
11779
11780
11781
11782
11783
11784
11785
11786
11787
11788
11789
11790
11791
11792
11793
11794
11795
11796
11797
11798
11799
11800
11801
11802
11803
11804
11805
11806
11807
11808
11809
11810
11811
11812
11813
11814
11815
11816
11817
11818
11819
11820
11821
11822
11823
11824
11825
11826
11827
11828
11829
11830
11831
11832
11833
11834
11835
11836
11837
11838
11839
11840
11841
11842
11843
11844
11845
11846
11847
11848
11849
11850
11851
11852
11853
11854
11855
11856
11857
11858
11859
11860
11861
11862
11863
11864
11865
11866
11867
11868
11869
11870
11871
11872
11873
11874
11875
11876
11877
11878
11879
11880
11881
11882
11883
11884
11885
11886
11887
11888
11889
11890
11891
11892
11893
11894
11895
11896
11897
11898
11899
11900
11901
11902
11903
11904
11905
11906
11907
11908
11909
11910
11911
11912
11913
11914
11915
11916
11917
11918
11919
11920
11921
11922
11923
11924
11925
11926
11927
11928
11929
11930
11931
11932
11933
11934
11935
11936
11937
11938
11939
11940
11941
11942
11943
11944
11945
11946
11947
11948
11949
11950
11951
11952
11953
11954
11955
11956
11957
11958
11959
11960
11961
11962
11963
11964
11965
11966
11967
11968
11969
11970
11971
11972
11973
11974
11975
11976
11977
11978
11979
11980
11981
11982
11983
11984
11985
11986
11987
11988
11989
11990
11991
11992
11993
11994
11995
11996
11997
11998
11999
12000
12001
12002
12003
12004
12005
12006
12007
12008
12009
12010
12011
12012
12013
12014
12015
12016
12017
12018
12019
12020
12021
12022
12023
12024
12025
12026
12027
12028
12029
12030
12031
12032
12033
12034
12035
12036
12037
12038
12039
12040
12041
12042
12043
12044
12045
12046
12047
12048
12049
12050
12051
12052
12053
12054
12055
12056
12057
12058
12059
12060
12061
12062
12063
12064
12065
12066
12067
12068
12069
12070
12071
12072
12073
12074
12075
12076
12077
12078
12079
12080
12081
12082
12083
12084
12085
12086
12087
12088
12089
12090
12091
12092
12093
12094
12095
12096
12097
12098
12099
12100
12101
12102
12103
12104
12105
12106
12107
12108
12109
12110
12111
12112
12113
12114
12115
12116
12117
12118
12119
12120
12121
12122
12123
12124
12125
12126
12127
12128
12129
12130
12131
12132
12133
12134
12135
12136
12137
12138
12139
12140
12141
12142
12143
12144
12145
12146
12147
12148
12149
12150
12151
12152
12153
12154
12155
12156
12157
12158
12159
12160
12161
12162
12163
12164
12165
12166
12167
12168
12169
12170
12171
12172
12173
12174
12175
12176
12177
12178
12179
12180
12181
12182
12183
12184
12185
12186
12187
12188
12189
12190
12191
12192
12193
12194
12195
12196
12197
12198
12199
12200
12201
12202
12203
12204
12205
12206
12207
12208
12209
12210
12211
12212
12213
12214
12215
12216
12217
12218
12219
12220
12221
12222
12223
12224
12225
12226
12227
12228
12229
12230
12231
12232
12233
12234
12235
12236
12237
12238
12239
12240
12241
12242
12243
12244
12245
12246
12247
12248
12249
12250
12251
12252
12253
12254
12255
12256
12257
12258
12259
12260
12261
12262
12263
12264
12265
12266
12267
12268
12269
12270
12271
12272
12273
12274
12275
12276
12277
12278
12279
12280
12281
12282
12283
12284
12285
12286
12287
12288
12289
12290
12291
12292
12293
12294
12295
12296
12297
12298
12299
12300
12301
12302
12303
12304
12305
12306
12307
12308
12309
12310
12311
12312
12313
12314
12315
12316
12317
12318
12319
12320
12321
12322
12323
12324
12325
12326
12327
12328
12329
12330
12331
12332
12333
12334
12335
12336
12337
12338
12339
12340
12341
12342
12343
12344
12345
12346
12347
12348
12349
12350
12351
12352
12353
12354
12355
12356
12357
12358
12359
12360
12361
12362
12363
12364
12365
12366
12367
12368
12369
12370
12371
12372
12373
12374
12375
12376
12377
12378
12379
12380
12381
12382
12383
12384
12385
12386
12387
12388
12389
12390
12391
12392
12393
12394
12395
12396
12397
12398
12399
12400
12401
12402
12403
12404
12405
12406
12407
12408
12409
12410
12411
12412
12413
12414
12415
12416
12417
12418
12419
12420
12421
12422
12423
12424
12425
12426
12427
12428
12429
12430
12431
12432
12433
12434
12435
12436
12437
12438
12439
12440
12441
12442
12443
12444
12445
12446
12447
12448
12449
12450
12451
12452
12453
12454
12455
12456
12457
12458
12459
12460
12461
12462
12463
12464
12465
12466
12467
12468
12469
12470
12471
12472
12473
12474
12475
12476
12477
12478
12479
12480
12481
12482
12483
12484
12485
12486
12487
12488
12489
12490
%!PS-Adobe-3.0
%%Creator: Basser Lout Version 3.29 (August 2003)
%%CreationDate: Thu Aug 14 08:17:36 2003
%%DocumentData: Binary
%%DocumentNeededResources: (atend)
%%DocumentSuppliedResources: (atend)
%%DocumentMedia: A4 595 842 0 white ()
%%PageOrder: Ascend
%%LanguageLevel: 2
%%Pages: (atend)
%%BoundingBox: 0 0 595 842
%%EndComments
%%BeginProlog
%%BeginResource: procset LoutStartUp
/save_cp { currentpoint /cp_y exch def /cp_x exch def } def
/restore_cp { cp_x cp_y moveto } def
/outline { gsave 1 1 1 setrgbcolor dup show save_cp
  grestore true charpath stroke restore_cp } bind def
/m  { 3 1 roll moveto show } bind def
/mo { 3 1 roll moveto outline } bind def
/s  { exch currentpoint exch pop moveto show } bind def
/so { exch currentpoint exch pop moveto outline } bind def
/k  { exch neg 0 rmoveto show } bind def
/ko { exch neg 0 rmoveto outline } bind def
/r  { exch 0 rmoveto show } bind def
/ro { exch 0 rmoveto outline } bind def
/c  { gsave 3 1 roll rmoveto show grestore } bind def
/co { gsave 3 1 roll rmoveto outline grestore } bind def
/ul { gsave setlinewidth dup 3 1 roll
      moveto lineto stroke grestore } bind def
/in { 1440 mul } def
/cm { 567 mul } def
/pt { 20 mul } def
/em { 120 mul } def
/sp { louts mul } def
/vs { loutv mul } def
/ft { loutf mul } def
/dg {           } def

/LoutGraphic {
  /louts exch def
  /loutv exch def
  /loutf exch def
  /ymark exch def
  /xmark exch def
  /ysize exch def
  /xsize exch def
} def

/LoutGr2 { gsave translate LoutGraphic gsave } def

/LoutFont
{ findfont exch scalefont setfont
} bind def

/LoutRecode {
  { findfont dup length dict begin
    {1 index /FID ne {def} {pop pop} ifelse} forall
    /Encoding exch def
    currentdict end definefont pop
  }
  stopped pop
} bind def

/LoutStartEPSF { % prepare for EPSF inclusion
  userdict begin
    /PreEPSF_state save def
    /dict_stack countdictstack def
    /ops_count count 1 sub def
    /showpage {} def
    0 setgray 0 setlinecap
    1 setlinewidth 0 setlinejoin
    10 setmiterlimit [] 0 setdash newpath
    /languagelevel where
    { pop languagelevel
      1 ne
      { false setstrokeadjust false setoverprint
      } if
    } if
} bind def

/LoutEPSFCleanUp { % clean up after EPSF inclusion
    count ops_count sub { pop } repeat
    countdictstack dict_stack sub { end } repeat
    PreEPSF_state restore
  end % userdict
} bind def

% Find current texture (may be null)
% - LoutCurrentP p
/LoutCurrentP
{
  currentcolorspace
  0 get /Pattern eq
  {
    [ currentcolor ]
    dup length 1 sub get
  }
  {
    null
  } ifelse
} def

% Find current color and color space
% - LoutCurrentCCS c cs
/LoutCurrentCCS
{
  LoutCurrentP dup null eq
  {
    pop [ currentcolor ]
    currentcolorspace
  }
  {
    dup
    /UnderlyingColor get
    exch /UnderlyingColorSpace get
  } ifelse
} def

% Install c, cs, and (a copy of) p into graphics state
% c cs p LoutSetCCSP -
/LoutSetCCSP
{
  dup null eq
  {
    pop setcolorspace
    aload pop setcolor
  }
  {
    % copy pattern dictionary
    12 dict copy

    % record cs and c in p
    dup /UnderlyingColorSpace 3 index
    put
    dup /UnderlyingColor 4 index
    put

    % do setcolorspace and setcolor
    dup /PaintType get 1 eq
    {
      [ /Pattern ] setcolorspace
      setcolor
      pop pop
    }
    {
      [ /Pattern
      4 -1 roll
      ] setcolorspace
      exch aload length 1 add
      -1 roll
      setcolor
    } ifelse
  } ifelse
} def

% num LoutSetGray -
/LoutSetGray
{
  [ 2 1 roll ]
  [ /DeviceGray ]
  LoutCurrentP
  LoutSetCCSP
} def

% r g b LoutSetRGBColor -
/LoutSetRGBColor
{
  [ 4 1 roll ]
  [ /DeviceRGB ]
  LoutCurrentP
  LoutSetCCSP
} def

% h s b LoutSetHSBColor -
/LoutSetHSBColor
{
  gsave sethsbcolor
  currentrgbcolor grestore
  LoutSetRGBColor
} def

% c m y k LoutSetRGBColor -
/LoutSetCMYKColor
{
  [ 5 1 roll ]
  [ /DeviceCMYK ]
  LoutCurrentP
  LoutSetCCSP
} def

% p LoutSetTexture -
/LoutSetTexture
{
  LoutCurrentCCS
  3 -1 roll
  LoutSetCCSP
} def

% <scale > <scalex> <scaley> <rotate> <hshift> <vshift>
% <painttype> <bbox> <xstep> <ystep> <paintproc> LoutMakeTexture p
/LoutMakeTexture
{
  12 dict begin
  /PaintProc exch def
  /YStep exch def
  /XStep exch def
  /BBox exch def
  /PaintType exch def
  /PatternType 1 def
  /TilingType 1 def
  currentdict end
  7 1 roll
  matrix translate
  5 1 roll
  matrix rotate
  4 1 roll
  matrix scale
  exch dup matrix scale
  matrix concatmatrix
  matrix concatmatrix
  matrix concatmatrix
  /makepattern where
  {
    pop makepattern
  }
  {
    pop pop null
  } ifelse
} def

/LoutTextureSolid
{
  null
  LoutSetTexture
} def
%%EndResource

%%BeginResource: procset LoutTabPrependGraphic
% @PrependGraphic file /home/jeff/lout.lib/include/tabf.lpg
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                  %
%  PostScript @SysPrependGraphic file for @Tab     %
%                                                  %
%  To assist in avoiding name clashes, the names   %
%  of all these symbols begin with "ltab".         %
%                                                  %
%  Jeffrey H. Kingston                             %
%  24 September 1991                               %
%  22 December 1992                                %
%                                                  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% linewidth ltabhs -
% horizontal single line
/ltabhs
{  0 0 moveto xsize 0 lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabhsp -
% horizontal single line with projecting ends
/ltabhsp
{  0 0 moveto xsize 0 lineto
   setlinewidth 2 setlinecap stroke
} def

% linewidth ltabhd -
% horizontal double line
/ltabhd
{  dup dup
   0 0 moveto xsize 0 lineto
   0 exch 3 mul moveto xsize exch 3 mul lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabhdb -
% horizontal double line below mark
/ltabhdb
{  dup dup
   0 0 moveto xsize 0 lineto
   0 exch -3 mul moveto xsize exch -3 mul lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabhdnw -
% horizontal double line with northwest corner
/ltabhdnw
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   xsize exch 3 mul moveto
   -3 mul exch 3 mul lineto
   -3 mul 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabhdne -
% horizontal double line with northeast corner
/ltabhdne
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   0 exch 3 mul moveto
   3 mul xsize add exch 3 mul lineto
   3 mul xsize add 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabhdsw -
% horizontal double line with southwest corner
/ltabhdsw
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   xsize exch -3 mul moveto
   -3 mul exch -3 mul lineto
   -3 mul 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabhdse -
% horizontal double line with southeast corner
/ltabhdse
{  dup dup dup dup
   0 0 moveto xsize 0 lineto
   0 exch -3 mul moveto
   3 mul xsize add exch -3 mul lineto
   3 mul xsize add 0 lineto
   setlinewidth 0 setlinejoin 2 setlinecap stroke
} def

% linewidth ltabvs -
% vertical single line
/ltabvs
{  0 0 moveto 0 ysize lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabvd -
% vertical double line
/ltabvd
{  dup dup
   0 0 moveto 0 ysize lineto
   -3 mul 0 moveto -3 mul ysize lineto
   setlinewidth 0 setlinecap stroke
} def

% linewidth ltabvdr -
% vertical double line to right of mark
/ltabvdr
{  dup dup
   0 0 moveto 0 ysize lineto
   3 mul 0 moveto 3 mul ysize lineto
   setlinewidth 0 setlinecap stroke
} def
%%EndResource

%%BeginResource: procset LoutFigPrependGraphic
% @PrependGraphic file /home/jeff/lout.lib/include/figf.lpg
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                    %
%  PostScript @SysPrependGraphic file for @Fig  Jeffrey H. Kingston  %
%  Version 2.0 (includes CIRCUM label)                 January 1992  %
%                                                                    %
%  Although Fig is now obsolete I have updated it 20 October 2002    %
%  to work with textures, i.e. replacing setrgbcolor with            %
%  LoutSetRGBColor.                                                  %
%                                                                    %
%  To assist in avoiding name clashes, the names of all symbols      %
%  defined here begin with "lfig".  However, this is not feasible    %
%  with user-defined labels and some labels used by users.           %
%                                                                    %
%  <point>      is two numbers, a point.                             %
%  <length>     is one number, a length                              %
%  <angle>      is one number, an angle in degrees                   %
%  <dashlength> is one number, the preferred length of a dash        %
%                                                                    %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

errordict begin
   /handleerror
   {
      {  /Times-Roman findfont 8 pt scalefont setfont
	 0 setgray 4 pt 4 pt moveto
	 $error /errorname get
	 dup lfigdict exch known
	 { lfigdict exch get }
	 { 30 string cvs } ifelse
	 show
	 (  Command: ) show
	 $error /command get 30 string cvs show
      } stopped {} if
      showpage stop
   } def
end

% concat strings: <string> <string> lfigconcat <string>
% must be defined outside lfigdict since used in lfigpromotelabels
/lfigconcat
{ 2 copy length exch length add string
  dup 0 4 index putinterval
  dup 3 index length 3 index putinterval
  3 1 roll pop pop
} def

% <string> lfigdebugprint -
% must be defined outside lfigdict since used in arbitrary places
% /lfigdebugprint
% { print
%   (;  operand stack:\n) print
%   count copy
%   count 2 idiv
%   { ==
%     (\n) print
%   } repeat
%   (\n) print
% } def

/lfigdict 120 dict def
lfigdict begin

% error messages
/dictfull (dictfull error:  too many labels?) def
/dictstackoverflow (dictstackoverflow error:  labels nested too deeply?) def
/execstackoverflow (execstackoverflow error:  figure nested too deeply?) def
/limitcheck (limitcheck error:  figure nested too deeply or too large?) def
/syntaxerror (syntaxerror error:  syntax error in text of figure?) def
/typecheck (typecheck error:  syntax error in text of figure?) def
/undefined (undefined error:  unknown or misspelt label?) def
/VMError (VMError error:  run out of memory?) def

% push pi onto stack:  - lfigpi <num>
/lfigpi 3.14159 def

% arc directions
/clockwise     false def
/anticlockwise true  def

% maximum of two numbers:  <num> <num> lfigmax <num>
/lfigmax { 2 copy gt { pop } { exch pop } ifelse } def

% minimum of two numbers:  <num> <num> lfigmin <num>
/lfigmin { 2 copy lt { pop } { exch pop } ifelse } def

% add two points:  <point> <point> lfigpadd <point>
/lfigpadd { exch 3 1 roll add 3 1 roll add exch } def

% subtract first point from second:  <point> <point> lfigpsub <point>
/lfigpsub { 3 2 roll sub 3 1 roll exch sub exch } def

% max two points:  <point> <point> lfigpmax <point>
/lfigpmax { exch 3 1 roll lfigmax 3 1 roll lfigmax exch } def

% min two points:  <point> <point> lfigpmin <point>
/lfigpmin { exch 3 1 roll lfigmin 3 1 roll lfigmin exch } def

% scalar multiplication: <point> <num> lfigpmul <point>
/lfigpmul { dup 3 1 roll mul 3 1 roll mul exch } def

% point at angle and distance:  <point> <length> <angle> lfigatangle <point>
/lfigatangle { 2 copy cos mul 3 1 roll sin mul lfigpadd } def

% angle from one point to another:  <point> <point> lfigangle <angle>
/lfigangle { lfigpsub 2 copy 0 eq exch 0 eq and {pop} {exch atan} ifelse } def

% distance between two points:  <point> <point> lfigdistance <length>
/lfigdistance { lfigpsub dup mul exch dup mul add sqrt } def

% difference in x coords: <point> <point> lfigxdistance <length>
/lfigxdistance { pop 3 1 roll pop sub } def

%difference in y coords: <point> <point> lfigydistance <length>
/lfigydistance { 3 1 roll pop sub exch pop } def

% stroke a solid line:  <length> <dashlength> lfigsolid -
/lfigsolid
{  pop pop [] 0 setdash stroke
} def

% stroke a lfigdashed line:   <length> <dashlength> lfigdashed -
/lfigdashed
{  2 copy div 2 le 1 index 0 le or
   {  exch pop 1 pt lfigmax [ exch dup ] 0 setdash }
   {  dup [ exch 4 2 roll 2 copy div
      1 sub 2 div ceiling dup 4 1 roll
      1 add mul sub exch div ] 0 setdash
   } ifelse stroke
} def

% stroke a lfigcdashed line:  <length> <dashlength> lfigcdashed -
/lfigcdashed
{  2 copy le 1 index 0 le or
   { exch pop 1 pt lfigmax [ exch dup ] dup 0 get 2 div setdash }
   { dup [ 4 2 roll exch 2 copy exch div
     2 div ceiling div 1 index sub
     ] exch 2 div setdash
   } ifelse stroke
} def

% stroke a dotted line:  <length> <dashlength> lfigdotted -
/lfigdotted
{  2 copy le 1 index 0 le or
   { exch pop 1 pt lfigmax [ exch 0 exch ] 0 setdash }
   { 1 index exch div ceiling div
     [ 0 3 2 roll ] 0 setdash
   } ifelse stroke
} def

% stroke a noline line:  <length> <dashlength> lfignoline -
/lfignoline
{ pop pop
} def

% painting (i.e. filling): - lfigwhite - (etc.)
/lfignopaint		{			           } def
/lfignochange		{ 			      fill } def
/lfigdarkblue		{ 0.0 0.0 0.5 LoutSetRGBColor fill } def
/lfigblue		{ 0.0 0.0 1.0 LoutSetRGBColor fill } def
/lfiglightblue		{ 0.5 0.5 1.0 LoutSetRGBColor fill } def
/lfigdarkgreen		{ 0.0 0.5 0.0 LoutSetRGBColor fill } def
/lfiggreen		{ 0.0 1.0 0.0 LoutSetRGBColor fill } def
/lfiglightgreen		{ 0.5 1.0 0.5 LoutSetRGBColor fill } def
/lfigdarkred		{ 0.5 0.0 0.0 LoutSetRGBColor fill } def
/lfigred		{ 1.0 0.0 0.0 LoutSetRGBColor fill } def
/lfiglightred		{ 1.0 0.5 0.5 LoutSetRGBColor fill } def
/lfigdarkcyan		{ 0.0 0.5 0.5 LoutSetRGBColor fill } def
/lfigcyan		{ 0.0 1.0 1.0 LoutSetRGBColor fill } def
/lfiglightcyan		{ 0.5 1.0 1.0 LoutSetRGBColor fill } def
/lfigdarkmagenta	{ 0.5 0.0 0.5 LoutSetRGBColor fill } def
/lfigmagenta		{ 1.0 0.0 1.0 LoutSetRGBColor fill } def
/lfiglightmagenta	{ 1.0 0.5 1.0 LoutSetRGBColor fill } def
/lfigdarkyellow		{ 0.5 0.5 0.0 LoutSetRGBColor fill } def
/lfigyellow		{ 1.0 1.0 0.0 LoutSetRGBColor fill } def
/lfiglightyellow	{ 1.0 1.0 0.5 LoutSetRGBColor fill } def
/lfigdarkgray		{ 0.2 0.2 0.2 LoutSetRGBColor fill } def
/lfiggray		{ 0.5 0.5 0.5 LoutSetRGBColor fill } def
/lfiglightgray		{ 0.8 0.8 0.8 LoutSetRGBColor fill } def
/lfigdarkgrey		{ 0.2 0.2 0.2 LoutSetRGBColor fill } def
/lfiggrey		{ 0.5 0.5 0.5 LoutSetRGBColor fill } def
/lfiglightgrey		{ 0.8 0.8 0.8 LoutSetRGBColor fill } def
/lfigblack		{ 0.0 0.0 0.0 LoutSetRGBColor fill } def
/lfigwhite		{ 1.0 1.0 1.0 LoutSetRGBColor fill } def

% line caps (and joins, not currently used)
/lfigbutt       0 def
/lfiground      1 def
/lfigprojecting 2 def
/lfigmiter      0 def
/lfigbevel      2 def

% shape and labels of the @Box symbol
/lfigbox
{
   0     0     /SW  lfigpointdef
   xsize 0     /SE  lfigpointdef
   xsize ysize /NE  lfigpointdef
   0     ysize /NW  lfigpointdef
   SE 0.5 lfigpmul /S   lfigpointdef
   NW 0.5 lfigpmul /W   lfigpointdef
   W SE lfigpadd   /E   lfigpointdef
   S NW lfigpadd   /N   lfigpointdef
   NE 0.5 lfigpmul /CTR lfigpointdef
   [ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef
   SW SE NE NW SW
} def

% shape and labels of the @CurveBox symbol
/lfigcurvebox
{

   xsize 0.5 mul	ysize 0.5 mul	/CTR lfigpointdef
   xsize 0.5 mul	0		/S   lfigpointdef
   xsize		ysize 0.5 mul	/E   lfigpointdef
   xsize 0.5 mul	ysize		/N   lfigpointdef
   0			ysize 0.5 mul	/W   lfigpointdef

   xmark 0.293 mul		xmark 0.293 mul		  /SW  lfigpointdef
   xsize xmark 0.293 mul sub	xmark 0.293 mul		  /SE  lfigpointdef
   xsize xmark 0.293 mul sub	ysize xmark 0.293 mul sub /NE  lfigpointdef
   xmark 0.293 mul		ysize xmark 0.293 mul sub /NW  lfigpointdef

   [ xsize ysize 0.5 lfigpmul xmark /lfigcurveboxcircum cvx ] lfigcircumdef

   xmark		0
   xsize xmark sub	0
   [ xsize xmark sub	xmark		]
   xsize		xmark
   xsize		ysize xmark sub
   [ xsize xmark sub	ysize xmark sub	]
   xsize xmark sub	ysize
   xmark		ysize
   [ xmark		ysize xmark sub	]
   0			ysize xmark sub
   0			xmark
   [ xmark		xmark		]
   xmark		0
} def

% shadow of the @ShadowBox symbol
% its shape and labels are done, somewhat inaccurately, with lfigbox
/lfigshadow
{ xmark 2 mul 0 moveto xsize 0 lineto
  xsize ysize xmark 2 mul sub lineto
  xsize xmark sub ysize xmark 2 mul sub lineto
  xsize xmark sub xmark lineto
  xmark 2 mul xmark lineto closepath fill
} def

% shape and labels of the @Square symbol
/lfigsquare
{
   xsize ysize 0.5 lfigpmul /CTR lfigpointdef
   CTR xsize xsize ysize ysize lfigpmax 0.5 lfigpmul lfigpadd /NE lfigpointdef
   CTR 0 0 CTR NE lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef
   CTR 0 0 CTR NE lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef
   CTR 0 0 CTR NE lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef
   SW 0.5 lfigpmul SE 0.5 lfigpmul lfigpadd /S lfigpointdef
   NW 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /N lfigpointdef
   SW 0.5 lfigpmul NW 0.5 lfigpmul lfigpadd /W lfigpointdef
   SE 0.5 lfigpmul NE 0.5 lfigpmul lfigpadd /E lfigpointdef
   [ CTR NE lfigpsub /lfigboxcircum cvx ] lfigcircumdef
   SW SE NE NW SW
} def

% shape and labels of the @Diamond symbol
/lfigdiamond
{
   xsize 0 0.5 lfigpmul /S   lfigpointdef
   0 ysize 0.5 lfigpmul /W   lfigpointdef
   S W         lfigpadd /CTR lfigpointdef
   CTR W       lfigpadd /N   lfigpointdef
   CTR S       lfigpadd /E   lfigpointdef
   [ xsize ysize 0.5 lfigpmul /lfigdiamondcircum cvx ] lfigcircumdef
   S E N W S
} def

% shape and labels of the @Ellipse symbol
/lfigellipse
{
   xsize 0 0.5 lfigpmul /S   lfigpointdef
   0 ysize 0.5 lfigpmul /W   lfigpointdef
   S W         lfigpadd /CTR lfigpointdef
   CTR W       lfigpadd /N   lfigpointdef
   CTR S       lfigpadd /E   lfigpointdef
   CTR xsize 0 0.3536 lfigpmul lfigpadd 0 ysize 0.3536 lfigpmul lfigpadd /NE lfigpointdef
   0 ysize 0.3536 lfigpmul CTR xsize 0 0.3536 lfigpmul lfigpadd lfigpsub /SE lfigpointdef
   xsize 0 0.3536 lfigpmul CTR lfigpsub 0 ysize 0.3536 lfigpmul lfigpadd /NW lfigpointdef
   0 ysize 0.3536 lfigpmul xsize 0 0.3536 lfigpmul CTR lfigpsub lfigpsub /SW lfigpointdef
   [ xsize ysize 0.5 lfigpmul /lfigellipsecircum cvx ] lfigcircumdef
   S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S
} def

% shape and labels of the @Circle symbol
/lfigcircle
{
   xsize ysize 0.5 lfigpmul /CTR lfigpointdef
   CTR xsize 0 ysize 0 lfigpmax 0.5 lfigpmul lfigpadd /E lfigpointdef
   CTR 0 0 CTR E lfigdistance 45 lfigatangle lfigpadd /NE lfigpointdef
   CTR 0 0 CTR E lfigdistance 90 lfigatangle lfigpadd /N lfigpointdef
   CTR 0 0 CTR E lfigdistance 135 lfigatangle lfigpadd /NW lfigpointdef
   CTR 0 0 CTR E lfigdistance 180 lfigatangle lfigpadd /W lfigpointdef
   CTR 0 0 CTR E lfigdistance 225 lfigatangle lfigpadd /SW lfigpointdef
   CTR 0 0 CTR E lfigdistance 270 lfigatangle lfigpadd /S lfigpointdef
   CTR 0 0 CTR E lfigdistance 315 lfigatangle lfigpadd /SE lfigpointdef
   [ S E lfigpsub /lfigellipsecircum cvx ] lfigcircumdef
   S [ CTR ] E [ CTR ] N [ CTR ] W [ CTR ] S
} def

% shape and labels of the @HLine and @HArrow symbols
/lfighline
{
   0 ymark lfigprevious /FROM lfigpointdef
   xsize ymark lfigprevious /TO lfigpointdef
} def

% shape and labels of the @VLine and @VArrow symbols
/lfigvline
{
   xmark ysize lfigprevious /FROM lfigpointdef
   xmark 0 lfigprevious /TO lfigpointdef
} def

% points of a polygon around base with given no of sides, vert init angle:
% <sides> <angle> figpolygon <point> ... <point>
/lfigpolygon
{  xsize ysize 0.5 lfigpmul /CTR lfigpointdef
   90 sub CTR 2 copy lfigmax 5 3 roll
   [ 4 copy pop /lfigpolycircum cvx ] lfigcircumdef
   exch dup 360 exch div exch
   1 1  3 2 roll
   {  4 string cvs (P) exch lfigconcat cvn
      6 copy pop pop lfigatangle 2 copy 10 2 roll
      3 2 roll lfigpointdef
      dup 3 1 roll add exch
   }  for
   pop lfigatangle
} def

% next array element:  <array> <index> lfiggetnext <array> <index> <any> true
%                                               or <array> <index> false
/lfiggetnext
{  2 copy exch length ge
   { false }
   { 2 copy get exch 1 add exch true } ifelse
} def

% check whether thing is number:  <any> lfigisnumbertype <any> <bool>
/lfigisnumbertype
{  dup type dup
   /integertype eq exch /realtype eq or
} def

% check whether thing is an array:  <any> lfigisarraytype <any> <bool>
/lfigisarraytype { dup type /arraytype eq } def

% get next item:  <array> <index> lfiggetnextitem <array> <index> 0
%                                              or <array> <index> <array> 1
%                                              or <array> <index> <point> 2
/lfiggetnextitem
{   lfiggetnext
    {	lfigisarraytype
	{   1
	}
	{   lfigisnumbertype
	    {	3 1 roll
		lfiggetnext
		{   lfigisnumbertype
		    {	4 3 roll exch  2
		    }
		    {	pop 3 2 roll pop  0
		    } ifelse
		}
		{   3 2 roll pop  0
		} ifelse
	    }
	    {	pop 0
	    } ifelse
	} ifelse
    }
    {	0
    } ifelse
} def

% set arc path:  bool x1 y1  x2 y2  x0 y0  lfigsetarc  <angle> <angle> <dist>
% the path goes from x1 y1 to x2 y2 about centre x0 y0,
% anticlockwise if bool is true else clockwise.
% The orientations of backwards pointing and forwards pointing
% arrowheads are returned in the two angles, and
% the length of the arc is returned in <dist>.
/lfigsetarc
{
  20 dict begin
     matrix currentmatrix 8 1 roll
     2 copy translate 2 copy 8 2 roll
     4 2 roll lfigpsub 6 2 roll lfigpsub
     dup /y1 exch def dup mul /y1s exch def
     dup /x1 exch def dup mul /x1s exch def
     dup /y2 exch def dup mul /y2s exch def
     dup /x2 exch def dup mul /x2s exch def

     y1s y2s eq
     {	-1
     }
     {	y1s x2s mul y2s x1s mul sub y1s y2s sub div
     } ifelse
     /da exch def

     x1s x2s eq
     {	-1
     }
     {	x1s y2s mul x2s y1s mul sub x1s x2s sub div
     } ifelse
     /db exch def

     da 0 gt db 0 gt and
     {	/LMax da sqrt db sqrt lfigmax def
	/scalex da sqrt LMax div def
	/scaley db sqrt LMax div def
	scalex scaley scale
	0 0 LMax
	0 0 x1 scalex mul y1 scaley mul lfigangle
	0 0 x2 scalex mul y2 scaley mul lfigangle
	2 copy eq { 360 add } if
	2 copy 8 2 roll
	5 index { arc } { arcn } ifelse
	2 index 1 index
	{ 90 sub } { 90 add } ifelse
	dup sin scaley mul exch cos scalex mul atan
	2 index 2 index
	{ 90 add } { 90 sub } ifelse
	dup sin scaley mul exch cos scalex mul atan
	5 2 roll  % res1 res2 ang1 ang2 anticlockwise
	{ exch sub } { sub } ifelse
	dup 0 le { 360 add } if  lfigpi mul LMax mul 180 div
     }
     {	0 0 x1 y1 lfigdistance 0 0 x2 y2 lfigdistance eq
	0 0 x1 y1 lfigdistance 0 gt and
	{	0 0
		0 0 x1 y1 lfigdistance
		0 0 x1 y1 lfigangle
		0 0 x2 y2 lfigangle
		2 copy eq { 360 add } if
		2 copy 8 2 roll
		5 index { arc } { arcn } ifelse
		2 index 1 index
		{ 90 sub } { 90 add } ifelse
		2 index 2 index
		{ 90 add } { 90 sub } ifelse
		5 2 roll % res1 res2 ang1 ang2 clockwise
		{ exch sub } { sub } ifelse
		dup 0 le { 360 add } if lfigpi mul 0 0 x1 y1 lfigdistance mul 180 div
	}
	{	x2 y2 lineto pop
		x2 y2 x1 y1 lfigangle
		x1 y1 x2 y2 lfigangle
		x1 y1 x2 y2 lfigdistance
	} ifelse
     } ifelse
     4 -1 roll setmatrix
   end
} def

% lfigsetcurve: set up a Bezier curve from x0 y0 to x3 y3
% and return arrowhead angles and length of curve (actually 0)
% x0 y0 x1 y1 x2 y2 x3 y3 lfigsetcurve <angle> <angle> <length>
/lfigsetcurve
{ 8 copy curveto pop pop
  lfigangle
  5 1 roll
  4 2 roll lfigangle
  exch
  0
} def

% lfigpaintpath: paint a path of the given shape
% /paint [ shape ] lfigpaintpath -
/lfigpaintpath
{
  10 dict begin
    0 newpath
    /prevseen false def
    /curveseen false def
    { lfiggetnextitem
      dup 0 eq { pop exit }
      { 1 eq
        { /curveseen true def
	  /curve exch def
	  curve length 0 eq { /curveseen false def } if
        }
        { /ycurr exch def
	  /xcurr exch def
	  prevseen
	  { curveseen
	    { curve length 4 eq
	      { xprev yprev
		curve 0 get curve 1 get
		curve 2 get curve 3 get
		xcurr ycurr
		lfigsetcurve pop pop pop
	      }
	      { xprev yprev xcurr ycurr
	        curve length 1 ge { curve 0 get } { 0 } ifelse
	        curve length 2 ge { curve 1 get } { 0 } ifelse
	        curve length 3 ge { curve 2 get } { true } ifelse
	        7 1 roll
	        lfigsetarc pop pop pop
	      } ifelse
	    }
	    { xcurr ycurr lineto
	    } ifelse
	  }
	  { xcurr ycurr moveto
	  } ifelse
	  /xprev xcurr def
	  /yprev ycurr def
	  /prevseen true def
	  /curveseen false def
        } ifelse
      } ifelse
    } loop pop pop cvx exec
  end
} def

% stroke a path of the given shape in the given linestyle and dash length.
% Return the origin and angle of the backward and forward arrow heads.
% dashlength /linestyle [shape] lfigdopath  [<point> <angle>] [<point> <angle>] 
/lfigdopath
{
  10 dict begin
    0
    /prevseen  false def
    /curveseen false def
    /backarrow []    def
    /fwdarrow  []    def
    {
	lfiggetnextitem
	dup 0 eq { pop exit }
	{
	    1 eq
	    {	/curveseen true def
		/curve exch def
		curve length 0 eq { /prevseen false def } if
	    }
	    {	/ycurr exch def
		/xcurr exch def
		prevseen
		{   newpath xprev yprev moveto
		    curveseen
		    {	curve length 4 eq
			{   xprev yprev
			    curve 0 get curve 1 get
			    curve 2 get curve 3 get
			    xcurr ycurr lfigsetcurve
			}
			{   xprev yprev xcurr ycurr
			    curve length 1 ge { curve 0 get } { 0 } ifelse
			    curve length 2 ge { curve 1 get } { 0 } ifelse
			    curve length 3 ge { curve 2 get } { true } ifelse
			    7 1 roll
			    lfigsetarc
			} ifelse
		    }
		    {	xcurr ycurr lineto
			xcurr ycurr xprev yprev lfigangle dup 180 sub
			xprev yprev xcurr ycurr lfigdistance
		    } ifelse
		    6 index 6 index cvx exec
		    [ xprev yprev 5 -1 roll ]
		    backarrow length 0 eq
		    { /backarrow exch def }
		    { pop } ifelse
		    [ xcurr ycurr 4 -1 roll ] /fwdarrow exch def
		} if
		/xprev xcurr def
		/yprev ycurr def
		/prevseen true def
		/curveseen false def
	    } ifelse
	} ifelse
    } loop
    pop pop pop pop
    backarrow length 0 eq { [ 0 0 0 ] } { backarrow } ifelse
    fwdarrow  length 0 eq { [ 0 0 0 ] } { fwdarrow  } ifelse
  end
} def

% lfigdoarrow: draw an arrow head of given form
% dashlength /lstyle /pstyle hfrac height width [ <point> <angle> ] lfigdoarrow -
/lfigdoarrow
{  matrix currentmatrix 8 1 roll
   dup 0 get 1 index 1 get translate
   2 get rotate
   [ 2 index neg 2 index 0 0
     3 index 3 index neg
     1 index 10 index mul 0
     7 index 7 index ]
   4 1 roll pop pop pop
   dup 3 1 roll
   gsave lfigpaintpath grestore lfigdopath pop pop
   setmatrix
} def

% arrow head styles
/lfigopen     0.0 def
/lfighalfopen 0.5 def
/lfigclosed   1.0 def

% stroke no arrows, forward, back, and both
/lfignoarrow { pop pop pop pop pop pop pop pop                        } def
/lfigforward { 7 -1 roll lfigdoarrow pop                              } def
/lfigback    { 8 -2 roll pop lfigdoarrow                              } def
/lfigboth    { 8 -1 roll 7 copy lfigdoarrow pop 7 -1 roll lfigdoarrow } def

% lfigprevious: return previous point on path
/lfigprevious
{ lfigisnumbertype
  { 2 copy }
  { lfigisarraytype
    { 2 index 2 index }
    { 0 0 }
    ifelse
  } ifelse
} def

% label a point in 2nd top dictionary:  <point> /name lfigpointdef -
/lfigpointdef
{
  % (Entering lfigpointdef) lfigdebugprint
  [ 4 2 roll transform
    /itransform cvx ] cvx
    currentdict end
    3 1 roll
    % currentdict length currentdict maxlength lt
    % { def }
    % { exec moveto (too many labels) show stop }
    % ifelse
    def
    begin
  % (Leaving lfigpointdef) lfigdebugprint
} def

% promote labels from second top to third top dictionary
% <string> lfigpromotelabels -
/lfigpromotelabels
{
  % (Entering lfigpromotelabels) lfigdebugprint
  currentdict end exch currentdict end
  { exch 20 string cvs 2 index
    (@) lfigconcat exch lfigconcat cvn exch def
  } forall pop begin
  % (Leaving lfigpromotelabels) lfigdebugprint
} def

% show labels (except CIRCUM): - lfigshowlabels -
/lfigshowlabels
{
  % (Entering lfigshowlabels) lfigdebugprint
  currentdict end
    currentdict
    { 1 index 20 string cvs (CIRCUM) search % if CIRCUM in key
      { pop pop pop pop pop }
      { pop cvx exec 2 copy
        newpath 1.5 pt 0 360 arc
        0 setgray fill
        /Times-Roman findfont 8 pt scalefont setfont
        moveto 0.2 cm 0.1 cm rmoveto 20 string cvs show
      }
      ifelse
    } forall
  begin
  % (Leaving lfigshowlabels) lfigdebugprint
} def

% fix an angle to 0 <= res < 360:  <angle> lfigfixangle <angle>
/lfigfixangle
{
  % (Entering lfigfixangle) lfigdebugprint
  { dup 0 ge { exit } if
    360 add
  } loop
  { dup 360 lt { exit } if
    360 sub
  } loop
  % (Leaving lfigfixangle) lfigdebugprint
} def

% find point on circumference of box:  alpha a b lfigboxcircum x y
/lfigboxcircum
{
  % (Entering lfigboxcircum) lfigdebugprint
  4 dict begin
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def
    0 0 a b lfigangle /theta exch def

    % if alpha <= theta, return (a, a*tan(alpha))
    alpha theta le
    { a  a alpha sin mul alpha cos div }
    {
      % else if alpha <= 180 - theta, return (b*cot(alpha), b)
      alpha 180 theta sub le
      { b alpha cos mul alpha sin div  b }
      {
        % else if alpha <= 180 + theta, return (-a, -a*tan(alpha))
        alpha 180 theta add le
        { a neg  a neg alpha sin mul alpha cos div }
        {
	  % else if alpha <= 360 - theta, return (-b*cot(alpha), -b)
	  alpha 360 theta sub le
          { b neg alpha cos mul alpha sin div  b neg }
	  {
	    % else 360 - theta <= alpha, return (a, a*tan(alpha))
	    a  a alpha sin mul alpha cos div
	  } ifelse
        } ifelse
      } ifelse
    } ifelse
  end
  % (Leaving lfigboxcircum) lfigdebugprint
} def

% find quadratic roots (assume a != 0): a b c lfigqroots x1 x2 2
%                                                     or    x2 1
%                                                     or       0
/lfigqroots
{
  4 dict begin
    /c exch def
    /b exch def
    /a exch def
    /disc b b mul 4 a c mul mul sub def
    disc 0 lt
    { 0
    }
    { disc 0 eq
      { b neg 2 a mul div
	1
      }
      { b neg disc sqrt add 2 a mul div
        b neg disc sqrt sub 2 a mul div
	2
      }
      ifelse
    }
    ifelse
  end
} def

% work our which quadrant: <angle> lfigquadrant <0-3>
/lfigquadrant
{ dup 90 lt
  { pop 0
  }
  { dup 180 lt
    { pop 1
    }
    { 270 lt
      { 2
      }
      { 3
      } ifelse
    } ifelse
  } ifelse
} def

% find curvebox circum, assuming upper right quadrant: alpha a b xmk lfigcb x y
/lfigcb
{
  6 dict begin
    /xmk exch def
    /b exch def
    /a exch def
    /alpha exch def
    /theta1 0 0 a b xmk sub lfigangle def
    /theta2 0 0 a xmk sub b lfigangle def
    alpha theta1 le
    { % if alpha <= theta1, return (a, a*tan(alpha))
      a  a alpha sin mul alpha cos div
    }
    { alpha theta2 ge
      { % else if alpha > theta2, return (b*cot(alpha), b)
	b alpha cos mul alpha sin div  b
      }
      {
	% else, return the intersection of line and circle
	a xmk sub b xmk sub xmk  0 0 alpha lfigcircleintersect
	dup 0 eq
	{ % should never happen, just return any reasonable point
	  pop
	  a b 0.5 lfigpmul
	}
	{ 1 eq
	  { % should never happen, just return the point on top of stack
	  }
	  { % the usual case, two points on stack, return the larger
	    lfigpmax
	  } ifelse
	} ifelse
      } ifelse
    } ifelse
  end
} def

% find point on circumference of curvebox: alpha a b xmk lfigcurveboxcircum x y
/lfigcurveboxcircum
{
  % (Entering lfigcurveboxcircum) lfigdebugprint
  5 dict begin
    /xmk exch def
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def

    % work out which quadrant we are in, and reflect accordingly
    /quad alpha lfigquadrant def
    quad 0 eq
    { alpha a b xmk lfigcb
    }
    { quad 1 eq
      { 180 alpha sub a b xmk lfigcb exch neg exch
      }
      { quad 2 eq
	{ alpha 180 sub a b xmk lfigcb neg exch neg exch
	}
	{ 360 alpha sub a b xmk lfigcb neg
	} ifelse
      } ifelse
    } ifelse
  end
  % (Leaving lfigcurveboxcircum) lfigdebugprint
} def

% find point on circumference of diamond:  alpha a b lfigdiamondcircum x y
/lfigdiamondcircum
{
  % (Entering lfigdiamondcircum) lfigdebugprint
  4 dict begin
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def
    b alpha cos abs mul  a alpha sin abs mul  add  /denom exch def
    a b mul alpha cos mul denom div
    a b mul alpha sin mul denom div
  end
  % (Leaving lfigdiamondcircum) lfigdebugprint
} def

% find point on circumference of ellipse:  alpha a b lfigellipsecircum x y
/lfigellipsecircum
{
  % (Entering lfigellipsecircum) lfigdebugprint
  4 dict begin
    /b exch def
    /a exch def
    lfigfixangle /alpha exch def
    b alpha cos mul dup mul  a alpha sin mul dup mul  add sqrt /denom exch def
    a b mul alpha cos mul denom div
    a b mul alpha sin mul denom div
  end
  % (Leaving lfigellipsecircum) lfigdebugprint
} def

% find point of intersection of two lines each defined by two points
% x1 y1 x2 y2  x3 y3 x4 y4  lfiglineintersect x y
/lfiglineintersect
{
  % (Entering lfiglineintersect) lfigdebugprint
  13 dict begin
    /y4 exch def
    /x4 exch def
    /y3 exch def
    /x3 exch def
    /y2 exch def
    /x2 exch def
    /y1 exch def
    /x1 exch def
    x2 x1 sub /x21 exch def
    x4 x3 sub /x43 exch def
    y2 y1 sub /y21 exch def
    y4 y3 sub /y43 exch def
    y21 x43 mul y43 x21 mul sub /det exch def
  
    % calculate x 
    y21 x43 mul x1 mul
    y43 x21 mul x3 mul sub
    y3 y1 sub x21 mul x43 mul add
    det div

    % calculate y
    x21 y43 mul y1 mul
    x43 y21 mul y3 mul sub
    x3 x1 sub y21 mul y43 mul add
    det neg div

  end
  % (Leaving lfiglineintersect) lfigdebugprint
} def

% find point on circumference of polygon
% alpha radius num theta lfigpolycircum x y
/lfigpolycircum
{
  % (Entering lfigpolycircum) lfigdebugprint
  13 dict begin
    /theta exch def
    /num exch def
    /radius exch def
    /alpha exch def

    % calculate delta, the angle from theta to alpha
    alpha theta sub lfigfixangle

    % calculate the angle which is the multiple of 360/num closest to delta
    360 num div div truncate 360 num div mul theta add /anglea exch def

    % calculate the next multiple of 360/num after anglea
    anglea 360 num div add /angleb exch def

    % intersect the line through these two points with the alpha line
    anglea cos anglea sin  angleb cos angleb sin
    0 0  alpha cos 2 mul alpha sin 2 mul
    lfiglineintersect radius lfigpmul

  end
  % (Leaving lfigpolycircum) lfigdebugprint
} def

% find point of intersection of a point and a circle
% x0 y0 r  x1 y1 theta  lfigcircleintersect xa ya xb yb 2
%                                        or       xb yb 1
%                                        or             0
/lfigcircleintersect
{
  % (Entering lfigcircleintersect) lfigdebugprint
  15 dict begin
    /theta exch def
    /y1    exch def
    /x1    exch def
    /r     exch def
    /y0    exch def
    /x0    exch def

    % if sin(theta) = 0 then line is horizontal and y must be y1
    theta sin abs 0.00001 lt
    { 
      /a 1 def
      /b -2 x0 mul def
      /c x0 dup mul y1 y0 sub dup mul add r dup mul sub def
      a b c lfigqroots dup
      0 eq
      { pop
	0
      }
      { 1 eq
	{ y1 1
	}
	{ y1 exch y1 2
	} ifelse
      } ifelse
    }
    {
      /ct theta cos theta sin div def
      /a ct ct mul 1 add def
      /b ct x1 x0 sub mul y1 add y0 sub 2 mul def
      /c x1 x0 sub dup mul y1 y0 sub dup mul add r dup mul sub def
      a b c lfigqroots dup
      0 eq
      { pop
	0
      }
      { 1 eq
	{ y1 add /yb exch def
	  yb y1 sub ct mul x1 add /xb exch def
	  xb yb 1
	}
	{ y1 add /ya exch def
	  ya y1 sub ct mul x1 add /xa exch def
	  y1 add /yb exch def
	  yb y1 sub ct mul x1 add /xb exch def
	  xa ya xb yb 2
	} ifelse
      } ifelse
    } ifelse
  end
  % (Leaving lfigcircleintersect) lfigdebugprint
} def

% add CIRCUM operator with this body:  <array> lfigcircumdef -
/lfigcircumdef
{   % (Entering lfigcircumdef) lfigdebugprint
    /CIRCUM exch cvx
    currentdict end
    3 1 roll
    % currentdict length currentdict maxlength lt
    % { def }
    % { exec moveto (too many labels) show stop }
    % ifelse
    def
    begin
    % (Leaving lfigcircumdef) lfigdebugprint
} def

end
%%EndResource

%%BeginResource: procset LoutBasicSetup
% @PrependGraphic file /home/jeff/lout.lib/include/bsf.lpg

% width height linethickness louteuro -
% draw a Euro symbol of this width and height with this line thickness
/louteuro {
  20 dict begin
    /eurothick exch def
    /euroheight exch def
    /eurowidth exch def
    /eurostrokewidth euroheight 0.8 mul def
    /eurostep eurothick 60 cos mul 60 sin div def
    /eurotheta 40 def

    % llx lly width thickness louteurobox -
    % draw angled box starting at (llx, lly) with given width and thickness
    /louteurobox
    {
      /euroboxthick exch def
      /euroboxwidth exch def
      newpath moveto euroboxwidth 0 rlineto
      eurostep euroboxthick rlineto
      euroboxwidth neg 0 rlineto closepath fill
    } def

    % lower cross stroke
    0 euroheight 2 div eurothick 1.5 mul sub
    eurostrokewidth eurothick louteurobox

    % upper cross stroke
    0 euroheight 2 div eurothick 0.5 mul add
    eurostrokewidth eurostep 2 mul add eurothick louteurobox

    % circular part
    /eurohctr eurowidth euroheight 2 div eurotheta cos mul sub def
    /eurovctr euroheight 2 div def
    newpath
    eurohctr eurovctr eurovctr eurotheta 350 eurotheta sub arc
    eurohctr eurovctr eurovctr eurothick sub 365 eurotheta sub eurotheta arcn
    closepath fill
  end
} def

% path for @FullWidthRule symbol
/LoutRule
{ 0 0 moveto xsize 0 lineto
} def

% path for @Box symbol
/LoutBox
{ 0 0 moveto xsize 0 lineto
  xsize ysize lineto 0 ysize lineto
  closepath
} def

% path for @CurveBox symbol
/LoutCurveBox
{ xmark 0 moveto
  xsize xmark sub xmark xmark 270 360 arc
  xsize xmark sub ysize xmark sub xmark 0 90 arc
  xmark ysize xmark sub xmark 90 180 arc
  xmark xmark xmark 180 270 arc
  closepath
} def

% path for @ShadowBox symbol
/LoutShadowBox
{ xmark 2 mul 0 moveto xsize 0 lineto
  xsize ysize xmark 2 mul sub lineto
  xsize xmark sub ysize xmark 2 mul sub lineto
  xsize xmark sub xmark lineto
  xmark 2 mul xmark lineto
  closepath
} def

% set up dictionary containing margin note data: parity LoutMargSet -
/LoutMargSet
{ /LoutMargDict 12 dict def
  LoutMargDict begin
    /parity exch def
    /matr matrix currentmatrix def
    /rightx xsize def
    /lefty ysize def   % highest allowable point for top of next left note
    /righty ysize def  % highest allowable point for top of next right note
    /max { 2 copy gt { pop } { exch pop } ifelse } def
    /min { 2 copy lt { pop } { exch pop } ifelse } def
  end
} def

%translate coordinate system for marginal notes:  type LoutMargShift -
% where type 0 is left margin, 1 is right margin, 2 is outer, 3 is inner
/LoutMargShift
{ LoutMargDict begin

    % y coordinate of top of note, in margin coords, before vertical adjust
    0 ysize transform matr itransform exch pop

    % decide whether left or right margin based on type and parity
    exch [ 0 1 parity 1 parity sub ] exch get 0 eq
    {
      % left margin: adjust top of note downwards if overlaps previous note
      lefty min

      % bottom of note is new lefty position and also translate position
      ysize sub dup /lefty exch def

      % want right edge of note at coordinate zero
      xsize neg exch
    }
    {
      % right margin: adjust top of note downwards if overlaps previous note
      righty min

      % bottom of note is new righty position and also translate position
      ysize sub dup /righty exch def

      % want left edge of note at coordinate rightx
      rightx exch
    } ifelse

    % stack now contains coord of bottom left corner in margin coordinates
    matr setmatrix translate
  end
} def

% create LoutPageDict with left, right, foot, top for @Place symbol users
/LoutPageSet
{
  /LoutPageDict 5 dict def
  LoutPageDict begin
    /matr matrix currentmatrix def
    /left 0 def
    /right xsize def
    /foot 0 def
    /top ysize def
  end

} def

%%EndResource

%%EndProlog

%%BeginSetup
%%BeginResource: encoding vec2
/vec2 [
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef /.notdef
/space /exclam /quotedbl /numbersign /dollar /percent /ampersand /quoteright
/parenleft /parenright /asterisk /plus /comma /hyphen /period /slash
/zero /one /two /three /four /five /six /seven
/eight /nine /colon /semicolon /less /equal /greater /question
/at /A /B /C /D /E /F /G
/H /I /J /K /L /M /N /O
/P /Q /R /S /T /U /V /W
/X /Y /Z /bracketleft /backslash /bracketright /asciicircum /underscore
/quoteleft /a /b /c /d /e /f /g
/h /i /j /k /l /m /n /o
/p /q /r /s /t /u /v /w
/x /y /z /braceleft /bar /braceright /asciitilde /.notdef
/quotesinglbase /quotedblbase /ellipsis /OE /oe /quotedblleft /quotedblright /fi
/fl /endash /emdash /bullet /dagger /daggerdbl /florin /fraction
/dotlessi /grave /acute /circumflex /tilde /macron /breve /dotaccent
/dieresis /.notdef /ring /cedilla /.notdef /hungarumlaut /ogonek /caron
/space /exclamdown /cent /sterling /currency /yen /brokenbar /section
/dieresis /copyright /ordfeminine /guillemotleft /logicalnot /hyphen /registered /macron
/degree /plusminus /twosuperior /threesuperior /acute /mu /paragraph /periodcentered
/cedilla /onesuperior /ordmasculine /guillemotright /onequarter /onehalf /threequarters /questiondown
/Agrave /Aacute /Acircumflex /Atilde /Adieresis /Aring /AE /Ccedilla
/Egrave /Eacute /Ecircumflex /Edieresis /Igrave /Iacute /Icircumflex /Idieresis
/Eth /Ntilde /Ograve /Oacute /Ocircumflex /Otilde /Odieresis /multiply
/Oslash /Ugrave /Uacute /Ucircumflex /Udieresis /Yacute /Thorn /germandbls
/agrave /aacute /acircumflex /atilde /adieresis /aring /ae /ccedilla
/egrave /eacute /ecircumflex /edieresis /igrave /iacute /icircumflex /idieresis
/eth /ntilde /ograve /oacute /ocircumflex /otilde /odieresis /divide
/oslash /ugrave /uacute /ucircumflex /udieresis /yacute /thorn /ydieresis
] def
%%EndResource

/pdfmark where {pop} {userdict /pdfmark /cleartomark load put} ifelse
%%EndSetup

%%Page: i 1
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup

gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
240 fnt2 2897 12401(The)m
3352(Design)s 4099(and)s 4540(Implementation)s 4239 11998(of)m 4511(the)s
2589 11595(Lout)m 3141(Document)s 4250(F)s 6(ormatting)k 5468(Language)s
240 fnt3 3630 11097(J)m 6(ef)k 4(fr)k 8(e)k 7(y)k
4310(H.)s 4577(Kingston)s 240 fnt1 2551 10596(Basser)m 3248(Department)s
4436(of)s 4707(Computer)s 5724(Science,)s 3007 10308(The)m 3435(Uni)s 6(v)k 3(ersity)k
4489(of)s 4760(Sydne)s 3(y)k 5530(2006,)s 4095 10020(Australia)m
3739 9568(27)m 4027(January)s 15(,)k 4863(1993)s 240 fnt2
3901 8775(SUMMAR)m 8(Y)k 240 fnt1 0 8320(Lout)m 543(is)s
784(a)s 982(high-le)s 6(v)k 3(el)k 2028(language)s
2979(for)s 3349(document)s 4384(formatting,)s 5530(whose)s 6230(ease)s
6728(of)s 7030(use)s 7437(has)s 7838(permitted)s 8843(an)s
0 8032(unprecedented)m 1501(number)s 2340(of)s 2659(adv)s 6(anced)k
3663(features)s 4517(to)s 4804(be)s 5134(added)s 5812(quickly)s
6632(and)s 7084(reliably)s 15(.)k 8010(This)s 8535(paper)s
0 7744(charts)m 625(the)s 978(e)s 6(v)k 4(olution)k
1933(of)s 2209(the)s 2561(design)s 3248(and)s 3656(implementation)s
5218(of)s 5493(Lout)s 6010(from)s 6538(conception)s 7650(in)s
7897(mid-1984)s 8887(to)s 0 7456(public)m 672(release)s 1412(in)s
1677(October)s 2529(1991.)s 3194(It)s 3421(includes)s 4291(e)s 3(xtensi)k 6(v)k 3(e)k
5260(discussions)s 6422(of)s 6715(remaining)s 7759(problems)s 8722(and)s
0 7168(possible)m 840(solutions.)s 240 fnt2 0 6664(K)m 6(eyw)k 2(ords)k
240 fnt1 1143 6665(document)m 2147(formatting)s 3208(typesetting)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 1 2
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
9066 14006 0 14006 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
240 fnt2 2897 12401(The)m
3352(Design)s 4099(and)s 4540(Implementation)s 4239 11998(of)m 4511(the)s
2589 11595(Lout)m 3141(Document)s 4250(F)s 6(ormatting)k 5468(Language)s
240 fnt3 3630 11097(J)m 6(ef)k 4(fr)k 8(e)k 7(y)k
4310(H.)s 4577(Kingston)s 240 fnt1 2551 10596(Basser)m 3248(Department)s
4436(of)s 4707(Computer)s 5724(Science,)s 3007 10308(The)m 3435(Uni)s 6(v)k 3(ersity)k
4489(of)s 4760(Sydne)s 3(y)k 5530(2006,)s 4095 10020(Australia)m
3739 9568(27)m 4027(January)s 15(,)k 4863(1993)s 240 fnt2
0 8926(1.)m 291(Intr)s 4(oduction)k 
[ /Dest /LOUT18_651_s1_0_1 /DEST pdfmark
240 fnt1 480 8495(Lout)m
985([1,)s 1284(2])s 1515(is)s 1718(a)s 1877(high-le)s 6(v)k 3(el)k
2885(language)s 3798(for)s 4129(document)s 5126(formatting,)s 6234(designed)s
7136(and)s 7533(implemented)s 8832(by)s 0 8207(the)m 341(author)s 13(.)k
1096(The)s 1517(implementation,)s 3117(kno)s 6(wn)k 3814(as)s
4057(Basser)s 4747(Lout,)s 5299(is)s 5502(a)s 5661(fully)s
6159(operational)s 7282(production)s 8368(v)s 3(ersion)k 0 7919(written)m
736(in)s 983(C)s 1198(for)s 1540(the)s 1891(Unix)s
2429(operating)s 3389(system,)s 153 fnt1 4100 8008(1)m 240 fnt1
4223 7919(which)m 4869(translates)s 5824(Lout)s 6340(source)s 7023(code)s
7535(into)s 7964(PostScript,)s 153 fnt1 8993 8008(2)m 240 fnt1
0 7631(a)m 201(de)s 6(vice-independent)k 2164(graphics)s 3061(rendering)s
4066(language)s 5021(accepted)s 5951(by)s 6281(man)s 3(y)k
6900(high-resolution)s 8454(output)s 0 7343(de)m 6(vices,)k 833(including)s
1805(most)s 2346(laser)s 2871(printers.)s 3779(Basser)s 4492(Lout)s
5019(is)s 5244(a)s 4(v)k 6(ailable)k 6168(free)s
6609(of)s 6895(char)s 4(ge)k 7600([3].)s 8057(It)s
8278(includes)s 0 7055(installation)m 1118(instructions,)s 2339(C)s 2550(source,)s
3281(se)s 6(v)k 3(en)k 3873(standard)s 4740(packages,)s
5723(and)s 6127(complete)s 7058(documentation)s 8536(in)s 8778(the)s
0 6767(form)m 524(of)s 795(six)s 1129(technical)s 2046(reports)s
2760(and)s 3164(a)s 3330(manual)s 4089(page.)s 480 6393(The)m
900(Lout)s 1404(project)s 2118(arose)s 2670(out)s 3027(of)s
3290(the)s 3629(author')s 13(s)k 4442(desire)s 5060(to)s
5290(bring)s 5840(to)s 6070(document)s 7066(formatting)s 8118(languages)s
0 6105(the)m 343(ele)s 3(g)k 1(ance)k 1225(of)s
1491(e)s 3(xpression)k 2562(found)s 3174(in)s 3411(programming)s
4761(languages)s 5763(lik)s 2(e)k 6170(Algol-)s 6783(60)s
7072(and)s 7471(P)s 3(ascal.)k 8236(This)s 8706(em)s
8998(-)s 0 5817(phasis)m 638(on)s 924(e)s 3(xpressi)k 6(v)k 3(eness)k
2373(has)s 2731(produced)s 3669(an)s 3941(order)s 4493(of)s
4753(magnitude)s 5808(reduction)s 6757(in)s 6988(the)s 7325(cost)s
7759(of)s 8018(de)s 6(v)k 3(eloping)k 0 5529(document)m
998(formatting)s 2053(applications.)s 3366(F)s 3(or)k 3748(e)s 3(xample,)k
4656(an)s 4933(equation)s 5807(formatting)s 6862(application,)s 8025(which)s
8660(may)s 0 5241(be)m 282(dif\207cult)s 1098(or)s 1357(impossible)s
2449(to)s 2688(add)s 3092(to)s 3331(other)s 3882(systems,)s
4746(can)s 5135(be)s 5417(written)s 6150(in)s 6393(Lout)s
6905(in)s 7148(a)s 7314(fe)s 6(w)k 7720(days.)s
480 4867(When)m 1099(e)s 3(xpert)k 1742(users)s 2274(can)s
2652(implement)s 3724(such)s 4209(applications)s 5405(quickly)s 15(,)k
6204(non-)s 6632(e)s 3(xperts)k 7360(bene\207t.)s 8164(Although)s
0 4579(Lout)m 509(itself)s 1053(pro)s 3(vides)k 1922(only)s
2398(a)s 2560(small)s 3129(k)s 2(ernel)k 3775(of)s
4042(carefully)s 4941(chosen)s 5659(primiti)s 6(v)k 3(es,)k
6721(packages)s 7646(written)s 8375(in)s 8614(Lout)s 0 4291(and)m
399(distrib)s 4(uted)k 1470(with)s 1946(Basser)s 2638(Lout)s
3145(pro)s 3(vide)k 3923(an)s 4201(unprecedented)s 5649(array)s
6187(of)s 6453(adv)s 6(anced)k 7404(features)s 8204(in)s
8442(a)s 8602(form)s 0 4003(accessible)m 1035(to)s 1286(non-)s
1714(e)s 3(xpert)k 2380(users.)s 3047(The)s 3487(features)s
4305(include)s 5076(rotation)s 5888(and)s 6304(scaling,)s 7100(fonts,)s
7697(paragraph)s 8722(and)s 0 3715(page)m 500(breaking,)s 1436(displays)s
2263(and)s 2659(lists,)s 3141(\210oating)s 3917(\207gures)s 4611(and)s
5007(tables,)s 5662(footnotes,)s 6651(chapters)s 7490(and)s 7886(sections)s
8698(\(au)s 8998(-)s 0 3427(tomatically)m 1128(numbered\),)s 2272(running)s
3070(page)s 3579(headers)s 4361(and)s 4765(footers,)s 5536(odd-)s
5964(e)s 6(v)k 3(en)k 6464(page)s 6973(layouts,)s
7772(automatically)s 0 3139(generated)m 975(tables)s 1570(of)s 1829(contents,)s
2720(sorted)s 3350(inde)s 3(x)k 3(es)k 4113(and)s
4505(reference)s 5435(lists,)s 5914(bibliographic)s 7229(and)s 7621(other)s
8159(databases)s 0 2851(\(including)m 1038(databases)s 2008(of)s 2281(formats)s
3064(for)s 3405(printing)s 4217(references\),)s 5386(equations,)s 6412(tables,)s
7079(diagrams,)s 8065(formatting)s 0 2563(of)m 271(P)s 3(ascal)k
933(programs,)s 1943(and)s 2347(automatically)s 3701(maintained)s 4821(cross)s
5363(references.)s 480 2189(This)m 1015(paper)s 1666(charts)s 2347(the)s
2755(e)s 6(v)k 4(olution)k 3766(of)s 4097(Lout)s
4669(from)s 5253(conception)s 6420(in)s 6723(mid-1984)s 7768(to)s
8067(the)s 8475(public)s 0 1901(release)m 722(of)s 997(Basser)s
1699(Lout)s 2215(in)s 2462(October)s 3297(1991.)s 3945(Lout)s
4461(is)s 4676(or)s 4(g)k 1(anized)k 5676(around)s
6403(four)s 6866(k)s 2(e)k 3(y)k 7265(concepts)s
8157(\211)s 8342(objects,)s 0 1613(de\207nitions,)m 1131(g)s 1(alle)k 3(ys,)k
1925(and)s 2343(cross)s 2899(references)s 3944(\211)s 4138(and)s
4556(the)s 3(y)k 5033(were)s 5567(de)s 6(v)k 3(eloped)k
6614(in)s 6871(the)s 7233(order)s 7811(listed,)s 8449(so)s
8730(this)s 0 1325(paper)m 593(will)s 1022(treat)s 1508(each)s
2006(in)s 2252(turn,)s 2747(discussing)s 3800(its)s 4079(design,)s
4814(implementation,)s 6424(problems,)s 7424(and)s 7831(prospects)s 8788(for)s
1134 0 0 0 240 288 60 0 574 LoutGr2
0 0 moveto xsize 0 lineto stroke
grestore

grestore
122 fnt1 0 379(1)m 192 fnt1 58 309(Unix)m 485(is)s
653(a)s 786(trademark)s 1609(of)s 1825(A)s 21(T&T)k
2370(Bell)s 2733(Laboratories.)s 122 fnt1 0 112(2)m 192 fnt1
67 42(PostScript)m 900(is)s 1068(a)s 1201(trademark)s 2024(of)s
2240(Adobe)s 2796(Systems,)s 3519(Incorporated.)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 2 3
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Symbol
%%+ font Times-Italic
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5765 -1579(-)m 5893(2)s
6067(-)s 9066 13419 0 13310 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13256(further)m 709(impro)s 3(v)k 3(ement.)k
240 fnt2 0 12463(2.)m 291(Objects)s 
[ /Dest /LOUT18_651_s2_0_1 /DEST pdfmark
240 fnt1 480 11987(The)m
923(essence)s 1725(of)s 2011(an)s 3(y)k 2424(mo)s 3(v)k 3(e)k
3021(to)s 3276(a)s 3457(higher)s 4144(le)s 6(v)k 3(el)k
4669(is)s 4895(the)s 5258(introduction)s 6500(of)s 6786(some)s
7363(abstraction)s 8484(which)s 0 11699(serv)m 3(es)k 639(to)s
872(or)s 4(g)k 1(anize)k 1740(the)s 2082(lo)s 6(w-)k
2503(le)s 6(v)k 3(el)k 3006(operations,)s 4103(resulting)s
4986(in)s 5223(a)s 5383(more)s 5923(succinct)s 6760(e)s 3(xpression)k
7831(of)s 8096(their)s 8586(com)s 8998(-)s 0 11411(mon)m
475(combinations)s 1806(at)s 2030(the)s 2369(cost)s 2805(of)s
3068(some)s 3620(loss)s 4034(of)s 4297(detailed)s 5102(control.)s
5934(The)s 6354(early)s 6876(part)s 7298(of)s 7561(the)s
7900(Lout)s 8403(project)s 0 11123(w)m 2(as)k 426(spent)s
996(in)s 1245(the)s 1598(de)s 6(v)k 3(elopment)k
2891(of)s 3167(such)s 3668(an)s 3957(abstraction)s 5067(for)s
5411(the)s 5764(b)s 4(uilding)k 6616(blocks)s 7298(of)s
7574(documents,)s 8724(one)s 0 10835(which)m 635(could)s 1217(e)s 3(xplain,)k
2017(not)s 2375(just)s 2772(the)s 3113(simple)s 3798(phenomena)s
4954(of)s 5217(w)s 2(ords,)k 5899(lines,)s 6450(and)s
6846(paragraphs,)s 7994(b)s 4(ut)k 8348(also)s 8778(the)s
0 10547(alignment)m 1016(of)s 1287(columns)s 2149(in)s 2392(tables,)s
3056(and)s 3460(the)s 3808(comple)s 3(x)k 4684(nested)s
5353(structures)s 6332(of)s 6603(equations.)s 240 fnt2 0 9898(2.1.)m
471(The)s 926(genesis)s 1697(of)s 1969(the)s 2343(object)s
3026(abstraction)s 
[ /Dest /LOUTgenesis /DEST pdfmark
240 fnt1 480 9421(When)m 1163(one)s 1620(e)s 3(xamines)k
2626(pre)s 6(vious)k 3549(document)s 4608(formatting)s 5724(systems)s
6587([4])s 6958(looking)s 7798(for)s 8191(ideas)s 8788(for)s
0 9133(abstractions,)m 1245(as)s 1492(the)s 1837(author)s 2505(did)s
2866(in)s 3106(1984,)s 3690(the)s 4035(Eqn)s 4475(formatting)s
5533(language)s 6450([5])s 6764(stands)s 7410(out)s 7773(lik)s 2(e)k
8182(a)s 8344(beacon.)s 0 8845(In)m 256(Eqn,)s 749(a)s
915(mathematical)s 2256(formula)s 3072(such)s 3568(as)s 167 fnt4
586 8392(2)m 240 fnt3 480 8332(x)m 240 fnt4 737 8324(+)m
938(1)s gsave
480 8276 translate
240 fnt3 552 0 0 0 240 288 12 LoutGraphic
gsave
0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke
grestore

grestore
699 8048(4)m 240 fnt1 0 7537(is)m
210(produced)s 1159(by)s 1453(typing)s 220 fnt5 480 7039({ x sup 2 + 1 } o)m 3(v)k 5(er 4)k
240 fnt1 0 6543(in)m 261(the)s 627(input)s 1197(\207le;)s
220 fnt5 1632 6540(sup)m 240 fnt1 2056 6543(and)m 220 fnt5
2478 6540(o)m 3(v)k 5(er)k 240 fnt1 2975 6543(are)m
3340(binary)s 4023(operators,)s 5037(and)s 5459(braces)s 6138(are)s
6503(used)s 7018(for)s 7374(grouping.)s 8421(This)s 8916(is)s
0 6255(document)m 1017(formatting)s 2091(at)s 2337(a)s 2516(v)s 3(ery)k
3006(high)s 3502(le)s 6(v)k 3(el,)k 4077(close)s
4638(to)s 4890(the)s 5252(language)s 6185(of)s 6469(mathematics)s
7741(itself,)s 8337(with)s 8833(all)s 0 5967(reference)m 943(to)s
1182(font)s 1627(changes)s 2449(and)s 2853(spacing)s 3637(suppressed.)s
480 5593(Eqn)m 916(pro)s 3(vides)k 1780(a)s 1938(single)s
2557(data)s 3008(type)s 3468(\(let)s 3837(us)s 4093(call)s
4485(it)s 4669(the)s 240 fnt3 5009 5595(e)m 4(xpr)k 8(ession)k
240 fnt1 6014 5593(\),)m 6192(b)s 4(uilt)k 6679(up)s
6964(recursi)s 6(v)k 3(ely)k 8062(in)s 8297(conte)s 3(xt-)k
0 5305(free)m 457(style:)s 1106(where)s 1778(one)s 2212(e)s 3(xpression)k
3321(may)s 3819(appear)s 9(,)k 4586(an)s 3(y)k
5015(e)s 3(xpression)k 6124(may)s 6622(appear)s 13(.)k
7442(This)s 7950(approach)s 8916(is)s 0 5017(common)m 905(in)s
1158(algebra)s 1931(and)s 2345(programming)s 3710(languages,)s 4785(where)s
5435(its)s 5721(simplicity)s 6740(and)s 7154(e)s 3(xpressi)k 6(v)k 3(eness)k
8625(ha)s 4(v)k 3(e)k 0 4729(long)m 478(been)s
986(appreciated;)s 2198(b)s 4(ut)k 2559(Eqn)s 3001(w)s 2(as)k
3421(the)s 3768(\207rst)s 4198(language)s 5117(to)s 5355(demonstrate)s
6578(its)s 6853(utility)s 7476(in)s 7718(document)s 8720(for)s
8998(-)s 0 4441(matting.)m 480 4067(Each)m 1015(e)s 3(xpression)k
2092(is)s 2302(treated)s 3009(by)s 3304(Eqn)s 3747(as)s
3997(a)s 4163(rectangle)s 5094(with)s 5577(a)s 240 fnt3
5743 4069(horizontal)m 6787(axis)s 240 fnt1 7167 4067(,)m 7274(used)s
7771(for)s 8110(alignment)s 0 3779(with)m 482(adjacent)s 1338(e)s 3(xpressions:)k
552 517 0 288 240 288 60 480 2922 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
552 517 0 288 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
552 517 0 288 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd

 ] lfigdopath
pop pop
grestore
167 fnt4 106 404(2)m 240 fnt3 0 344(x)m 240 fnt4
257 336(+)m 458(1)s gsave
0 288 translate
240 fnt3 552 0 0 0 240 288 12 LoutGraphic
gsave
0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke
grestore

grestore
219 60(4)m 
grestore

grestore
end end restore
grestore
0 2471(The)m
425(size)s 848(and)s 1248(rendering)s 2213(of)s 2481(the)s
2825(e)s 3(xpression)k 3898(on)s 4191(the)s 4536(printed)s
5267(page)s 5771(are)s 6114(kno)s 6(wn)k 6815(only)s
7291(to)s 7526(the)s 7870(implementa)s 8998(-)s 0 2183(tion,)m
481(ne)s 6(v)k 3(er)k 1066(e)s 3(xplicitly)k
2022(calculated)s 3051(or)s 3313(accessed)s 4209(by)s 4506(the)s
4857(user)s 13(.)k 5409(This)s 5888(prohibition)s 7010(is)s
7223(crucial)s 7930(to)s 8172(the)s 8523(main)s 8998(-)s
0 1895(tenance)m 785(of)s 1055(the)s 1402(conte)s 3(xt-)k
2171(free)s 2596(property)s 3459(in)s 3701(practice.)s 4619(In)s
4874(Lout,)s 5432(for)s 5769(e)s 3(xample,)k 6682(equations,)s
7705(\207gures,)s 8462(tables,)s 0 1607(and)m 393(arbitrary)s 1256(objects)s
1972(may)s 2427(be)s 2697(mix)s 3(ed)k 3338(together)s
4169(freely)s 15(.)k 4863(This)s 5327(w)s 2(ould)k
5970(be)s 6241(impossible)s 7321(if)s 7526(size)s 7941(information)s
0 1319(w)m 2(as)k 421(hidden)s 1130(from)s 1654(the)s
2002(implementation)s 3559(in)s 3802(user)s 4260(calculations.)s 480 945(The)m
927(object)s 1591(abstraction)s 2715(of)s 3006(Lout)s 3537(is)s
3767(a)s 3952(direct)s 4575(descendant)s 5717(of)s 6008(the)s
6375(Eqn)s 6838(e)s 3(xpression.)k 8041(It)s 8266(emplo)s 2(ys)k
0 657(the)m 385(same)s 969(conte)s 3(xt-free)k 2212(recursi)s 6(v)k 3(e)k
3171(style)s 3715(of)s 4023(construction,)s 5350(and)s 5791(each)s
6323(object)s 7004(is)s 7251(treated)s 7995(by)s 8326(Lout)s
8876(as)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 3 4
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Times-Bold
%%+ font Symbol
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5770 -1579(-)m 5898(3)s
6062(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13253(a)m 166(rectangle:)s 1701 453 567 198 240 288 60 480 12460 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
1701 453 567 198 240 288 60 0 0 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
1701 453 567 198 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1701 453 567 198 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore

grestore

grestore
end end restore
grestore
end end restore
grestore
0 12007(The)m 442(horizontal)s
1481(axis,)s 1987(called)s 2630(a)s 240 fnt3 2810 12009(r)m 10(ow)k
3244(mark)s 240 fnt1 3814 12007(in)m 4072(Lout,)s 4645(has)s
5030(a)s 5210(v)s 3(ertical)k 5992(analogue)s 6926(called)s
7569(a)s 240 fnt3 7749 12009(column)m 8523(mark)s 240 fnt1
9019 12007(,)m 0 11719(creating)m 822(a)s 988(v)s 6(aluable)k
1848(symmetry)s 2857(between)s 3711(horizontal)s 4735(and)s 5139(v)s 3(ertical.)k
6014(Multiple)s 6893(column)s 7668(and)s 8072(ro)s 6(w)k
8491(marks)s 0 11431(are)m 347(permitted:)s 1984 1189 0 1189 240 288 60 480 9902 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
680 453 0 453 240 288 60 0 736 LoutGr2
currentdict end 200 dict begin begin
grestore
680 453 0 453 240 288 60 0 0 LoutGr2
/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(A) lfigpromotelabels
grestore
737 453 0 453 240 288 60 1247 736 LoutGr2
currentdict end 200 dict begin begin
grestore
567 453 0 453 240 288 60 0 0 LoutGr2
/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(B) lfigpromotelabels
grestore
680 453 0 453 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
396 453 0 453 240 288 60 0 0 LoutGr2
/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(C) lfigpromotelabels
grestore
737 453 0 453 240 288 60 1247 0 LoutGr2
currentdict end 200 dict begin begin
grestore
737 453 0 453 240 288 60 0 0 LoutGr2
/lfiggrey [ lfigbox ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(D) lfigpromotelabels
grestore
0 0 0 0 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ 0.3 cm 0 A@W lfigpsub lfigprevious /FROM lfigpointdef
B@W 1.6 cm 0 lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
0 0 0 0 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ 0.3 cm 0 C@W lfigpsub lfigprevious /FROM lfigpointdef
D@W 1.6 cm 0 lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
0 0 0 0 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ A@NW 0 0.3 cm lfigpadd lfigprevious /FROM lfigpointdef
0 0.3 cm C@SW lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
0 0 0 0 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ B@NW 0.3 cm 0.3 cm lfigpadd lfigprevious /FROM lfigpointdef
D@SW 0.3 cm -0.3 cm lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 9451(so)m 266(that)s
684(objects)s 1412(are)s 1759(able)s 2213(to)s 2452(represent)s
3387(tables.)s 480 9077(This)m 946(abstraction)s 2041(has)s 2401(some)s
2952(limitations,)s 4069(the)s 4407(most)s 4922(ob)s 3(vious)k
5719(being)s 6293(the)s 6631(restriction)s 7645(of)s 7906(size)s
8322(calcula)s 8998(-)s 0 8789(tions)m 507(to)s 736(rectangular)s
1860(bounding)s 2809(box)s 3(es.)k 3519(Non-)s 4000(rectangular)s
5124(and)s 5518(disconnected)s 6815(shapes)s 7494(arise)s 7990(naturally)s
8883(in)s 0 8501(\207gures)m 704(and)s 1111(in)s 1356(the)s
1707(characters)s 2727(of)s 3001(fonts;)s 3594(the)s 3944(e)s 3(xtension)k
4918(to)s 5159(them)s 5700(is)s 5912(conceptually)s 7191(straightforw)s 2(ard)k
8722(and)s 0 8213(might)m 615(help)s 1076(to)s 1311(e)s 3(xplain)k
2066(some)s 2623(\207ne)s 3034(points)s 3667(of)s 3934(layout)s
4588(such)s 5081(as)s 5327(k)s 2(erning.)k 6216(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k
7173(there)s 7702(are)s 8045(implemen)s 8998(-)s 0 7925(tation)m
599(and)s 1001(language)s 1918(design)s 2598(problems,)s 3592(particularly)s
4744(when)s 5317(\207lling)s 5939(non-)s 6367(rectangular)s 7498(shapes)s
8185(with)s 8664(te)s 3(xt,)k 0 7637(and)m 404(so)s
670(the)s 1018(author)s 1689(chose)s 2290(to)s 2529(k)s 2(eep)k
3032(to)s 3271(Eqn')s 13(s)k 3867(rectangles.)s 480 7263(A)m
766(more)s 1370(fundamental)s 2676(limitation)s 3718(of)s 4045(the)s
4450(object)s 5151(abstraction)s 6312(arises)s 6963(from)s 7543(the)s
7948(inability)s 8855(of)s 0 6975(recursi)m 6(v)k 3(e)k
936(data)s 1408(types)s 1978(to)s 2231(describe)s 3097(cross-link)s 2(ed)k
4335(structures,)s 5384(which)s 6040(seem)s 6605(to)s 6858(require)s
7604(some)s 8179(means)s 8855(of)s 0 6687(naming)m 756(the)s
1089(multiply)s 1938(referenced)s 2988(parts.)s 3601(Lout)s 4098(is)s
4293(obliged)s 5054(to)s 5278(introduce)s 6222(additional)s 7218(abstractions)s
8395(to)s 8618(cope)s 0 6399(with)m 490(cross)s 1040(linking:)s
1892(g)s 1(alle)k 3(ys)k 2624(for)s 2970(inserting)s
3867(te)s 3(xt)k 4291(into)s 4724(pages)s 5328(\(Section)s
6189(5.1\),)s 6683(cross)s 7233(references)s 8273(\(Section)s 0 6111(6.1\),)m
490(and)s 898(labelled)s 1716(points)s 2356(in)s 2603(\207gure)s
3221(dra)s 3(wing)k 4059([6].)s 4506(An)s 4860(abstraction)s
5969(closer)s 6603(to)s 6846(h)s 1(yperte)k 3(xt)k
7809(might)s 8431(form)s 8960(a)s 0 5823(more)m 547(uni\207ed)s
1270(basis)s 1799(for)s 2137(these)s 2684(features.)s 240 fnt2
0 5224(2.2.)m 471(Grammatical)s 1893(and)s 2334(lexical)s 3039(structur)s 4(e)k

[ /Dest /LOUTlexical /DEST pdfmark
240 fnt1 480 4792(If)m 700(objects)s 1418(are)s 1755(to)s
1984(be)s 2256(constructed)s 3406(lik)s 2(e)k 3807(mathematical)s
5138(e)s 3(xpressions,)k 6348(the)s 6686(natural)s 7394(notation)s
8225(is)s 8425(a)s 8580(func)s 8998(-)s 0 4504(tional)m
599(language)s 1519(based)s 2122(on)s 2419(operators,)s 3415(as)s
3665(in)s 3908(Eqn.)s 4458(The)s 4886(grammar)s 5808(of)s
6079(Lout)s 6591(objects)s 7319(is)s 7529(accordingly)s 240 fnt4
1332 3945(\256)m 1332 3612(\256)m 1332 3279(\256)m 1332 2995(\256)m 1332 2662(\256)m
1332 2368(\256)m 1332 2035(\256)m 1332 1751(\256)m 240 fnt3 480 3953(object)m
1826(object)s 2498(in\207xop)s 3227(object)s 1826 3620(pr)m 8(e\207xop)k
2680(object)s 1826 3287(object)m 2498(post\207xop)s 1826 3003(nopar)m 2(sop)k
1826 2670(liter)m 3(alwor)k 8(d)k 220 fnt5 1826 2371({)m
240 fnt3 1974 2376(object)m 220 fnt5 2646 2371(})m 240 fnt3
1826 2043(object)m 2498(object)s 240 fnt1 0 1248(where)m 240 fnt3
640 1250(in\207xop)m 240 fnt1 1285 1248(,)m 240 fnt3 1391 1250(pr)m 8(e\207xop)k
240 fnt1 2161 1248(,)m 240 fnt3 2267 1250(post\207xop)m 240 fnt1
3125 1248(,)m 3232(and)s 240 fnt3 3635 1250(nopar)m 2(sop)k
240 fnt1 4591 1248(are)m 4938(identi\207ers)s 5943(naming)s 6713(operators)s
7653(which)s 8294(tak)s 2(e)k 8745(0,)s 8971(1)s
0 960(or)m 255(2)s 424(parameters,)s 1573(as)s 1819(sho)s 6(wn,)k
2541(and)s 240 fnt3 2940 962(liter)m 3(alwor)k 8(d)k
240 fnt1 4067 960(is)m 4272(a)s 4433(sequence)s 5362(of)s
5628(non-space)s 6649(characters,)s 7719(or)s 7973(an)s 8251(arbitrary)s
0 672(sequence)m 969(of)s 1276(characters)s 2330(enclosed)s 3262(in)s
3541(double)s 4285(quotes.)s 5110(Ambiguities)s 6380(are)s 6763(resolv)s 3(ed)k
7664(by)s 7995(precedence)s 0 384(and)m 404(associati)s 6(vity)k 15(.)k

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 4 5
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5765 -1579(-)m 5893(4)s
6067(-)s 9066 13419 0 13310 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
480 13256(The)m 941(last)s 1366(production)s 2494(allo)s 6(ws)k
3197(a)s 3397(meaning)s 4307(for)s 4679(e)s 3(xpressions)k
5877(such)s 6407(as)s 220 fnt5 6691 13253({})m 240 fnt1
6828 13256(,)m 6968(in)s 7245(which)s 7921(an)s 8238(object)s
8916(is)s 0 12968(missing.)m 907(The)s 1333(v)s 6(alue)k
1899(of)s 2168(this)s 240 fnt3 2562 12970(empty)m 3187(object)s
240 fnt1 3833 12968(is)m 4041(a)s 4205(rectangle)s 5135(of)s
5404(size)s 5829(0)s 6002(by)s 6294(0,)s 6519(with)s
6999(one)s 7399(column)s 8172(mark)s 8722(and)s 0 12680(one)m
402(ro)s 6(w)k 822(mark,)s 1420(that)s 1838(prints)s
2433(as)s 2683(nothing.)s 480 12306(The)m 938(second-last)s 2103(production)s
3227(generates)s 4210(sequences)s 5261(of)s 5562(arbitrary)s 6467(objects)s
7225(separated)s 8215(by)s 8539(white)s 0 12018(space,)m 671(called)s
240 fnt3 1333 12020(par)m 3(a)k 2(gr)k 3(aphs)k
240 fnt1 2439 12018(.)m 2636(Ignoring)s 3547(paragraph)s 4593(breaking)s
5517(for)s 5888(no)s 6(w)k 15(,)k 6421(the)s
6802(natural)s 7554(meaning)s 8464(is)s 8708(that)s 0 11730(the)m
361(tw)s 2(o)k 784(objects)s 1525(should)s 2235(appear)s
2946(side)s 3400(by)s 3707(side,)s 4212(and)s 4629(Lout')s 13(s)k
5305(parser)s 5961(accordingly)s 7157(interpolates)s 8335(an)s 8632(in\207x)s
0 11442(horizontal)m 1017(concatenation)s 2395(operator)s 3244(\(see)s 3677(belo)s 6(w\))k
4377(between)s 5224(them.)s 5859(This)s 6328(operator)s 7177(is)s
7380(associati)s 6(v)k 3(e,)k 8519(so)s 8778(the)s
0 11154(grammatical)m 1262(ambiguity)s 2301(does)s 2806(no)s 3113(harm.)s
3783(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k
4758(the)s 5120(Algol-60)s 6054(rule)s 6496(that)s 6928(white)s
7530(space)s 8132(should)s 8844(be)s 0 10866(signi\207cant)m 1056(only)s
1536(as)s 1786(a)s 1952(separator)s 2887(is)s 3097(necessarily)s
4212(brok)s 2(en)k 4932(by)s 5226(Lout)s 5738(in)s
5981(just)s 6386(this)s 6782(one)s 7184(place.)s 480 10492(Algol-lik)m 2(e)k
1506(languages)s 2504(distinguish)s 3601(literal)s 4201(strings)s 4879(from)s
5393(identi\207ers)s 6389(by)s 6673(enclosing)s 7633(them)s 8161(in)s
8394(quotes,)s 0 10204(b)m 4(ut)k 372(literals)s 1082(are)s
1440(f)s 2(ar)k 1773(too)s 2143(frequent)s 3010(in)s
3264(document)s 4278(formatting)s 5350(for)s 5699(this)s 6106(to)s
6356(be)s 6649(viable.)s 7408(The)s 7847(con)s 9(v)k 3(entional)k
0 9916(solution)m 829(is)s 1041(to)s 1282(be)s 3(gin)k
1870(identi\207ers)s 2878(with)s 3362(a)s 3530(special)s 4250(character)s 9(,)k
5224(and)s 5630(Lout)s 6144(follo)s 6(ws)k 6908(Scribe)s
7576([7])s 7895(in)s 8140(using)s 8714(`@')s 0 9628(rather)m
616(than)s 1085(the)s 1433(`\\')s 1690(of)s 1961(trof)s 6(f)k
2450([8])s 2767(and)s 3171(T)s 3313 9580(E)m 3456 9628(X)m
3685([9].)s 480 9254(Ho)m 6(we)k 6(v)k 3(er)k 9(,)k
1447(Lout)s 1966(tak)s 2(es)k 2513(the)s 2868(unusual)s
3675(step)s 4120(of)s 4398(making)s 5176(an)s 5466(initial)s
6084(`@')s 6503(optional.)s 7458(The)s 7893(designers)s 8855(of)s
0 8966(Eqn)m 449(apparently)s 1519(considered)s 2620(such)s 3122(characters)s
4147(dis\207guring)s 5244(in)s 5494(\207ne-grained)s 6713(input)s 7272(lik)s 2(e)k
7691(equations,)s 8722(and)s 0 8678(this)m 401(author)s 1077(agrees.)s
1856(The)s 2289(implementation)s 3851(is)s 4066(straightforw)s 2(ard:)k
5707(`@')s 6124(is)s 6339(classed)s 7092(as)s 7347(just)s
7757(another)s 8539(letter)s 9(,)k 0 8390(and)m 407(e)s 6(v)k 3(ery)k
986(w)s 2(ord)k 1537(is)s 1750(searched)s 2647(for)s
2988(in)s 3234(the)s 3585(symbol)s 4348(table.)s 4979(If)s
5212(it)s 5407(is)s 5620(found,)s 6289(it)s 6484(is)s
6697(an)s 6983(identi\207er)s 9(,)k 7946(otherwise)s 8934(it)s
0 8102(is)m 214(a)s 384(literal.)s 1107(A)s 1341(w)s 2(arning)k
2181(message)s 3051(is)s 3265(printed)s 4004(when)s 4585(a)s
4755(literal)s 5369(be)s 3(ginning)k 6381(with)s 6867(`@')s
7284(is)s 7498(found,)s 8168(since)s 8719(it)s 8916(is)s
0 7814(probably)m 905(a)s 1071(mis-spelt)s 2006(identi\207er)s 13(.)k
3019(No)s 3365(such)s 3861(safety)s 4485(net)s 4837(is)s
5047(possible)s 5887(for)s 6225(identi\207ers)s 7231(without)s 8022(`@'.)s
480 7440(Equation)m 1418(formatting)s 2496(also)s 2951(demands)s 3871(symbols)s
4737(made)s 5328(from)s 5869(punctuation)s 7074(characters,)s 8165(such)s
8678(as)s 220 fnt5 8946 7437(+)m 240 fnt1 0 7152(and)m
220 fnt5 404 7149(<=)m 240 fnt1 652 7152(.)m 816(It)s
1021(is)s 1231(traditional)s 2267(to)s 2506(allo)s 6(w)k
3085(such)s 3581(symbols)s 4430(to)s 4669(be)s 4951(juxtaposed,)s
6095(which)s 6737(means)s 7399(that)s 7817(the)s 8165(input)s
220 fnt5 480 6702(<=++)m 240 fnt1 0 6251(for)m 354(e)s 3(xample)k
1234(must)s 1776(be)s 2075(interpreted)s 3184(within)s 3869(the)s
4234(le)s 3(xical)k 4939(analyser)s 5812(by)s 6123(searching)s
7109(the)s 7474(symbol)s 8251(table)s 8788(for)s 0 5963(its)m
306(pre\207x)s 3(es)k 1142(in)s 1416(the)s 1795(order)s
220 fnt5 2390 5960(<=++)m 240 fnt1 2894 5963(,)m 220 fnt5
3032 5960(<=+)m 240 fnt1 3408 5963(,)m 220 fnt5 3546 5960(<=)m
240 fnt1 3794 5963(.)m 3988(Although)s 4981(this)s 5408(tak)s 2(es)k
5979(quadratic)s 6952(time,)s 7514(in)s 7788(practice)s 8630(such)s
0 5675(sequences)m 1021(are)s 1368(too)s 1727(short)s 2265(to)s
2504(mak)s 2(e)k 3076(a)s 3242(more)s 3789(sophisticated)s
5095(linear)s 5698(method)s 6474(lik)s 2(e)k 6886(tries)s
7347(w)s 2(orthwhile.)k 240 fnt2 0 5026(2.3.)m 471(Basic)s
1073(structural)s 2149(operators)s 
[ /Dest /LOUTobjects /DEST pdfmark
240 fnt1 480 4549(A)m 696(programming)s
2036(language)s 2941(may)s 3393(be)s 3660(considered)s 4739(complete)s
5656(when)s 6218(it)s 6395(attains)s 7054(the)s 7388(po)s 6(wer)k
8025(of)s 8281(a)s 8432(T)s 10(uring)k 0 4261(machine,)m
917(b)s 4(ut)k 1280(no)s 1574(such)s 2071(criterion)s
2937(seems)s 3573(rele)s 6(v)k 6(ant)k 4390(to)s
4630(document)s 5635(formatting.)s 6808(Instead,)s 7606(as)s 7857(the)s
8206(language)s 0 3973(de)m 6(v)k 3(elops)k 913(and)s
1338(ne)s 6(w)k 1806(applications)s 3033(are)s 3401(attempted,)s
4471(de\207ciencies)s 5670(are)s 6038(e)s 3(xposed)k 6899(and)s
7324(the)s 7693(operator)s 8570(set)s 8916(is)s 0 3685(re)m 6(vised)k
742(to)s 981(o)s 3(v)k 3(ercome)k 1974(them.)s
480 3311(Lout)m 1025(has)s 1429(a)s 1629(repertoire)s 2646(of)s
2950(23)s 3268(primiti)s 6(v)k 3(e)k 4224(operators)s
5198(\(Figure)s 5990(1\),)s 6390(which)s 7066(has)s 7470(pro)s 3(v)k 3(en)k
8220(adequate)s 0 3023(for)m 348(a)s 525(wide)s 1056(v)s 6(ariety)k
1778(of)s 2059(features,)s 2932(including)s 3899(equations,)s 4934(tables,)s
5609(and)s 6023(page)s 6542(layout,)s 7257(and)s 7672(so)s
7948(seems)s 8594(to)s 8844(be)s 0 2735(reasonably)m 1077(complete)s
1995(in)s 2225(this)s 2607(pragmatic)s 3602(sense.)s 4270(In)s
4513(this)s 4895(section)s 5616(we)s 5937(introduce)s 6883(the)s
7217(eight)s 7741(concatenation)s 0 2447(and)m 424(mark-hiding)s 1680(operators.)s
2754(T)s 19(o)k 3075(them)s 3634(f)s 2(alls)k
4114(the)s 4482(basic)s 5047(task)s 5514(of)s 5806(assembling)s
6956(comple)s 3(x)k 7853(objects)s 8602(from)s 0 2159(simple)m
693(ones,)s 1239(and)s 1643(the)s 3(y)k 2106(were)s
2626(the)s 2974(\207rst)s 3405(to)s 3644(be)s 3926(designed)s
4835(and)s 5239(implemented.)s 480 1785(Man)m 3(y)k 1094(of)s
1370(the)s 1723(operators)s 2668(of)s 2944(Eqn)s 3392(can)s
3786(be)s 4073(vie)s 6(wed)k 4821(as)s 5076(b)s 4(uilding)k
5928(small)s 6505(tables.)s 7231(A)s 7466(b)s 4(uilt-up)k
8277(fraction,)s 0 1497(for)m 367(e)s 3(xample,)k 1310(has)s
1710(one)s 2141(column)s 2945(and)s 3379(three)s 3941(ro)s 6(ws)k
4480(\(numerator)s 9(,)k 5669(line,)s 6163(and)s 6596(denominator\).)s
8078(Numerous)s 0 1209(in)m 9(v)k 3(estig)k 1(ations)k
1377(of)s 1660(this)s 2068(kind)s 2564(con)s 9(vinced)k
3609(the)s 3969(author)s 4652(that)s 5082(operators)s 6034(capable)s
6832(of)s 7115(assembling)s 8256(the)s 8616(ro)s 6(ws)k
0 921(and)m 404(columns)s 1266(of)s 1537(tables)s 2145(w)s 2(ould)k
2800(suf\207ce)s 3493(for)s 3831(b)s 4(uilding)k 4678(all)s
4971(kinds)s 5541(of)s 5812(objects.)s 480 547(The)m 906(simplest)s
1759(objects)s 2485(are)s 2829(empty)s 3479(objects)s 4204(and)s
4605(literal)s 5213(w)s 2(ords)k 5844(lik)s 2(e)k
220 fnt5 6254 544(metempsychosis)m 240 fnt1 7882 547(,)m 7986(which)s
8625(ha)s 4(v)k 3(e)k 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 5 6
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5769 -1582(-)m 5897(5)s
6063(-)s 9066 13413 0 13413 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
240 fnt3 266 13217(object)m 220 fnt5 974 13212(/)m
240 fnt3 1038 13217(gap)m 1511(object)s 240 fnt1 3816 13215(V)m 26(ertical)k
4613(concatenation)s 5998(with)s 6480(mark)s 7032(alignment)s 240 fnt3
266 12929(object)m 220 fnt5 974 12924(//)m 240 fnt3 1099 12929(gap)m
1572(object)s 240 fnt1 3816 12927(V)m 26(ertical)k 4613(concatenation)s
5998(with)s 6480(left)s 6857(justi\207cation)s 240 fnt3 266 12641(object)m
220 fnt5 974 12636(|)m 240 fnt3 1011 12641(gap)m 1484(object)s
240 fnt1 3816 12639(Horizontal)m 4893(concatenation)s 6278(with)s 6760(mark)s
7312(alignment)s 240 fnt3 266 12353(object)m 220 fnt5 974 12348(||)m
240 fnt3 1068 12353(gap)m 1541(object)s 240 fnt1 3816 12351(Horizontal)m
4893(concatenation)s 6278(with)s 6760(top-justi\207cation)s 240 fnt3 266 12065(object)m
220 fnt5 974 12060(&)m 240 fnt3 1116 12065(gap)m 1589(object)s
240 fnt1 3816 12063(Horizontal)m 4893(concatenation)s 6278(within)s 6946(paragraphs)s
220 fnt5 266 11772(@OneCol)m 240 fnt3 1338 11777(object)m 240 fnt1
3816 11775(Hide)m 4337(all)s 4630(b)s 4(ut)k 4992(one)s
5394(column)s 6169(mark)s 6721(of)s 240 fnt3 6992 11777(object)m
220 fnt5 266 11484(@OneRo)m 3(w)k 240 fnt3 1457 11489(object)m
240 fnt1 3816 11487(Hide)m 4337(all)s 4630(b)s 4(ut)k
4992(one)s 5394(ro)s 6(w)k 5814(mark)s 6366(of)s
240 fnt3 6637 11489(object)m 266 11201(font)m 220 fnt5 762 11196(@F)m 6(ont)k
240 fnt3 1534 11201(object)m 240 fnt1 3816 11199(Render)m 240 fnt3
4567 11201(object)m 240 fnt1 5215 11199(in)m 5458(nominated)s 6526(font)s
240 fnt3 266 10913(br)m 8(eakstyle)k 220 fnt5 1353 10908(@Break)m
240 fnt3 2269 10913(object)m 240 fnt1 3816 10911(Break)m 4448(paragraphs)s
5548(of)s 240 fnt3 5819 10913(object)m 240 fnt1 6467 10911(in)m
6710(nominated)s 7778(style)s 240 fnt3 266 10625(spacestyle)m 220 fnt5
1361 10620(@Space)m 240 fnt3 2318 10625(object)m 240 fnt1 3816 10623(Render)m
4567(spaces)s 5242(between)s 6096(w)s 2(ords)k 6730(in)s
6973(nominated)s 8041(style)s 240 fnt3 266 10337(length)m 220 fnt5
979 10332(@Wide)m 240 fnt3 1813 10337(object)m 240 fnt1 3816 10335(Render)m
240 fnt3 4567 10337(object)m 240 fnt1 5215 10335(to)m 5454(width)s
240 fnt3 6056 10337(length)m 266 10049(length)m 220 fnt5 979 10044(@High)m
240 fnt3 1758 10049(object)m 240 fnt1 3816 10047(Render)m 240 fnt3
4567 10049(object)m 240 fnt1 5215 10047(to)m 5454(height)s 240 fnt3
6112 10049(length)m 220 fnt5 266 9756(@HExpand)m 240 fnt3 1499 9761(object)m
240 fnt1 3816 9759(Expand)m 4606(horizontal)s 5630(g)s 1(aps)k
6119(to)s 6358(\207ll)s 6678(a)s 4(v)k 6(ailable)k
7586(space)s 220 fnt5 266 9468(@VExpand)m 240 fnt3 1487 9473(object)m
240 fnt1 3816 9471(Expand)m 4606(v)s 3(ertical)k 5373(g)s 1(aps)k
5862(to)s 6101(\207ll)s 6421(a)s 4(v)k 6(ailable)k
7329(space)s 220 fnt5 266 9180(@HScale)m 240 fnt3 1307 9185(object)m
240 fnt1 3816 9183(Horizontal)m 4893(geometrical)s 6075(scaling)s 6805(to)s
7044(\207ll)s 7364(a)s 4(v)k 6(ailable)k 8272(space)s
220 fnt5 266 8892(@VScale)m 240 fnt3 1295 8897(object)m 240 fnt1
3816 8895(V)m 26(ertical)k 4613(geometrical)s 5795(scaling)s 6525(to)s
6764(\207ll)s 7084(a)s 4(v)k 6(ailable)k 7992(space)s
240 fnt3 266 8609(angle)m 220 fnt5 911 8604(@Rotate)m 240 fnt3
1892 8609(object)m 240 fnt1 3816 8607(Rotate)m 240 fnt3 4496 8609(object)m
240 fnt1 5144 8607(by)m 240 fnt3 5438 8609(angle)m 266 8321(P)m 19(ostScript)k
220 fnt5 1367 8316(@Gr)m 2(aphic)k 240 fnt3 2471 8321(object)m
240 fnt1 3816 8319(Escape)m 4549(to)s 4788(graphics)s 5649(language)s
220 fnt5 266 8028(@Ne)m 6(xt)k 240 fnt3 1050 8033(object)m
240 fnt1 3816 8031(Add)m 4287(1)s 4442(to)s 4681(an)s
4964(object)s 5608(denoting)s 6499(a)s 6665(number)s 240 fnt3
266 7745(object)m 220 fnt5 974 7740(@Case)m 240 fnt3 1821 7745(alternatives)m
240 fnt1 3816 7743(Select)m 4459(from)s 4983(a)s 5149(set)s
5474(of)s 5745(alternati)s 6(v)k 3(e)k 6799(objects)s
240 fnt3 266 7457(identi\207er)m 220 fnt5 1254 7452(&&)m 240 fnt3
1662 7457(object)m 240 fnt1 3816 7455(Cross)m 4412(reference)s 240 fnt3
266 7169(cr)m 10(oss-r)k 8(efer)k 8(ence)k 220 fnt5
1839 7164(@Open)m 240 fnt3 2705 7169(object)m 240 fnt1 3816 7167(Retrie)m 6(v)k 3(e)k
4672(v)s 6(alue)k 5240(from)s 5764(cross)s 6306(reference)s
240 fnt3 266 6881(cr)m 10(oss-r)k 8(efer)k 8(ence)k
220 fnt5 1839 6876(@T)m 26(agged)k 240 fnt3 2888 6881(object)m
240 fnt1 3816 6879(Attach)m 4510(cross)s 5052(referencing)s 6192(tag)s
6537(to)s 6776(object)s 
[ /Dest /LOUTprimitives /DEST pdfmark
200 fnt2 1346 6226(Figur)m 3(e)k
1954(1.)s 200 fnt1 2196 6227(The)m 2552(23)s 2789(primiti)s 5(v)k 3(e)k
3556(operators)s 4338(of)s 4564(Lout,)s 5030(in)s 5232(order)s
5702(of)s 5928(increasing)s 6789(precedence.)s 240 fnt1 0 5596(one)m
402(column)s 1177(mark)s 1729(and)s 2133(one)s 2535(ro)s 6(w)k
2955(mark:)s 1572 215 0 106 240 288 60 480 5090 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
1572 215 0 106 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1572 215 0 106 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 52(metempsychosis)m 
grestore

grestore
end end restore
grestore
0 4639(T)m 19(o)k 337(place)s
934(tw)s 2(o)k 1381(arbitrary)s 2294(objects)s 3059(side)s
3537(by)s 3868(side,)s 4398(we)s 4770(use)s 5182(the)s
5567(in\207x)s 6099(operator)s 220 fnt5 6992 4636(|)m 240 fnt1
7029 4639(,)m 7173(denoting)s 8102(horizontal)s 0 4351(concatenation.)m 1492(F)s 3(or)k
1881(e)s 3(xample,)k 220 fnt5 480 3850(USA  |0.2i  A)m 6(ustr)k 2(alia)k
240 fnt1 0 3395(produces)m 915(the)s 1263(object)s 476 166 0 57 240 288 60 480 2889 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
476 165 0 57 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
476 165 0 57 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 3(USA)m

grestore

grestore
end end restore
grestore
875 166 0 57 240 288 60 1244 2889 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
875 165 0 56 240 288 60 0 1 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
875 165 0 56 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 2(Australia)m 
grestore

grestore
end end restore
grestore
0 2438(The)m 443(ro)s 6(w)k 879(marks)s
1529(are)s 1892(mer)s 4(ged)k 2678(into)s 3119(one,)s
3587(\207xing)s 4215(the)s 4579(v)s 3(ertical)k 5361(position)s
6205(of)s 6491(the)s 6855(objects)s 7598(relati)s 6(v)k 3(e)k
8376(to)s 8631(each)s 0 2150(other;)m 611(their)s 1116(horizontal)s
2148(separation)s 3196(is)s 3414(determined)s 4555(by)s 4857(the)s
240 fnt3 5214 2152(gap)m 240 fnt1 5635 2150(attached)m 6497(to)s
6744(the)s 7101(operator)s 9(,)k 8003(in)s 8254(this)s
8659(case)s 0 1862(0.2)m 361(inches.)s 1143(W)s 19(e)k
1519(think)s 2080(of)s 2358(the)s 2713(g)s 1(ap)k
3118(as)s 3376(part)s 3814(of)s 4092(the)s 4448(operator)s 9(,)k
5349(although)s 6251(strictly)s 6974(it)s 7174(is)s 7391(a)s
7564(third)s 8081(parameter)s 13(.)k 0 1574(It)m 205(may)s
671(be)s 953(omitted,)s 1790(def)s 2(aulting)k 2810(to)s
220 fnt5 3049 1571(0i)m 240 fnt1 3205 1574(.)m 240 fnt3
480 1202(V)m 26(ertical)k 1294(concatenation)s 240 fnt1 2644 1200(,)m
2762(denoted)s 3590(by)s 3895(the)s 4254(in\207x)s 4760(operator)s
220 fnt5 5627 1197(/)m 240 fnt1 5691 1200(,)m 5809(is)s
6031(the)s 6390(same)s 6948(apart)s 7497(from)s 8032(the)s
8392(change)s 0 912(of)m 271(direction:)s 220 fnt5 480 461(A)m 6(ustr)k 2(alia  /0.1i  USA)k

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 6 7
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5765 -1581(-)m 5893(6)s
6066(-)s 9066 13414 0 13305 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13251(produces)m 915(the)s 1263(object)s 875 165 0 56 240 288 60 480 12746 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
875 165 0 56 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
875 165 0 56 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 2(Australia)m

grestore

grestore
end end restore
grestore
875 165 0 57 240 288 60 480 12437 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
476 165 0 57 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
476 165 0 57 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 3(USA)m 
grestore

grestore
end end restore
grestore
0 11986(with)m 482(column)s 1257(marks)s 1892(mer)s 4(ged)k
2663(and)s 3067(a)s 3233(0.1)s 3568(inch)s 4037(g)s 1(ap.)k
480 11612(Consider)m 1404(no)s 6(w)k 1865(what)s 2390(happens)s
3226(when)s 3802(horizontal)s 4826(and)s 5230(v)s 3(ertical)k
5997(are)s 6344(combined:)s 220 fnt5 1000 11111({)m 1186(USA)s
2442(|0.2i)s 2958(A)s 6(ustr)k 2(alia)k 3919(})s
480 10823(/0.1i)m 1000({)s 1186(W)s 8(ashington)k 2442(|)s
2958(Canberr)s 2(a)k 3987(})s 240 fnt1 0 10324(The)m
445(tw)s 2(o)k 872(parameters)s 1987(of)s 220 fnt5
2275 10321(/)m 240 fnt1 2416 10324(no)m 6(w)k 2895(ha)s 4(v)k 3(e)k
3413(tw)s 2(o)k 3840(column)s 4632(marks)s 5284(each,)s
5846(and)s 6268(the)s 3(y)k 6748(will)s 7191(be)s
7490(mer)s 4(ged)k 8278(with)s 8778(the)s 0 10036(corresponding)m
1422(marks)s 2057(in)s 2300(the)s 2648(other)s 3199(parameter)s 9(,)k
4251(yielding)s 5088(the)s 5436(object)s 476 166 0 57 240 288 60 480 9530 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
476 165 0 57 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
476 165 0 57 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 3(USA)m 
grestore

grestore
end end restore
grestore
659 166 0 57 240 288 60 956 9530 LoutGr2
0 ymark moveto xsize 10 pt add ymark lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
876 166 0 57 240 288 60 1903 9530 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
875 165 0 56 240 288 60 0 1 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
875 165 0 56 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 2(Australia)m

grestore

grestore
end end restore
grestore
1135 215 0 106 240 288 60 480 9171 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
1135 215 0 106 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1135 215 0 106 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 52(W)m 19(ashington)k 
grestore

grestore
end end restore
grestore
876 215 0 106 240 288 60 1903 9171 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
876 166 0 57 240 288 60 0 49 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
876 166 0 57 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 3(Canberra)m 
grestore

grestore
end end restore
grestore
0 8720(The)m 220 fnt5
425 8717(0.2i)m 240 fnt1 821 8720(g)m 1(ap)k 1216(separates)s
2139(columns,)s 3054(not)s 3416(indi)s 6(vidual)k 4432(items)s
4997(in)s 5237(columns,)s 6152(so)s 6414(a)s 6577(g)s 1(ap)k
6972(attached)s 7823(to)s 8059(the)s 8403(second)s 220 fnt5
0 8429(|)m 240 fnt1 96 8432(w)m 2(ould)k 749(serv)s 3(e)k
1304(no)s 1595(purpose;)s 2464(an)s 3(y)k 2859(such)s
3353(g)s 1(ap)k 3749(is)s 3957(ignored.)s 4851(If)s
5079(the)s 5425(number)s 6214(of)s 6484(marks)s 7117(to)s
7354(be)s 7634(mer)s 4(ged)k 8403(dif)s 6(fers,)k
0 8144(empty)m 638(columns)s 1485(are)s 1818(added)s 2433(at)s
2651(the)s 2984(right)s 3481(to)s 3705(equalize)s 4542(the)s
4876(number)s 13(.)k 5743(The)s 6157(four)s 6600(marks)s
7221(protruding)s 8269(from)s 8778(the)s 0 7856(result)m 601(are)s
959(all)s 1263(a)s 4(v)k 6(ailable)k 2182(for)s
2531(mer)s 4(ging)k 3389(with)s 3882(neighbouring)s 5223(marks)s
5869(by)s 6174(other)s 6736(concatenation)s 8133(operators.)s 0 7568(The)m
428(precedence)s 1559(of)s 220 fnt5 1830 7565(|)m 240 fnt1
1927 7568(is)m 2137(higher)s 2808(than)s 3277(the)s 3625(precedence)s
4756(of)s 220 fnt5 5027 7565(/)m 240 fnt1 5091 7568(,)m
5198(so)s 5464(the)s 5812(braces)s 6473(could)s 7063(be)s
7345(omitted.)s 480 7194(When)m 1131(lines)s 1656(of)s 1950(te)s 3(xt)k
2387(are)s 2757(concatenated,)s 4135(it)s 4349(is)s 4582(con)s 9(v)k 3(entional)k
5884(to)s 6145(measure)s 7020(their)s 7540(separation)s 8602(from)s
0 6906(baseline)m 832(to)s 1063(baseline)s 1894(\(mark)s 2517(to)s
2748(mark)s 3292(in)s 3527(Lout\),)s 4157(rather)s 4765(than)s
5226(from)s 5742(edge)s 6242(to)s 6473(edge)s 6973(as)s
7215(abo)s 3(v)k 3(e.)k 7937(This)s 8405(idea)s
8855(of)s 0 6618(dif)m 6(ferent)k 863(reference)s 1794(points)s
2417(for)s 2743(measurement)s 4065(e)s 6(v)k 4(olv)k 3(ed)k
4855(o)s 3(v)k 3(er)k 5322(the)s 5658(years)s
6200(into)s 6613(a)s 6767(system)s 7478(of)s 7737(six)s
240 fnt3 8059 6620(gap)m 8459(modes)s 240 fnt1 0 6330(\(Figure)m
769(2\),)s 1085(e)s 3(xpressed)k 2094(by)s 2398(appending)s
3460(a)s 3636(letter)s 4195(to)s 4445(the)s 4803(length.)s
5576(F)s 3(or)k 5975(e)s 3(xample,)k 220 fnt5
6899 6327(|0.2i)m 240 fnt1 7366 6330(is)m 7586(an)s 7880(abbre)s 6(viation)k
0 6042(for)m 220 fnt5 377 6039(|0.2ie)m 240 fnt1 901 6042(,)m
1047(meaning)s 1963(0.2)s 2356(inches)s 3057(measured)s 4070(from)s
4633(edge)s 5180(to)s 5458(edge;)s 220 fnt5 6061 6039(|0.3ix)m
240 fnt1 6678 6042(produces)m 7632(a)s 7837(0.3)s 8220(inch)s
8728(g)s 1(ap)k 0 5754(measured)m 972(from)s 1493(mark)s
2043(to)s 2279(mark)s 2829(and)s 3230(widened)s 4097(if)s
4311(necessary)s 5292(to)s 5528(pre)s 6(v)k 3(ent)k
6294(o)s 3(v)k 3(erstriking;)k 7552(and)s 220 fnt5
7954 5751(|2.5it)m 240 fnt1 8478 5754(places)m 0 5466(its)m 273(right)s
781(parameter)s 1792(2.5)s 2135(inches)s 2794(from)s 3314(the)s
3659(current)s 4392(left)s 4766(mar)s 4(gin,)k 5543(irrespecti)s 6(v)k 3(e)k
6699(of)s 6967(the)s 7312(position)s 8137(of)s 8405(the)s
8749(left)s 0 5178(parameter)m 13(.)k 1098(There)s 1704(is)s
1907(also)s 2338(a)s 2496(choice)s 3169(of)s 3433(ele)s 6(v)k 3(en)k
4098(units)s 4606(of)s 4870(measurement)s 6197(\(inches,)s 6987(centimetres,)s
8186(multiples)s 0 4890(of)m 288(the)s 654(current)s 1407(font)s
1870(size,)s 2365(etc.\),)s 2907(the)s 3272(most)s 3815(interesting)s
4894(being)s 5496(the)s 220 fnt5 5862 4887(r)m 240 fnt1
6012 4890(unit:)m 6568(one)s 220 fnt5 6987 4887(r)m 240 fnt1
7138 4890(is)m 7365(the)s 7731(column)s 8524(width)s 0 4602(minus)m
635(the)s 982(width)s 1583(of)s 1852(the)s 2199(follo)s 6(wing)k
3175(object,)s 3864(so)s 4129(that)s 220 fnt5 4546 4599(|1r)m -8(t)k
240 fnt1 4921 4602(produces)m 5835(suf\207cient)s 6783(space)s 7368(to)s
7606(right)s 8116(justify)s 8778(the)s 0 4314(follo)m 6(wing)k
987(object,)s 1688(and)s 220 fnt5 2103 4311(|0.5r)m -8(t)k
240 fnt1 2673 4314(to)m 2923(center)s 3576(it.)s 3883(These)s
4520(features)s 5337(implement)s 6429(spacings)s 7315(needed)s 8061(in)s
8315(practice)s 0 4026(rather)m 608(than)s 1069(suggested)s 2063(by)s
2349(theory)s 15(.)k 3101(The)s 3(y)k 3636(w)s 2(ork)k
4179(with)s 4653(all)s 4938(\207v)s 3(e)k 5342(concatenation)s
6719(operators,)s 7707(horizontal)s 8722(and)s 0 3738(v)m 3(ertical.)k
480 3364(When)m 1113(we)s 1452(construct)s 2392(a)s 2562(b)s 4(uilt-up)k
3372(fraction,)s 4225(the)s 4577(result)s 5171(has)s 5545(three)s
6082(ro)s 6(w)k 6506(marks,)s 7201(b)s 4(ut)k
7567(only)s 8051(the)s 8403(second)s 0 3076(should)m 697(be)s
979(visible)s 1672(outside)s 2419(the)s 2767(object:)s gsave
480 2245 translate
240 fnt3
156 491 0 288 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
156 491 0 288 240 288 12 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
156 491 0 288 240 288 12 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
0 336(X)m 156 0 0 0 240 288 12 0 288 LoutGr2
0 0 moveto xsize 0 lineto 0.05 ft setlinewidth stroke
grestore

grestore
2 68(Y)m 
grestore

grestore
end end restore
grestore
0 1794(This)m 493(is)s 721(a)s
905(common)s 1817(problem,)s 2739(and)s 3161(accordingly)s 4361(a)s
220 fnt5 4545 1791(@OneRo)m 3(w)k 240 fnt1 5694 1794(operator)m
6567(w)s 2(as)k 7006(introduced)s 8105(for)s 8461(hiding)s
0 1506(all)m 291(b)s 4(ut)k 650(one)s 1050(of)s
1318(the)s 1663(ro)s 6(w)k 2081(marks)s 2713(of)s
2981(its)s 3255(parameter)s 13(.)k 4357(Normally)s 15(,)k
5363(the)s 5708(\207rst)s 6136(mark)s 6686(is)s 6893(the)s
7238(survi)s 6(v)k 4(or)k 9(,)k 8121(b)s 4(ut)k
8480(a)s 8643(later)s 0 1218(mark)m 552(can)s 941(be)s
1223(chosen)s 1945(by)s 2239(pre\207xing)s 220 fnt5 3156 1215(^)m
240 fnt1 3322 1218(to)m 3561(the)s 3909(preceding)s 4905(concatenation)s
6290(operator:)s 220 fnt5 480 717(@OneRo)m 3(w { X  ^/2p  @HLine  /2p  )k 19(Y })k

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 7 8
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
%%+ font Symbol
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5768 -1575(-)m 5896(7)s
6064(-)s 9066 13422 0 13422 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
6693 8221 0 8221 240 288 60 1186 5201 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
0 7447(Edge-to-edge)m 220 fnt5 1786 7444(|)m 240 fnt3
1843 7449(length)m 220 fnt5 2456 7444(e)m 240 fnt1 0 6238(Hyphenation)m
220 fnt5 1786 6235(|)m 240 fnt3 1843 6240(length)m 220 fnt5
2456 6235(h)m 240 fnt1 0 5029(Ov)m 3(erstrik)k 2(e)k
220 fnt5 1786 5026(|)m 240 fnt3 1843 5031(length)m 220 fnt5
2456 5026(o)m 240 fnt1 0 3820(Mark-to-mark)m 220 fnt5 1786 3817(|)m
240 fnt3 1843 3822(length)m 220 fnt5 2456 3817(x)m 240 fnt1
0 2611(K)m 6(erning)k 220 fnt5 1786 2608(|)m 240 fnt3
1843 2613(length)m 220 fnt5 2456 2608(k)m 240 fnt1 0 1402(T)m 19(ab)k 4(ulation)k
220 fnt5 1786 1399(|)m 240 fnt3 1843 1404(length)m 220 fnt5
2456 1399(t)m gsave
3291 0 translate
240 fnt1 3402 8221 0 8221 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
567 7485 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
680 7371 translate
180 fnt1 2722 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 7485 translate
180 fnt1
680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
2551 7371 translate
180 fnt1 851 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2267 7394 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 1020 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
1247 7394 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1
68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
1247 7394 translate
180 fnt1 1020 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
1247 7394 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
180 fnt3 1534 7192(length)m gsave
567 6304 translate
180 fnt1
680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
680 6190 translate
180 fnt1 2722 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 6304 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
2551 6190 translate
180 fnt1 851 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2267 6213 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1
1020 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
1247 6213 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
1247 6213 translate
180 fnt1 1020 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
1247 6213 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
1534 6011(length)m
gsave
567 5123 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
680 5009 translate
180 fnt1 2722 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 5123 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
2551 5009 translate
180 fnt1 851 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2551 4975 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1
68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 1871 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
680 4975 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
680 4975 translate
180 fnt1 1871 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
680 4975 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1
68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
1392 4774(length)m gsave
567 3886 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
680 3772 translate
180 fnt1 2722 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 3886 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
2551 3772 translate
180 fnt1
851 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2551 3738 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 1871 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
680 3738 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
680 3738 translate
180 fnt1
1871 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
680 3738 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
180 fnt1 941 3536(max)m 180 fnt4 1256 3531(\()m
180 fnt3 1319 3537(length)m 180 fnt4 1774 3531(,)m 180 fnt3
1854 3537(a)m 180 fnt4 1994 3531(+)m 180 fnt3 2145 3537(b)m
180 fnt4 2240 3531(\))m gsave
1247 4362 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 567 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1
68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
680 4362 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
680 4362 translate
180 fnt1 567 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
680 4362 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
180 fnt3 920 4431(a)m
gsave
2551 4362 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 283 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
2268 4362 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
2268 4362 translate
180 fnt1
283 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
2268 4362 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
2366 4387(b)m gsave
567 2590 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
680 2476 translate
180 fnt1 2722 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 2590 translate
180 fnt1
680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
2551 2476 translate
180 fnt1 851 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2551 2442 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 1871 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
680 2442 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1
68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
680 2442 translate
180 fnt1 1871 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
680 2442 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
180 fnt1 999 2240(max)m 180 fnt4
1314 2235(\()m 180 fnt3 1377 2241(length)m 180 fnt4 1832 2235(,)m
180 fnt3 1912 2241(a)m 180 fnt4 2007 2235(,)m 180 fnt3
2087 2241(b)m 180 fnt4 2182 2235(\))m gsave
1247 3066 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1
567 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
680 3066 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
680 3066 translate
180 fnt1 567 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
680 3066 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
180 fnt3
920 3135(a)m gsave
2551 3066 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 283 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
2268 3066 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1
68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
2268 3066 translate
180 fnt1 283 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
2268 3066 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
2366 3091(b)m gsave
567 1438 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
680 1324 translate
180 fnt1
2722 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 1438 translate
180 fnt1 680 340 0 340 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto
xsize ysize lineto 0 ysize lineto closepath
gsave 0.9 setgray fill grestore stroke
grestore

grestore
gsave
2551 1324 translate
180 fnt1 851 567 0 567 180 288 45 LoutGraphic
gsave
0 0 moveto 0 ysize lineto [ 3 pt ] 0 setdash stroke
grestore

grestore
gsave
2268 1233 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 2268 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1
68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
0 1233 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 1233 translate
180 fnt1 2268 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 1233 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
1587 1032(length)m gsave
3402 734 translate
180.0000 rotate
gsave
0 0 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1
68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 0 translate
180 fnt1 3402 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 0 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1 68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore

grestore
gsave
0 734 translate
30.0000 rotate
gsave
0 1 translate
180 fnt1 68 -1 0 -1 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
gsave
0 734 translate
180 fnt1 3402 0 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
gsave
0 734 translate
-30.0000 rotate
gsave
0 0 translate
180 fnt1
68 -1 0 0 180 288 45 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore

grestore
1189 522(curr)m 6(ent)k 1759(bound)s 
grestore
end end restore
grestore

[ /Dest /LOUTgapmodes /DEST pdfmark
200 fnt2 180 4638(Figur)m 3(e)k
788(2.)s 200 fnt1 1030 4639(The)m 1386(six)s 1664(g)s 1(ap)k
1995(modes)s 2557(\()s 200 fnt3 2618 4640(length)m 200 fnt1
3162 4639(is)m 3336(an)s 3(y)k 3666(length\).)s 4367(Hyphenation)s
5444(mode)s 5933(has)s 6240(an)s 6475(e)s 3(xtra)k
6919(property)s 7639(not)s 7944(sho)s 5(wn)k 8507(here.)s
240 fnt1 0 4008(has)m 396(the)s 770(desired)s 1545(result,)s
2208(where)s 220 fnt5 2874 4005(2p)m 240 fnt1 3197 4008(is)m
3433(tw)s 2(o)k 3870(points)s 4532(and)s 220 fnt5
4962 4005(@HLine)m 240 fnt1 5836 4008(is)m 6072(an)s 6381(easy)s
6887(combination)s 8166(of)s 8464(Lout')s 13(s)k 0 3720(graphics)m
861(operators.)s 1914(A)s 2144(similar)s 2866(operator)s 9(,)k
220 fnt5 3760 3717(@OneCol)m 240 fnt1 4712 3720(,)m 4819(hides)s
5375(column)s 6150(marks.)s 480 3346(A)m 728(v)s 6(ariant)k
1463(of)s 220 fnt5 1753 3343(/)m 240 fnt1 1895 3346(called)m
220 fnt5 2542 3343(//)m 240 fnt1 2745 3346(is)m 2974(pro)s 3(vided)k
3898(which)s 4558(performs)s 5490(v)s 3(ertical)k 6275(concatenation)s
7679(b)s 4(ut)k 8059(ignores)s 8833(all)s 0 3058(column)m
775(marks)s 1410(and)s 1814(simply)s 2519(left-justi\207es)s 3709(its)s
3985(tw)s 2(o)k 4395(parameters:)s 220 fnt5 480 2557(Heading  //0.1i)m
480 2269(A  |0.2i  B  /0.1i)m 480 1981(C  |  D)m 240 fnt1 0 1526(has)m 370(result)s
480 1073(Heading)m 480 716(A)m 938(B)s 480 410(C)m 938(D)s

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 8 9
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Bold
%%+ font Times-Italic
%%+ font Symbol
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5768 -1579(-)m 5896(8)s
6063(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13253(sho)m 6(wing)k 883(that)s 1325(spanning)s
2267(columns)s 3153(in)s 3420(tables)s 4052(moti)s 6(v)k 6(ate)k
4956(the)s 5328(inclusion)s 6286(of)s 6581(this)s 7001(operator)s 13(.)k
7972(There)s 8609(is)s 8843(an)s 0 12965(analogous)m 220 fnt5
1029 12962(||)m 240 fnt1 1191 12965(operator)m 13(.)k 2145(The)s
2581(author)s 3259(w)s 2(ould)k 3922(ha)s 4(v)k 3(e)k
4430(preferred)s 5370(to)s 5616(lea)s 4(v)k 3(e)k
6177(out)s 6550(these)s 7105(operators,)s 8108(since)s 8663(the)s 3(y)k
0 12677(complicate)m 1104(the)s 1452(implementation,)s 3059(and)s 3463(it)s
3655(is)s 3865(interesting)s 4926(to)s 5165(e)s 3(xamine)k
6028(the)s 6376(prospects)s 7330(of)s 7601(doing)s 8200(so.)s
480 12303(The)m 220 fnt5 953 12300(//)m 240 fnt1 1184 12303(operator)m
2086(is)s 2342(formally)s 3263(redundant,)s 4373(because)s 5232(in)s
5521(general)s 6324(the)s 6718(e)s 3(xpression)k 220 fnt5
7841 12300(x // y)m 240 fnt1 8409 12303(can)m 8844(be)s 0 12015(replaced)m
867(by)s 220 fnt5 480 11514(@OneCol {  |  x  }   /)m 480 11226(@OneCol {  |  y  })m 240 fnt1
0 10728(for)m 338(an)s 3(y)k 734(objects)s 220 fnt5
1462 10725(x)m 240 fnt1 1629 10728(and)m 220 fnt5 2032 10725(y)m
240 fnt1 2140 10728(.)m 2304(By)s 2637(concatenating)s 4017(an)s
4300(empty)s 4951(object)s 5594(at)s 5826(the)s 6173(left)s
6549(of)s 220 fnt5 6820 10725(x)m 240 fnt1 6987 10728(and)m
7390(hiding)s 8055(all)s 8347(b)s 4(ut)k 8708(that)s
0 10440(empty)m 641(object')s 13(s)k 1423(column)s 2186(mark,)s
2772(we)s 3095(ef)s 6(fecti)k 6(v)k 3(ely)k
4143(shift)s 220 fnt5 4615 10437(x)m 240 fnt1 4723 10440(')m 13(s)k
4921(column)s 5684(mark)s 6224(to)s 6452(its)s 6716(left)s
7081(edge.)s 7685(The)s 8101(same)s 8636(goes)s 0 10152(for)m
220 fnt5 349 10149(y)m 240 fnt1 457 10152(,)m 575(so)s
852(the)s 220 fnt5 1211 10149(/)m 240 fnt1 1347 10152(operator)m
2214(has)s 2595(just)s 3011(one)s 3424(column)s 4211(mark)s
4774(to)s 5024(mer)s 4(ge,)k 5735(at)s 5978(the)s
6338(e)s 3(xtreme)k 7171(left,)s 7606(and)s 8021(its)s
8308(ef)s 6(fect)k 8916(is)s 0 9864(indistinguishable)m 1690(from)s
220 fnt5 2214 9861(//)m 240 fnt1 2339 9864(.)m 480 9490(Unfortunately)m 15(,)k
1915(if)s 220 fnt5 2134 9487(y)m 240 fnt1 2304 9490(consists)m
3114(of)s 3387(tw)s 2(o)k 3799(ro)s 6(ws)k
4311(separated)s 5274(by)s 220 fnt5 5570 9487(/)m 240 fnt1
5634 9490(,)m 5743(as)s 5995(in)s 6240(the)s 6590(e)s 3(xample)k
7455(abo)s 3(v)k 3(e,)k 8130(both)s 8616(ro)s 6(ws)k
0 9202(must)m 533(be)s 823(placed)s 1513(inside)s 2148(the)s
220 fnt5 2504 9199(@OneCol)m 240 fnt1 3456 9202(,)m 3571(and)s
3983(the)s 4340(table)s 4868(cannot)s 5574(be)s 5864(entered)s
6633(in)s 6884(the)s 7240(simple)s 7942(ro)s 6(w-by-ro)k 6(w)k
0 8914(manner)m 777(that)s 1194(non-e)s 3(xpert)k 2287(users)s
2828(naturally)s 3731(e)s 3(xpect.)k 4515(Another)s 5359(adv)s 6(antage)k
6378(of)s 220 fnt5 6649 8911(//)m 240 fnt1 6833 8914(is)m
7043(that)s 7460(its)s 7736(left)s 8112(parameter)s 0 8626(can)m
382(be)s 657(printed)s 1385(before)s 2044(its)s 2313(right)s
2817(parameter)s 3824(is)s 4027(kno)s 6(wn;)k 4779(this)s
5168(is)s 5371(important)s 6353(when)s 6922(the)s 7263(left)s
7633(parameter)s 8640(is)s 8843(an)s 0 8338(entire)m 599(page.)s
480 7964(The)m 960(\207fth)s 1468(and)s 1924(\207nal)s 2457(concatenation)s
3895(operator)s 9(,)k 220 fnt5 4841 7961(&)m 240 fnt1
4983 7964(,)m 5143(is)s 5405(an)s 5741(e)s 3(xplicit)k
6567(v)s 3(ersion)k 7377(of)s 7701(the)s 8102(horizontal)s
0 7676(concatenation)m 1402(operator)s 2275(interpolated)s 3492(when)s 4085(objects)s
4830(are)s 5195(separated)s 6172(by)s 6483(white)s 7088(space.)s
7800(It)s 8022(is)s 8250(formally)s 0 7388(identical)m 907(to)s
220 fnt5 1177 7385(|)m 240 fnt1 1305 7388(e)m 3(xcept)k
2017(for)s 2386(taking)s 3068(higher)s 3770(precedence)s 4932(and)s
5367(being)s 5983(subject)s 6751(to)s 7021(replacement)s 8279(by)s
220 fnt5 8604 7385(//1vx)m 240 fnt1 0 7100(during)m 678(paragraph)s
1691(breaking)s 2581(\(Section)s 3434(2.5\).)s 240 fnt2 0 6451(2.4.)m
471(Implementation)s 2159(of)s 2431(objects)s 3201(and)s 3642(concatenation)s

[ /Dest /LOUTobjects_impl /DEST pdfmark
240 fnt1 480 5974(In)m 738(this)s 1136(section)s 1872(we)s
2210(discuss)s 2954(the)s 3304(implementation)s 4863(of)s 5137(objects)s
5867(and)s 6273(concatenation,)s 7710(and)s 8117(especially)s 0 5686(mark)m
552(alignment.)s 1672(The)s 2100(\207rst)s 2531(step)s 2969(is)s
3179(to)s 3418(use)s 3793(an)s 4076(operator)s 4932(precedence)s
6063(parser)s 6706(to)s 6945(con)s 9(v)k 3(ert)k
7710(input)s 8262(such)s 8758(as)s 220 fnt5 480 5185(a  |0.5i  b  /0.2i  c  |  d)m
240 fnt1 0 4730(into)m 425(parse)s 985(trees)s 1486(such)s
1982(as)s gsave
480 3036 translate
240 fnt3 3396 1354 0 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1867 338 56 282 240 288 12 1529 1016 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 136 106(\244)m 
grestore
(T) lfigpromotelabels
grestore
1413 846 0 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
876 338 56 282 240 288 12 537 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4
156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
511 338 56 282 240 288 12 451 0 LoutGr2
currentdict end 200 dict begin begin
grestore
511 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
511 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt4 56 105(0)m
192 fnt3 195 111(.)m 192 fnt4 270 105(5)m 192 fnt3
404 111(i)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 962 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 1075 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1413 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1413 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
517 846 56 790 240 288 12 1526 0 LoutGr2
currentdict end 200 dict begin begin
grestore
517 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
517 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt4 56 105(0)m
192 fnt3 195 111(.)m 192 fnt4 270 105(2)m 192 fnt3
410 111(i)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 2043 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1240 846 0 790 240 288 12 2156 0 LoutGr2
currentdict end 200 dict begin begin
grestore
789 338 56 282 240 288 12 451 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 451 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 789 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 902 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1240 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3396 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 2585(Missing)m 879(objects)s 1662(are)s
2065(replaced)s 2987(by)s 3336(empty)s 4044(objects,)s 4883(and)s
5342(sequences)s 6419(of)s 6745(concatenation)s 8186(operators)s 0 2297(are)m
347(consolidated:)s gsave
480 648 translate
240 fnt3 2492 1359 0 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1415 338 56 282 240 288 12 1077 1016 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
517 846 56 790 240 288 12 451 0 LoutGr2
currentdict end 200 dict begin begin
grestore
517 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
517 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt4 56 105(0)m 192 fnt3 195 111(.)m
192 fnt4 270 105(2)m 192 fnt3 410 111(i)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 968 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1411 846 0 790 240 288 12 1081 0 LoutGr2
currentdict end 200 dict begin begin
grestore
875 338 56 282 240 288 12 536 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4
156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
509 338 56 282 240 288 12 451 0 LoutGr2
currentdict end 200 dict begin begin
grestore
509 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
509 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt4 56 105(0)m
192 fnt3 195 111(.)m 192 fnt4 270 105(3)m 192 fnt3
402 111(i)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 960 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 1073 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1411 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 2492 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
240 fnt4 3284 1886(\336)m
gsave
3825 648 translate
240 fnt3 2492 1359 0 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1415 338 56 282 240 288 12 1077 1016 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
517 846 56 790 240 288 12 451 0 LoutGr2
currentdict end 200 dict begin begin
grestore
517 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
517 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt4 56 105(0)m 192 fnt3 195 111(.)m 192 fnt4
270 105(2)m 192 fnt3 410 111(i)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 968 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 846 56 790 240 288 12 1081 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1419 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
509 846 56 790 240 288 12 1532 0 LoutGr2
currentdict end 200 dict begin begin
grestore
509 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
509 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt4 56 105(0)m 192 fnt3 195 111(.)m 192 fnt4
270 105(3)m 192 fnt3 402 111(i)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 2041 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 846 56 790 240 288 12 2154 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 2492 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 9 10
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Symbol
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5766 -1579(-)m 5894(9)s
6065(-)s 9066 13414 0 13305 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13251(to)m 239(mak)s 2(e)k 811(manifest)s
1693(their)s 2190(associati)s 6(vity)k 3432(and)s 3836(reduce)s
4529(the)s 4877(depth)s 5466(of)s 5737(the)s 6085(tree)s
6498(for)s 6836(ef\207cienc)s 3(y)k 7829(later)s 13(.)k
480 12877(The)m 970(required)s 1887(semantic)s 2851(information)s 4099(is)s
4371(the)s 4782(size)s 5271(of)s 5605(each)s 6162(subobject,)s
7249(consisting)s 8334(of)s 8668(four)s 0 12589(inte)m 3(gers:)k
920(width)s 1524(to)s 1765(left)s 2144(and)s 2550(right)s
3062(of)s 3335(the)s 3685(distinguished)s 5021(column)s 5798(mark,)s
6397(and)s 6803(height)s 7463(abo)s 3(v)k 3(e)k
8087(and)s 8493(belo)s 6(w)k 0 12301(the)m 368(distinguished)s
1722(ro)s 6(w)k 2162(mark.)s 2837(These)s 3484(numbers)s
4379(are)s 4746(al)s 2(w)k 2(ays)k 5477(non-ne)s 3(g)k 1(ati)k 6(v)k 3(e)k
6789(in)s 7052(Basser)s 7769(Lout,)s 8348(b)s 4(ut)k
8730(this)s 0 12013(restriction)m 1024(is)s 1234(unnecessary)s 2457(and)s
2861(should)s 3558(be)s 3840(dropped.)s 480 11639(F)m 3(or)k
867(the)s 1212(lea)s 4(v)k 3(es,)k 1907(which)s
2546(are)s 2890(simple)s 3581(w)s 2(ords,)k 4268(the)s
4614(numbers)s 5486(are)s 5830(obtained)s 6710(from)s 7231(font)s
7674(tables.)s 8392(F)s 3(or)k 8778(the)s 0 11351(higher)m
678(le)s 6(v)k 3(els)k 1285(we)s 1628(apply)s
2222(recursi)s 6(v)k 3(e)k 3152(rules.)s 3788(Suppose)s
4664(that)s 240 fnt3 5090 11353(hgap)m 240 fnt4 5583 11345(\()m
240 fnt3 5675 11353(x)m 240 fnt4 5801 11345(,)m 240 fnt3
5932 11353(g)m 240 fnt4 6066 11345(,)m 240 fnt3 6197 11353(y)m
240 fnt4 6319 11345(\))m 240 fnt1 6453 11351(returns)m 7175(the)s
7531(desired)s 8287(distance)s 0 11063(between)m 846(the)s 1186(column)s
1952(marks)s 2579(of)s 2841(objects)s 240 fnt3 3561 11065(x)m
240 fnt1 3719 11063(and)m 240 fnt3 4114 11065(y)m 240 fnt1
4268 11063(when)m 4835(the)s 3(y)k 5290(are)s 5629(separated)s
6580(by)s 6866(g)s 1(ap)k 240 fnt3 7255 11065(g)m
240 fnt1 7369 11063(:)m 240 fnt3 7527 11065(right)m 240 fnt4
8000 11057(\()m 240 fnt3 8075 11065(x)m 240 fnt4 8185 11057(\))m
8298(+)s 240 fnt3 8473 11065(length)m 240 fnt4 0 10769(\()m
240 fnt3 89 10777(g)m 240 fnt4 221 10769(\))m 376(+)s
240 fnt3 594 10777(left)m 240 fnt4 920 10769(\()m 240 fnt3
1009 10777(y)m 240 fnt4 1129 10769(\))m 240 fnt1 1261 10775(when)m
1842(the)s 2196(g)s 1(ap)k 2600(mode)s 3193(is)s
3409(edge-to-edge,)s 4770(the)s 5124(lar)s 4(ger)k 5741(of)s
240 fnt3 6018 10777(length)m 240 fnt4 6629 10769(\()m 240 fnt3
6718 10777(g)m 240 fnt4 6850 10769(\))m 240 fnt1 6982 10775(and)m
240 fnt3 7391 10777(right)m 240 fnt4 7878 10769(\()m 240 fnt3
7968 10777(x)m 240 fnt4 8091 10769(\))m 8246(+)s 240 fnt3
8464 10777(left)m 240 fnt4 8790 10769(\()m 240 fnt3 8880 10777(y)m
240 fnt4 9000 10769(\))m 240 fnt1 0 10487(when)m 576(the)s
924(mode)s 1512(is)s 1722(mark-to-mark,)s 3155(and)s 3559(so)s
3825(on.)s 4229(Gi)s 6(v)k 3(en)k 4862(an)s
5145(object)s 240 fnt3 480 9992(X)m 240 fnt4 720 9984(=)m
240 fnt3 933 9992(x)m 167 fnt4 1039 9900(1)m 240 fnt4
1248 9984(|)m 240 fnt3 1293 9992(g)m 167 fnt4 1404 9900(1)m
240 fnt4 1613 9984(\274)m 200 fnt3 1971 10000(^)m 240 fnt4
2067 9984(|)m 240 fnt3 2112 9992(g)m 167 fnt3 2223 9905(i)m
167 fnt4 2289 9900(-)m 2400(1)s 240 fnt3 2609 9992(x)m
167 fnt3 2715 9905(i)m 240 fnt4 2903 9984(\274)m 3261(|)s
240 fnt3 3306 9992(g)m 167 fnt3 3417 9905(n)m 167 fnt4
3518 9900(-)m 3629(1)s 240 fnt3 3838 9992(x)m 167 fnt3
3944 9905(n)m 240 fnt1 0 9449(we)m 335(may)s 801(calculate)s
1705(its)s 1981(size)s 2408(as)s 2658(follo)s 6(ws:)k
240 fnt3 740 8946(left)m 240 fnt4 1060 8938(\()m 240 fnt3
1144 8946(X)m 240 fnt4 1312 8938(\))m 1474(=)s 240 fnt3
1687 8946(left)m 240 fnt4 2007 8938(\()m 240 fnt3 2091 8946(x)m
167 fnt4 2197 8854(1)m 240 fnt4 2274 8938(\))m 2412(+)s
240 fnt3 2613 8946(hgap)m 240 fnt4 3098 8938(\()m 240 fnt3
3182 8946(x)m 167 fnt4 3288 8854(1)m 240 fnt4 3365 8938(,)m
240 fnt3 3472 8946(g)m 167 fnt4 3583 8854(1)m 240 fnt4
3660 8938(,)m 240 fnt3 3767 8946(x)m 167 fnt4 3873 8854(2)m
240 fnt4 3964 8938(\))m 4102(+)s 4303(\274)s 4589(+)s
240 fnt3 4790 8946(hgap)m 240 fnt4 5275 8938(\()m 240 fnt3
5359 8946(x)m 167 fnt3 5465 8859(i)m 167 fnt4 5531 8854(-)m
5642(1)s 240 fnt4 5719 8938(,)m 240 fnt3 5826 8946(g)m
167 fnt3 5937 8859(i)m 167 fnt4 6003 8854(-)m 6114(1)s
240 fnt4 6191 8938(,)m 240 fnt3 6298 8946(x)m 167 fnt3
6404 8859(i)m 240 fnt4 6460 8938(\))m 240 fnt3 579 8543(right)m
240 fnt4 1060 8535(\()m 240 fnt3 1144 8543(X)m 240 fnt4
1312 8535(\))m 1474(=)s 240 fnt3 1687 8543(hgap)m 240 fnt4
2172 8535(\()m 240 fnt3 2256 8543(x)m 167 fnt3 2362 8456(i)m
240 fnt4 2418 8535(,)m 240 fnt3 2525 8543(g)m 167 fnt3
2636 8456(i)m 240 fnt4 2692 8535(,)m 240 fnt3 2799 8543(x)m
167 fnt3 2905 8456(i)m 167 fnt4 2971 8451(+)m 3083(1)s
240 fnt4 3160 8535(\))m 3298(+)s 3499(\274)s 3785(+)s
240 fnt3 3986 8543(hgap)m 240 fnt4 4471 8535(\()m 240 fnt3
4555 8543(x)m 167 fnt3 4661 8456(n)m 167 fnt4 4762 8451(-)m
4873(1)s 240 fnt4 4950 8535(,)m 240 fnt3 5057 8543(g)m
167 fnt3 5168 8456(n)m 167 fnt4 5269 8451(-)m 5380(1)s
240 fnt4 5457 8535(,)m 240 fnt3 5564 8543(x)m 167 fnt3
5670 8456(n)m 240 fnt4 5761 8535(\))m 5899(+)s 240 fnt3
6100 8543(right)m 240 fnt4 6581 8535(\()m 240 fnt3 6665 8543(x)m
167 fnt3 6771 8456(n)m 240 fnt4 6862 8535(\))m 240 fnt3
485 8140(abo)m 2(ve)k 240 fnt4 1060 8132(\()m 240 fnt3
1144 8140(X)m 240 fnt4 1312 8132(\))m 1474(=)s 240 fnt3
1687 8140(abo)m 2(ve)k 240 fnt4 2262 8132(\()m 240 fnt3
2346 8140(x)m 167 fnt4 2452 8046(1)m 240 fnt4 2529 8132(\))m
2679(\255)s 2900(\274)s 3198(\255)s 240 fnt3 3419 8140(abo)m 2(ve)k
240 fnt4 3994 8132(\()m 240 fnt3 4078 8140(x)m 167 fnt3
4184 8051(n)m 240 fnt4 4275 8132(\))m 240 fnt3 480 7737(below)m
240 fnt4 1060 7729(\()m 240 fnt3 1144 7737(X)m 240 fnt4
1312 7729(\))m 1474(=)s 240 fnt3 1687 7737(below)m 240 fnt4
2267 7729(\()m 240 fnt3 2351 7737(x)m 167 fnt4 2457 7643(1)m
240 fnt4 2534 7729(\))m 2684(\255)s 2905(\274)s 3203(\255)s
240 fnt3 3424 7737(below)m 240 fnt4 4004 7729(\()m 240 fnt3
4088 7737(x)m 167 fnt3 4194 7648(n)m 240 fnt4 4285 7729(\))m
240 fnt1 0 7143(where)m 240 fnt4 693 7137(\255)m 240 fnt1
943 7143(returns)m 1678(the)s 2046(lar)s 4(ger)k 2679(of)s
2971(its)s 3267(tw)s 2(o)k 3698(parameters.)s 4930(Similar)s
5712(formulas)s 6633(are)s 7001(easily)s 7632(deri)s 6(v)k 3(ed)k
8419(for)s 8778(the)s 0 6855(other)m 551(operators.)s 480 6481(F)m 3(or)k
866(purposes)s 1765(of)s 2033(e)s 3(xposition)k 3081(we)s
3412(will)s 3835(no)s 6(w)k 4293(mak)s 2(e)k
4862(the)s 5207(simplifying)s 6358(assumptions)s 7589(that)s 8004(all)s
8294(g)s 1(aps)k 8779(are)s 220 fnt5 0 6190(0i)m
240 fnt1 156 6193(,)m 248(all)s 525(column)s 1285(marks)s
1904(lie)s 2183(at)s 2399(the)s 2732(left)s 3093(edge,)s
3637(and)s 4025(all)s 4303(ro)s 6(w)k 4707(marks)s
5327(lie)s 5605(at)s 5822(the)s 6154(top)s 6498(edge.)s
7098(Then)s 7632(the)s 7964(size)s 8376(of)s 8631(each)s
0 5905(object)m 644(can)s 1033(be)s 1315(e)s 3(xpressed)k
2313(by)s 2607(just)s 3012(tw)s 2(o)k 3422(numbers,)s
4353(width)s 4955(and)s 5359(height,)s 6064(and)s 6468(the)s
6816(four)s 7274(formulas)s 8174(reduce)s 8867(to)s 240 fnt3
555 5402(width)m 240 fnt4 1094 5394(\()m 240 fnt3 1178 5402(x)m
167 fnt4 1284 5310(1)m 240 fnt4 1433 5394(|)m 1550(\274)s
1848(|)s 240 fnt3 1965 5402(x)m 167 fnt3 2071 5315(n)m
240 fnt4 2162 5394(\))m 2324(=)s 240 fnt3 2537 5402(width)m
240 fnt4 3076 5394(\()m 240 fnt3 3160 5402(x)m 167 fnt4
3266 5310(1)m 240 fnt4 3343 5394(\))m 3481(+)s 3682(\274)s
3968(+)s 240 fnt3 4169 5402(width)m 240 fnt4 4708 5394(\()m
240 fnt3 4792 5402(x)m 167 fnt3 4898 5315(n)m 240 fnt4
4989 5394(\))m 240 fnt3 480 4999(height)m 240 fnt4 1094 4991(\()m
240 fnt3 1178 4999(x)m 167 fnt4 1284 4907(1)m 240 fnt4
1433 4991(|)m 1550(\274)s 1848(|)s 240 fnt3 1965 4999(x)m
167 fnt3 2071 4912(n)m 240 fnt4 2162 4991(\))m 2324(=)s
240 fnt3 2537 4999(height)m 240 fnt4 3151 4991(\()m 240 fnt3
3235 4999(x)m 167 fnt4 3341 4907(1)m 240 fnt4 3418 4991(\))m
3568(\255)s 3789(\274)s 4087(\255)s 240 fnt3 4308 4999(height)m
240 fnt4 4922 4991(\()m 240 fnt3 5006 4999(x)m 167 fnt3
5112 4912(n)m 240 fnt4 5203 4991(\))m 240 fnt1 0 4456(The)m
428(corresponding)s 1850(formulas)s 2750(for)s 3088(v)s 3(ertical)k
3855(concatenation)s 5240(are)s 240 fnt3 555 3906(width)m 240 fnt4
1094 3898(\()m 240 fnt3 1178 3906(x)m 167 fnt4 1284 3814(1)m
240 fnt3 1433 3906(/)m 240 fnt4 1608 3898(\274)m 240 fnt3
1906 3906(/)m 2081(x)s 167 fnt3 2187 3819(n)m 240 fnt4
2278 3898(\))m 2440(=)s 240 fnt3 2653 3906(width)m 240 fnt4
3192 3898(\()m 240 fnt3 3276 3906(x)m 167 fnt4 3382 3814(1)m
240 fnt4 3459 3898(\))m 3609(\255)s 3830(\274)s 4128(\255)s
240 fnt3 4349 3906(width)m 240 fnt4 4888 3898(\()m 240 fnt3
4972 3906(x)m 167 fnt3 5078 3819(n)m 240 fnt4 5169 3898(\))m
240 fnt3 480 3503(height)m 240 fnt4 1094 3495(\()m 240 fnt3
1178 3503(x)m 167 fnt4 1284 3411(1)m 240 fnt3 1433 3503(/)m
240 fnt4 1608 3495(\274)m 240 fnt3 1906 3503(/)m 2081(x)s
167 fnt3 2187 3416(n)m 240 fnt4 2278 3495(\))m 2440(=)s
240 fnt3 2653 3503(height)m 240 fnt4 3267 3495(\()m 240 fnt3
3351 3503(x)m 167 fnt4 3457 3411(1)m 240 fnt4 3534 3495(\))m
3672(+)s 3873(\274)s 4159(+)s 240 fnt3 4360 3503(height)m
240 fnt4 4974 3495(\()m 240 fnt3 5058 3503(x)m 167 fnt3
5164 3416(n)m 240 fnt4 5255 3495(\))m 240 fnt1 0 2960(According)m
1063(to)s 1302(these)s 1849(formulas,)s 2805(the)s 3153(height)s
3811(of)s gsave
480 1266 translate
240 fnt3 3044 1354 56 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1240 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
338 338 56 282 240 288 12 451 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4
156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 789 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 902 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(T) lfigpromotelabels
grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1240 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(L) lfigpromotelabels
grestore
338 338 56 282 240 288 12 1353 1016 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 136 106(\244)m

grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1691 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1240 846 56 790 240 288 12 1804 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
338 338 56 282 240 288 12 451 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 789 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 902 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1240 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3044 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 10 11
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Symbol
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5704 -1579(-)m 5832(10)s
6127(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13253(is)m 240 fnt4 480 12745([)m 240 fnt3
563 12753(height)m 240 fnt4 1177 12745(\()m 240 fnt3 1261 12753(a)m
240 fnt4 1388 12745(\))m 1538(\255)s 240 fnt3 1759 12753(height)m
240 fnt4 2373 12745(\()m 240 fnt3 2457 12753(b)m 240 fnt4
2583 12745(\))m 2661(])s 2792(+)s 2993([)s 240 fnt3
3076 12753(height)m 240 fnt4 3690 12745(\()m 240 fnt3 3774 12753(c)m
240 fnt4 3888 12745(\))m 4038(\255)s 240 fnt3 4259 12753(height)m
240 fnt4 4873 12745(\()m 240 fnt3 4957 12753(d)m 240 fnt4
5095 12745(\))m 5173(])s 240 fnt1 0 12249(which)m 642(is)s
852(correct,)s 1621(b)s 4(ut)k 1983(for)s 2321(width)s
2923(the)s 3(y)k 3386(yield)s 240 fnt4 480 11691([)m
240 fnt3 563 11699(width)m 240 fnt4 1102 11691(\()m 240 fnt3
1186 11699(a)m 240 fnt4 1313 11691(\))m 1451(+)s 240 fnt3
1652 11699(width)m 240 fnt4 2191 11691(\()m 240 fnt3 2275 11699(b)m
240 fnt4 2401 11691(\))m 2479(])s 2622(\255)s 2843([)s
240 fnt3 2926 11699(width)m 240 fnt4 3465 11691(\()m 240 fnt3
3549 11699(c)m 240 fnt4 3663 11691(\))m 3801(+)s 240 fnt3
4002 11699(width)m 240 fnt4 4541 11691(\()m 240 fnt3 4625 11699(d)m
240 fnt4 4763 11691(\))m 4841(])s 240 fnt1 0 11195(which)m
645(is)s 859(not,)s 1276(since)s 1827(it)s 2023(does)s
2517(not)s 2887(tak)s 2(e)k 3343(the)s 3694(mer)s 4(ging)k
4544(of)s 4819(column)s 5598(marks)s 6237(into)s 6666(account.)s
7578(The)s 8010(asymmetry)s 0 10907(between)m 874(horizontal)s 1918(and)s
2342(v)s 3(ertical)k 3130(has)s 3520(come)s 4114(about)s
4726(because)s 5560(the)s 5928(ro)s 6(w)k 6368(entries,)s
7131(such)s 7648(as)s 240 fnt3 7918 10909(a)m 240 fnt1
8113 10907(and)m 240 fnt3 8537 10909(b)m 240 fnt1 8651 10907(,)m
8779(are)s 0 10619(adjacent)m 849(in)s 1085(the)s 1426(tree,)s
1883(b)s 4(ut)k 2238(the)s 2579(column)s 3346(entries,)s
4082(such)s 4571(as)s 240 fnt3 4814 10621(a)m 240 fnt1
4982 10619(and)m 240 fnt3 5379 10621(c)m 240 fnt1 5481 10619(,)m
5581(are)s 5920(not.)s 6383(It)s 6581(w)s 2(ould)k
7229(be)s 7504(possible)s 8337(to)s 8568(solv)s 3(e)k
0 10331(this)m 395(cross-linking)s 1694(problem)s 2550(by)s 2842(augmenting)s
4024(the)s 4370(size)s 4795(information)s 5979(stored)s 6619(in)s
6861(each)s 7354(node)s 7875(to)s 8112(record)s 8778(the)s
0 10043(number)m 791(of)s 1063(marks)s 1698(and)s 2103(the)s
2451(size)s 2879(of)s 3150(each,)s 3696(b)s 4(ut)k
4058(the)s 4407(author)s 5078(has)s 5449(preferred)s 6381(the)s
6730(follo)s 6(wing)k 7707(method)s 8484(which)s 0 9755(mak)m 2(es)k
660(structural)s 1616(changes)s 2438(to)s 2677(the)s 3025(tree)s
3438(instead.)s 480 9381(If)m 240 fnt3 715 9383(a)m 240 fnt1
896 9381(and)m 240 fnt3 1305 9383(c)m 240 fnt1 1473 9381(share)m
2038(a)s 2210(column)s 2990(mark,)s 3594(the)s 3(y)k
4063(each)s 4563(might)s 5187(as)s 5442(well)s 5914(ha)s 4(v)k 3(e)k
6420(width)s 240 fnt3 7028 9383(width)m 240 fnt4 7572 9375(\()m
240 fnt3 7662 9383(a)m 240 fnt4 7795 9375(\))m 7961(\255)s
240 fnt3 8199 9383(width)m 240 fnt4 8743 9375(\()m 240 fnt3
8833 9383(c)m 240 fnt4 8953 9375(\))m 240 fnt1 9019 9381(,)m
0 9093(since)m 547(all)s 840(width)s 1442(calculations)s 2635(apply)s
3221(to)s 3460(entire)s 4060(columns.)s 5035(Accordingly)s 15(,)k
6323(we)s 6659(introduce)s 7618(a)s 7784(ne)s 6(w)k
8232(operator)s 9(,)k 240 fnt3 0 8807(COL)m 240 fnt1
466 8805(,)m 573(de\207ned)s 1336(by)s 240 fnt3 480 8255(width)m
240 fnt4 1019 8247(\()m 240 fnt3 1103 8255(x)m 167 fnt4
1209 8163(1)m 240 fnt3 1346 8255(COL)m 240 fnt4 1884 8247(\274)m
240 fnt3 2170 8255(COL)m 2708(x)s 167 fnt3 2814 8168(n)m
240 fnt4 2905 8247(\))m 3055(=)s 240 fnt3 3268 8255(width)m
240 fnt4 3807 8247(\()m 240 fnt3 3891 8255(x)m 167 fnt4
3997 8163(1)m 240 fnt4 4074 8247(\))m 4224(\255)s 4445(\274)s
4743(\255)s 240 fnt3 4964 8255(width)m 240 fnt4 5503 8247(\()m
240 fnt3 5587 8255(x)m 167 fnt3 5693 8168(n)m 240 fnt4
5784 8247(\))m 240 fnt1 0 7712(and)m 440(replace)s 1221(both)s
240 fnt3 1741 7714(a)m 240 fnt1 1952 7712(and)m 240 fnt3
2393 7714(c)m 240 fnt1 2591 7712(by)m 240 fnt3 2922 7714(a)m
3218(COL)s 3865(c)s 240 fnt1 3967 7712(.)m 4168(T)s 19(o)k
4504(pre)s 6(v)k 3(ent)k 240 fnt3 5309 7714(COL)m
240 fnt1 5871 7712(operators)m 6848(from)s 7408(disturbing)s 8468(height)s
0 7424(calculations,)m 1248(we)s 1583(de\207ne)s 2224(a)s 2390(binary)s
3055(operator)s 3911(called)s 240 fnt3 4539 7426(SPLIT)m 240 fnt1
5228 7424(by)m 240 fnt3 555 6921(width)m 240 fnt4 1094 6913(\()m
240 fnt3 1178 6921(x)m 1356(SPLIT)s 2057(y)s 240 fnt4
2171 6913(\))m 2333(=)s 240 fnt3 2546 6921(width)m 240 fnt4
3085 6913(\()m 240 fnt3 3169 6921(x)m 240 fnt4 3287 6913(\))m
240 fnt3 480 6518(height)m 240 fnt4 1094 6510(\()m 240 fnt3
1178 6518(x)m 1356(SPLIT)s 2057(y)s 240 fnt4 2171 6510(\))m
2333(=)s 240 fnt3 2546 6518(height)m 240 fnt4 3160 6510(\()m
240 fnt3 3244 6518(y)m 240 fnt4 3358 6510(\))m 240 fnt1
0 6014(which)m 642(switches)s 1516(height)s 2174(and)s 2578(width)s
3180(calculations)s 4372(onto)s 4851(dif)s 6(ferent)k 5726(subtrees.)s
6673(Then)s 7222(the)s 7570(transformation)s gsave
480 4315 translate
240 fnt3 338 1359 56 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
338 1359 56 1298 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 1016 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
end end restore
grestore
240 fnt4 1130 5553(\336)m gsave
1671 4315 translate
240 fnt3 2564 1359 56 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1386 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
484 338 56 282 240 288 12 451 508 LoutGr2
currentdict end 200 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(COL)m 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 935 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 1048 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m

grestore
(T) lfigpromotelabels
grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1386 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(L) lfigpromotelabels
grestore
614 338 56 282 240 288 12 1499 1016 LoutGr2
currentdict end 200 dict begin begin
grestore
614 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(SPLIT)m 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 2113 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 846 56 790 240 288 12 2226 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 508 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 2564 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
240 fnt1
0 3815(widens)m 240 fnt3 740 3817(a)m 240 fnt1 926 3815(to)m
240 fnt3 1176 3817(width)m 240 fnt4 1726 3809(\()m 240 fnt3
1821 3817(a)m 240 fnt4 1959 3809(\))m 2142(\255)s 240 fnt3
2396 3817(width)m 240 fnt4 2946 3809(\()m 240 fnt3 3041 3817(c)m
240 fnt4 3166 3809(\))m 240 fnt1 3303 3815(without)m 4105(af)s 6(fecting)k
5011(its)s 5298(height;)s 6019(it)s 6222(is)s 6443(applied)s
7216(to)s 7466(e)s 6(v)k 3(ery)k 8053(object)s
8708(that)s 0 3527(shares)m 638(its)s 904(column)s 1669(mark)s
2211(with)s 2683(at)s 2905(least)s 3392(one)s 3784(other)s
4325(object.)s 5063(A)s 5283(similar)s 5995(transformation)s 7448(in)s 9(v)k 4(olving)k
8396(a)s 240 fnt3 8552 3529(R)m 9(O)k 12(W)k
240 fnt1 0 3239(operator)m 856(deals)s 1398(with)s 1880(shared)s
2562(ro)s 6(w)k 2982(marks.)s 3730(The)s 4158(ef)s 6(fect)k
4754(on)s 5051(our)s 5430(little)s 5922(table)s 6442(is)s
6652(to)s 6891(replace)s gsave
480 1545 translate
240 fnt3 3044 1354 56 1298 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1240 846 56 790 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m

grestore
(T) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
338 338 56 282 240 288 12 451 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 789 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 902 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(T) lfigpromotelabels
grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1240 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(L) lfigpromotelabels
grestore
338 338 56 282 240 288 12 1353 1016 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4
136 106(\244)m 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1691 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1240 846 56 790 240 288 12 1804 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
338 338 56 282 240 288 12 451 508 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m

grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 12 789 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 902 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1240 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3044 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 1094(by)m 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 11 12
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Symbol
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5714 -1579(-)m 5842(11)s
6117(-)s 9066 13419 0 13363 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
gsave
480 11049 translate
240 fnt3 6248 2370 0 2314 240 288 12 LoutGraphic
gsave
grestore save gsave 70 dict begin lfigdict begin
grestore
3293 338 56 282 240 288 12 2955 2032 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 136 106(\244)m 
grestore
(T) lfigpromotelabels
grestore
3096 1862 0 1806 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1717 338 56 282 240 288 12 1379 1524 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4
156 121(|)m 
grestore
(T) lfigpromotelabels
grestore
1520 1354 0 1298 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1067 338 56 282 240 288 12 453 1016 LoutGr2
currentdict end 70 dict begin begin
grestore
614 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(SPLIT)m 
grestore
(T) lfigpromotelabels
grestore
732 846 0 790 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
608 338 56 282 240 288 12 124 508 LoutGr2
currentdict end 70 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(COL)m

grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
732 846 0 790 240 288 12 788 0 LoutGr2
currentdict end 70 dict begin begin
grestore
628 338 56 282 240 288 12 104 508 LoutGr2
currentdict end 70 dict begin begin
grestore
524 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3
56 107(R)m 7(O)k 9(W)k 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1520 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1520 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1520 1354 0 1298 240 288 12 1576 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1067 338 56 282 240 288 12 453 1016 LoutGr2
currentdict end 70 dict begin begin
grestore
614 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(SPLIT)m 
grestore
(T) lfigpromotelabels
grestore
732 846 0 790 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
608 338 56 282 240 288 12 124 508 LoutGr2
currentdict end 70 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3
56 107(COL)m 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
732 846 0 790 240 288 12 788 0 LoutGr2
currentdict end 70 dict begin begin
grestore
628 338 56 282 240 288 12 104 508 LoutGr2
currentdict end 70 dict begin begin
grestore
524 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(R)m 7(O)k 9(W)k 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1520 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3096 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3096 1806 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
3096 1862 0 1806 240 288 12 3152 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1717 338 56 282 240 288 12 1379 1524 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt4 156 121(|)m

grestore
(T) lfigpromotelabels
grestore
1520 1354 0 1298 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1067 338 56 282 240 288 12 453 1016 LoutGr2
currentdict end 70 dict begin begin
grestore
614 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(SPLIT)m 
grestore
(T) lfigpromotelabels
grestore
732 846 0 790 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
608 338 56 282 240 288 12 124 508 LoutGr2
currentdict end 70 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(COL)m 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
123 128(a)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
732 846 0 790 240 288 12 788 0 LoutGr2
currentdict end 70 dict begin begin
grestore
628 338 56 282 240 288 12 104 508 LoutGr2
currentdict end 70 dict begin begin
grestore
524 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(R)m 7(O)k 9(W)k

grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1520 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1520 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1520 1354 0 1298 240 288 12 1576 0 LoutGr2
currentdict end 70 dict begin begin
grestore
1067 338 56 282 240 288 12 453 1016 LoutGr2
currentdict end 70 dict begin begin
grestore
614 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3
56 107(SPLIT)m 
grestore
(T) lfigpromotelabels
grestore
732 846 0 790 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
608 338 56 282 240 288 12 124 508 LoutGr2
currentdict end 70 dict begin begin
grestore
484 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(COL)m 
grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
732 846 0 790 240 288 12 788 0 LoutGr2
currentdict end 70 dict begin begin
grestore
628 338 56 282 240 288 12 104 508 LoutGr2
currentdict end 70 dict begin begin
grestore
524 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
192 fnt3 56 107(R)m 7(O)k 9(W)k

grestore
(T) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 338 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
338 338 56 282 240 288 12 394 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 70 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 118 105(d)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 732 282 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 1520 790 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 3096 1298 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 12 6248 1806 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 10598(In)m
244(f)s 2(act,)k 693(common)s 1576(sube)s 3(xpressions)k
3060(are)s 3395(identi\207ed)s 4343(\(tri)s 6(vially\))k 5286(and)s
5678(the)s 6013(result)s 6591(is)s 6788(a)s 6942(directed)s
7756(ac)s 3(yclic)k 8469(graph;)s 0 10310(each)m 486(af)s 6(fected)k
1296(leaf)s 1716(has)s 2076(tw)s 2(o)k 2477(parents,)s
3264(one)s 3657(for)s 3985(width)s 4578(and)s 4972(one)s
5365(for)s 5693(height;)s 6394(and)s 6788(each)s 240 fnt3
7274 10312(COL)m 240 fnt1 7790 10310(or)m 240 fnt3 8040 10312(R)m 9(O)k 12(W)k
240 fnt1 8604 10310(node)m 0 10022(has)m 360(one)s 752(parent)s
1398(and)s 1792(one)s 2184(child)s 2709(for)s 3037(each)s
3521(object)s 4155(lying)s 4690(on)s 4976(the)s 5314(corresponding)s
6726(mark.)s 7370(The)s 7788(data)s 8235(structure)s 0 9734(roughly)m
799(doubles)s 1595(in)s 1838(size,)s 2316(and)s 2720(this)s
3116(occurs)s 3791(only)s 4271(rarely)s 4881(in)s 5124(practice.)s
480 9360(This)m 956(method)s 1732(can)s 2121(cope)s 2629(with)s
3111(an)s 3(y)k 3508(le)s 3(g)k 1(al)k
4023(input,)s 4622(including)s 220 fnt5 480 8859({  a  //  c  |  d  }  |  {  b  /  e  })m 480 8571(/  {  f  /  i  }  |  {  g  |  h  //  j  })m
240 fnt1 0 8072(which)m 642(produces)s 1557(o)s 3(v)k 3(erlapping)k
2747(spanning)s 3665(columns:)s gsave
480 5924 translate
240 fnt3 1699 1808 0 1695 240 288 60 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1133 452 113 339 240 288 60 0 1356 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 511 178(a)m

grestore
566 452 113 339 240 288 60 1133 1356 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 228 150(b)m 
grestore
566 452 113 339 240 288 60 0 904 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 234 178(c)m 
grestore
566 452 113 339 240 288 60 566 904 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3
222 150(d)m 
grestore
566 452 113 339 240 288 60 1132 904 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 235 178(e)m 
grestore
566 452 113 339 240 288 60 0 452 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 235 173(f)m

grestore
566 452 113 339 240 288 60 566 452 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 228 200(g)m 
grestore
566 452 113 339 240 288 60 1132 452 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 228 149(h)m 
grestore
566 452 113 339 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3
253 153(i)m 
grestore
1133 452 113 339 240 288 60 566 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
230 fnt3 535 176(j)m 
grestore
end end restore
grestore
0 5473(The)m 428(box)s 3(es)k
1035(ha)s 4(v)k 3(e)k 1536(been)s 2045(added)s
2675(to)s 2914(clarify)s 3590(the)s 3938(structure.)s 4937(The)s
5365(width)s 5967(of)s 6238(this)s 6634(object)s 7278(is)s
7488(formally)s 240 fnt4 480 4915(\()m 564(\()s 240 fnt3
648 4923(width)m 240 fnt4 1187 4915(\()m 240 fnt3 1271 4923(a)m
240 fnt4 1398 4915(\))m 1548(\255)s 1769(\()s 240 fnt3
1853 4923(x)m 240 fnt4 2031 4915(+)m 240 fnt3 2232 4923(y)m
240 fnt4 2346 4915(\))m 2424(\))s 2562(+)s 240 fnt3
2763 4923(z)m 240 fnt4 2866 4915(\))m 3016(\255)s 3237(\()s
240 fnt3 3321 4923(x)m 240 fnt4 3499 4915(+)m 3700(\()s
3784(\()s 240 fnt3 3868 4923(y)m 240 fnt4 4042 4915(+)m
240 fnt3 4243 4923(z)m 240 fnt4 4346 4915(\))m 4496(\255)s
240 fnt3 4717 4923(width)m 240 fnt4 5256 4915(\()m 240 fnt3
5340 4923(j)m 240 fnt4 5418 4915(\))m 5496(\))s 5574(\))s
240 fnt1 0 4419(where)m 240 fnt3 480 3918(x)m 240 fnt4
670 3910(=)m 240 fnt3 883 3918(width)m 240 fnt4 1422 3910(\()m
240 fnt3 1506 3918(c)m 240 fnt4 1620 3910(\))m 1770(\255)s
240 fnt3 1991 3918(width)m 240 fnt4 2530 3910(\()m 240 fnt3
2662 3918(f)m 240 fnt4 2823 3910(\))m 2973(\255)s 240 fnt3
3194 3918(width)m 240 fnt4 3733 3910(\()m 240 fnt3 3817 3918(i)m
240 fnt4 3892 3910(\))m 
[ /Dest /LOUT12_1490_s2_4_1 /DEST pdfmark
240 fnt3 480 3367(y)m 240 fnt4
666 3359(=)m 240 fnt3 879 3367(width)m 240 fnt4 1418 3359(\()m
240 fnt3 1502 3367(d)m 240 fnt4 1688 3359(\))m 1838(\255)s
240 fnt3 2059 3367(width)m 240 fnt4 2598 3359(\()m 240 fnt3
2682 3367(g)m 240 fnt4 2808 3359(\))m 
[ /Dest /LOUT12_1490_s2_4_2 /DEST pdfmark
240 fnt3 480 2816(z)m
240 fnt4 655 2808(=)m 240 fnt3 868 2816(width)m 240 fnt4
1407 2808(\()m 240 fnt3 1491 2816(b)m 240 fnt4 1617 2808(\))m
1767(\255)s 240 fnt3 1988 2816(width)m 240 fnt4 2527 2808(\()m
240 fnt3 2611 2816(e)m 240 fnt4 2722 2808(\))m 2872(\255)s
240 fnt3 3093 2816(width)m 240 fnt4 3632 2808(\()m 240 fnt3
3716 2816(h)m 240 fnt4 3843 2808(\))m 
[ /Dest /LOUT12_1490_s2_4_3 /DEST pdfmark
240 fnt1 0 2312(It)m
224(seems)s 878(clear)s 1420(that)s 240 fnt3 1857 2314(y)m
240 fnt1 2038 2312(at)m 2289(least)s 2805(must)s 3349(appear)s
4065(twice)s 4657(in)s 4919(an)s 3(y)k 5335(e)s 3(xpression)k
6431(for)s 6788(the)s 7155(width)s 7776(of)s 8066(this)s
8482(object)s 0 2024(made)m 602(out)s 997(of)s 1297(simple)s
2019(addition)s 2889(and)s 3322(maxing)s 4121(operations,)s 5253(sho)s 6(wing)k
6141(that)s 6588(an)s 6900(ordinary)s 7793(tree)s 8235(structure)s
0 1736(is)m 227(insuf\207cient)s 1379(for)s 1734(o)s 3(v)k 3(erlapping)k
2941(spanning)s 3876(columns.)s 4868(The)s 5313(Basser)s 6027(Lout)s
6556(interpreter)s 7626(actually)s 8453(rejects)s 0 1448(such)m 521(structures,)s
1581(o)s 6(wing)k 2252(to)s 2517(the)s 2890(author')s 13(s)k
3736(doubts)s 4451(about)s 5069(the)s 5442(implementability)s 7153(of)s
240 fnt3 7449 1450(Constr)m 3(ained)k 240 fnt1 8722 1448(and)m
240 fnt3 0 1162(AdjustSize)m 240 fnt1 1049 1160(\(Section)m 1902(5.3\))s
2330(on)s 2627(them;)s 3217(b)s 4(ut)k 3579(with)s
4061(hindsight)s 5012(this)s 5408(caution)s 6169(w)s 2(as)k
6590(unnecessary)s 15(.)k 480 786(The)m 915(directed)s 1749(ac)s 3(yclic)k
2482(graph)s 3091(is)s 3308(ordered)s 4104(in)s 4354(the)s
4709(sense)s 5290(that)s 5715(the)s 6071(order)s 6642(of)s
6920(the)s 7275(edges)s 7878(entering)s 8722(and)s 0 498(lea)m 4(ving)k
746(each)s 1234(node)s 1748(matters.)s 2607(The)s 3028(structure)s
3911(is)s 4114(highly)s 4773(dynamic,)s 5696(and)s 6093(tra)s 4(v)k 3(ersals)k
7044(both)s 7519(with)s 7994(and)s 8390(ag)s 1(ainst)k

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 12 13
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Times-Bold
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1579(-)m 5833(12)s
6127(-)s 9066 13419 0 13310 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13256(the)m 349(arro)s 6(ws)k 1045(are)s
1394(required.)s 2355(After)s 2920(a)s 3087(fe)s 6(w)k
3494(ad-)s 3788(hoc)s 4189(attempts)s 5050(to)s 5291(e)s 3(xtend)k
5985(the)s 6334(usual)s 6896(tree)s 7310(representation)s 8722(had)s
0 12968(f)m 2(ailed,)k 665(the)s 1030(author)s 1718(de)s 6(v)k 3(eloped)k
2769(a)s 2952(representation)s 4379(based)s 5000(on)s 5314(doubly)s
6051(link)s 2(ed)k 6723(lists)s 7175(of)s 7463(records)s
8235(denoting)s 0 12680(links,)m 578(whose)s 1253(\210e)s 3(xibility)k
2240(more)s 2794(than)s 3270(compensated)s 4584(for)s 4929(the)s
5284(some)s 6(what)k 6315(e)s 3(xcessi)k 6(v)k 3(e)k
7282(memory)s 8140(consump)s 8998(-)s 0 12392(tion.)m 536(F)s 3(or)k
925(e)s 3(xample,)k gsave
480 10526 translate
240 fnt3 3282 1526 0 1470 240 288 12 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
338 338 56 282 240 288 12 0 1188 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 128(a)m

grestore
(A) lfigpromotelabels
grestore
338 338 56 282 240 288 12 2944 1188 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 123 105(b)m 
grestore
(B) lfigpromotelabels
grestore
338 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3 128 128(c)m 
grestore
(C) lfigpromotelabels
grestore
338 338 56 282 240 288 12 1472 0 LoutGr2
currentdict end 200 dict begin begin
grestore
338 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore
192 fnt3
118 105(d)m 
grestore
(D) lfigpromotelabels
grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR C@CTR lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
C@CTR C@CTR A@CTR lfigangle C@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR D@CTR lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
D@CTR D@CTR A@CTR lfigangle D@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ B@CTR B@CTR D@CTR lfigangle B@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
D@CTR D@CTR B@CTR lfigangle D@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
end end restore
grestore
0 10075(is)m 210(represented)s 1369(by)s gsave
1135 5559 translate
240 fnt3
6796 4176 0 4120 240 288 12 LoutGraphic
gsave
grestore save gsave 300 dict begin lfigdict begin
grestore
452 1014 0 958 240 288 12 0 3162 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3 180 128(a)m 
grestore
(BASE) lfigpromotelabels
grestore
(A) lfigpromotelabels
grestore
452 1014 0 958 240 288 12 6344 3162 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3
180 105(b)m 
grestore
(BASE) lfigpromotelabels
grestore
(B) lfigpromotelabels
grestore
452 1014 0 958 240 288 12 0 1581 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3 104 107(LK)m

grestore
(BASE) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
452 1014 0 958 240 288 12 1586 1581 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3 104 107(LK)m 
grestore
(BASE) lfigpromotelabels
grestore
(M) lfigpromotelabels
grestore
452 1014 0 958 240 288 12 4758 1581 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3
39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3 104 107(LK)m 
grestore
(BASE) lfigpromotelabels
grestore
(N) lfigpromotelabels
grestore
452 1014 0 958 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3
185 128(c)m 
grestore
(BASE) lfigpromotelabels
grestore
(C) lfigpromotelabels
grestore
452 1014 0 958 240 288 12 3172 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 676 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
gsave
206 150 translate
192 fnt3 39 39 0 39 192 288 48 LoutGraphic
gsave
/lfigblack [ lfigcircle ] gsave lfigpaintpath grestore
0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigcircle ] lfigdopath
pop pop
grestore

grestore

grestore
(TOP) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 338 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(MID) lfigpromotelabels
grestore
452 338 56 282 240 288 12 0 0 LoutGr2
currentdict end 300 dict begin begin
grestore
452 338 56 282 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
192 fnt3 175 105(d)m 
grestore
(BASE) lfigpromotelabels
grestore
(D) lfigpromotelabels
grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ 0.5 cm 0 A@MID@CTR L@MID@CTR A@MID@CTR M@MID@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef
A@MID@CTR L@MID@CTR A@MID@CTR M@MID@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef
BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef
BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef
BL
BR [ BR 0 0.5 cm lfigpadd ]
BR 0.5 cm 0.5 cm lfigpadd
TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ]
TR
TL [ 0 0.5 cm TL lfigpsub ]
0.5 cm 0.5 cm TL lfigpsub
BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ]
BL ] lfigdopath
pop pop
grestore

grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ 0.5 cm 0 L@TOP@CTR C@TOP@CTR L@TOP@CTR C@TOP@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef
L@TOP@CTR C@TOP@CTR L@TOP@CTR C@TOP@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef
BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef
BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef
BL
BR [ BR 0 0.5 cm lfigpadd ]
BR 0.5 cm 0.5 cm lfigpadd
TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ]
TR
TL [ 0 0.5 cm TL lfigpsub ]
0.5 cm 0.5 cm TL lfigpsub
BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ]
BL ] lfigdopath
pop pop
grestore

grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ 0.5 cm 0 M@TOP@CTR D@TOP@CTR N@TOP@CTR D@TOP@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef
M@TOP@CTR D@TOP@CTR N@TOP@CTR D@TOP@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef
BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef
BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef
BL
BR [ BR 0 0.5 cm lfigpadd ]
BR 0.5 cm 0.5 cm lfigpadd
TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ]
TR
TL [ 0 0.5 cm TL lfigpsub ]
0.5 cm 0.5 cm TL lfigpsub
BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ]
BL ] lfigdopath
pop pop
grestore

grestore
0 0 0 0 240 288 12 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ 0.5 cm 0 B@MID@CTR N@MID@CTR B@MID@CTR N@MID@CTR lfigpmin lfigpmin lfigpmin lfigpsub /BL lfigpointdef
B@MID@CTR N@MID@CTR B@MID@CTR N@MID@CTR lfigpmax lfigpmax lfigpmax 0.5 cm 0 lfigpadd /TR lfigpointdef
BL 0 BL TR lfigydistance lfigpadd /TL lfigpointdef
BL BL TR lfigxdistance 0 lfigpadd /BR lfigpointdef
BL
BR [ BR 0 0.5 cm lfigpadd ]
BR 0.5 cm 0.5 cm lfigpadd
TR 0.5 cm -0.5 cm lfigpadd [ 0 0.5 cm TR lfigpsub ]
TR
TL [ 0 0.5 cm TL lfigpsub ]
0.5 cm 0.5 cm TL lfigpsub
BL -0.5 cm 0.5 cm lfigpadd [ BL 0 0.5 cm lfigpadd ]
BL ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 5108(where)m
240 fnt3 645 5110(LK)m 240 fnt1 1017 5108(tags)m 1458(a)s
1630(record)s 2304(representing)s 3543(a)s 3715(link.)s 4257(The)s
4690(\207rst)s 5127(list)s 5484(in)s 5732(an)s 3(y)k
6135(node)s 6663(contains)s 7516(all)s 7815(the)s 8169(incoming)s
0 4820(links,)m 577(the)s 931(second)s 1660(contains)s 2514(the)s
2867(outgoing)s 3778(ones.)s 4387(The)s 4821(node)s 5348(serv)s 3(es)k
5999(as)s 6255(the)s 6609(header)s 7311(for)s 7655(both)s
8144(lists.)s 8698(The)s 0 4532(required)m 890(operations)s 1974(reduce)s
2704(to)s 2979(simple)s 3709(appends,)s 4638(deletes,)s 5444(and)s
5885(tra)s 4(v)k 3(ersals)k 6880(of)s 7187(doubly)s
7944(link)s 2(ed)k 8635(lists,)s 0 4244(all)m 325(ha)s 4(ving)k
1058(small)s 1663(constant)s 2552(cost.)s 3133(There)s 3779(is)s
4021(a)s 4219(highly)s 4918(tuned)s 5540(memory)s 6423(allocator)s 9(,)k
7389(and)s 7825(care)s 8310(is)s 8553(tak)s 2(en)k
0 3956(to)m 269(dispose)s 1073(of)s 1374(each)s 1900(node)s
2452(when)s 3058(the)s 3436(last)s 3858(incoming)s 4845(link)s
5308(is)s 5549(deleted,)s 6376(so)s 6672(that)s 7120(there)s
7684(is)s 7924(no)s 8247(need)s 8788(for)s 0 3668(g)m 1(arbage)k
812(collection.)s 480 3294(In)m 739(normal)s 1475(use)s 1854(the)s
2205(number)s 3000(of)s 3275(nodes)s 3888(at)s 4124(higher)s
4799(le)s 6(v)k 3(els)k 5402(of)s 5676(the)s
6028(dag)s 6431(is)s 6644(small)s 7220(in)s 7467(comparison)s
8644(with)s 0 3006(the)m 351(lea)s 4(v)k 3(es)k
995(and)s 1402(their)s 1903(incoming)s 2863(links,)s 3438(so)s
3707(we)s 4046(may)s 4515(estimate)s 5369(the)s 5720(space)s
6311(comple)s 3(xity)k 7441(at)s 7676(about)s 8271(60)s
8570(bytes)s 0 2718(per)m 355(input)s 896(w)s 2(ord)k
1433(\(20)s 1797(bytes)s 2342(per)s 2696(link,)s 3165(40)s
3449(per)s 3803(leaf)s 4222(node\).)s 4920(Careful)s 5680(optimization)s
6935(could)s 7514(easily)s 8114(halv)s 3(e)k 8674(this,)s
0 2430(b)m 4(ut)k 362(since)s 909(memory)s 1760(is)s
1970(reclaimed)s 2969(after)s 3465(printing)s 4275(each)s 4770(page)s
5278(there)s 5811(is)s 6021(little)s 6513(need.)s 240 fnt2
0 1781(2.5.)m 471(Context-sensiti)s 2(v)k 2(e)k 2274(attrib)s 4(utes)k
3318(of)s 3590(objects)s 
[ /Dest /LOUTstyle /DEST pdfmark
240 fnt1 480 1305(Although)m 1466(we)s
1826(are)s 2198(free)s 2649(to)s 2913(place)s 3498(an)s 3(y)k
3920(object)s 4588(in)s 4856(an)s 3(y)k 5278(conte)s 3(xt,)k
6111(the)s 6484(conte)s 3(xt)k 7270(must)s 7820(in\210uence)s
8778(the)s 0 1017(appearance)m 1131(of)s 1402(the)s 1750(object,)s
2441(since)s 2988(otherwise)s 220 fnt5 480 518(A shor)m -8(t par)k 2(ag)k 2(r)k 2(aph of te)k 6(xt.)k

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 13 14
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5710 -1579(-)m 5838(13)s
6122(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13253(could)m 588(not)s 952(appear)s 1647(in)s
1887(a)s 2051(v)s 6(ariety)k 2760(of)s 3028(fonts,)s
3611(column)s 4384(widths,)s 5126(etc.)s 5566(This)s 6040(in\210uence)s
6970(cannot)s 7666(tak)s 2(e)k 8116(the)s 8461(purely)s
0 12965(static)m 569(form)s 1106(that)s 1538(block-structured)s 3175(languages)s
4196(use)s 4585(to)s 4837(associate)s 5769(v)s 6(alues)k
6438(with)s 6933(identi\207ers,)s 8009(for)s 8360(then)s 8843(an)s
0 12677(operator)m 850(could)s 1434(not)s 1794(in\210uence)s 2721(the)s
3063(appearance)s 4188(of)s 4453(its)s 4723(parameters;)s 5876(and)s
6274(a)s 6434(state)s 6921(v)s 6(ariable)k 7734(solution)s
8556(is)s 8760(not)s 0 12389(compatible)m 1118(with)s 1600(the)s
1948(o)s 3(v)k 3(erall)k 2660(functional)s 3684(design.)s
480 12015(The)m 914(information)s 2105(needed)s 2848(from)s 3378(the)s
3733(conte)s 3(xt)k 4500(seems)s 5141(quite)s 5682(limited,)s
6471(comprising)s 7607(the)s 7961(font)s 8413(f)s 2(amily)k 15(,)k
0 11727(f)m 2(ace,)k 525(and)s 952(size)s 1402(to)s
1664(use,)s 2114(the)s 2485(style)s 3015(of)s 3309(paragraph)s
4345(breaking)s 5259(required,)s 6185(ho)s 6(w)k 6669(much)s
7281(space)s 7891(to)s 8154(substitute)s 0 11439(between)m 873(the)s
1240(w)s 2(ords)k 1893(of)s 2184(paragraphs,)s 3359(and)s
3782(ho)s 6(w)k 4263(much)s 4871(horizontal)s 5914(and)s
6337(v)s 3(ertical)k 7124(space)s 7730(is)s 7959(a)s 4(v)k 6(ailable)k
8887(to)s 0 11151(recei)m 6(v)k 3(e)k 763(the)s
1139(object.)s 1914(These)s 2569(four)s 3054(items)s 3650(constitute)s
4662(the)s 5038(so-called)s 5985(`style)s 6599(information')s 7866(of)s
8165(Lout.)s 8809(As)s 0 10863(graphics)m 902(rendering)s 1912(hardw)s 2(are)k
2896(impro)s 3(v)k 3(es,)k 3928(the)s 4317(style)s
4865(information)s 6091(will)s 6558(probably)s 7504(gro)s 6(w)k
8085(to)s 8366(include)s 0 10575(colour)m 671(and)s 1075(te)s 3(xture)k
1791(information.)s 480 10201(The)m 908(w)s 2(ay)k 1359(to)s
1598(deal)s 2051(with)s 2533(fonts)s 3062(at)s 3294(least)s
3791(is)s 4001(v)s 3(ery)k 4477(clear:)s 220 fnt5
480 9700({ )m 11(Times Slope 12p } @F)k 6(ont { Hello)k 8(, w)k 2(or)k -3(ld })k
240 fnt1 0 9204(should)m 697(ha)s 4(v)k 3(e)k
1198(result)s 240 fnt3 480 8750(Hello,)m 1104(world)s 240 fnt1
0 8268(Lout)m 528(also)s 983(pro)s 3(vides)k 220 fnt5
1872 8265(@Break)m 240 fnt1 2745 8268(and)m 220 fnt5 3166 8265(@Space)m
240 fnt1 4080 8268(symbols)m 4946(for)s 5301(controlling)s 6420(the)s
6785(paragraph)s 7815(breaking)s 8722(and)s 0 7980(space)m 610(styles)s
1229(mentioned)s 2320(abo)s 3(v)k 3(e.)k 3074(These)s
3724(w)s 2(ork)k 4299(in)s 4565(the)s 4937(same)s
5507(w)s 2(ay)k 15(,)k 6020(returning)s 6972(their)s
7493(right)s 8028(parameters)s 0 7692(in)m 261(the)s 627(style)s
1152(of)s 1441(their)s 1956(left.)s 2455(The)s 2901(implementation)s
4476(is)s 4704(v)s 3(ery)k 5198(simple:)s 6019(one)s
6439(merely)s 7174(broadcasts)s 8252(the)s 8619(style)s 0 7404(information)m
1183(do)s 6(wn)k 1765(into)s 2188(the)s 2533(parse)s
3091(tree)s 3502(of)s 3771(the)s 4116(right)s 4625(parameter)s 13(.)k
5728(A)s 5956(font,)s 6445(for)s 6781(e)s 3(xample,)k
7693(is)s 7901(con)s 9(v)k 3(erted)k 8887(to)s
0 7116(an)m 278(8-bit)s 783(internal)s 1562(name)s 2130(and)s
2529(stored)s 3165(in)s 3403(each)s 3892(leaf,)s 4351(while)s
4932(a)s 5093(breaking)s 5977(style)s 6479(is)s 6683(stored)s
7320(in)s 7557(the)s 7900(root)s 8339(node)s 8855(of)s
0 6828(each)m 495(paragraph.)s 480 6454(The)m 954(same)s 1547(language)s
2514(design)s 3242(can)s 3677(be)s 4006(used)s 4549(for)s
4933(a)s 4(v)k 6(ailable)k 5888(width)s 6536(and)s
6986(height,)s 7738(only)s 8264(here)s 8778(the)s 0 6166(implementation)m
1557(is)s 1767(much)s 2356(more)s 2903(demanding:)s 220 fnt5
480 5665(2i @Wide {)m 480 5377(\(1\)  |0.1i  An e)m 6(xample)k 480 5089(containing a small)m 480 4801(par)m 2(ag)k 2(r)k 2(aph of \207lled te)k 6(xt.)k
480 4513(})m 240 fnt1 0 4019(is)m 210(guaranteed)s 1317(to)s
1556(be)s 1838(tw)s 2(o)k 2248(inches)s 2910(wide:)s
480 3516(\(1\))m 891(An)s 1270(e)s 3(xample)k 2162(containing)s
3254(a)s 891 3228(small)m 1504(paragraph)s 2558(of)s 2871(\207lled)s
891 2940(te)m 3(xt.)k 0 2487(One)m 448(must)s 966(calculate)s
1863(that)s 2273(1.9)s 2617(inches)s 3272(minus)s 3900(the)s
4241(width)s 4836(of)s 220 fnt5 5100 2484(\(1\))m 240 fnt1
5406 2487(is)m 5609(a)s 4(v)k 6(ailable)k 6510(to)s
6741(the)s 7082(paragraph,)s 8138(and)s 8534(break)s 0 2199(it)m
186(accordingly;)s 1421(Basser)s 2111(Lout)s 2617(does)s 3100(this)s
3490(in)s 3727(tw)s 2(o)k 4130(stages.)s 4872(In)s
5121(the)s 5463(\207rst,)s 5935(upw)s 2(ard-mo)k 3(ving)k
7505(stage,)s 8097(widths)s 8779(are)s 0 1911(calculated)m 1018(using)s
1581(the)s 1920(formulae)s 2829(of)s 3091(Section)s 3856(2.3,)s
4254(which)s 4887(assume)s 5638(that)s 6047(a)s 4(v)k 6(ailable)k
6946(space)s 7524(is)s 7725(in\207nite.)s 8557(If)s 8778(the)s
0 1623(upw)m 2(ard)k 763(mo)s 3(v)k 3(ement)k
1815(reaches)s 2570(a)s 240 fnt3 2724 1625(WIDE)m 240 fnt1
3375 1623(node,)m 3936(corresponding)s 5346(to)s 5573(a)s 220 fnt5
5728 1620(@Wide)m 240 fnt1 6490 1623(operator)m 9(,)k 7372(and)s
7764(the)s 8100(calculated)s 0 1335(width)m 627(e)s 3(xceeds)k
1457(that)s 1900(allo)s 6(wed,)k 2784(a)s 2975(second,)s
3772(do)s 6(wnw)k 2(ard-mo)k 3(ving)k 5661(stage)s
6234(is)s 6469(initiated)s 7334(which)s 8001(attempts)s 8887(to)s
0 1047(reduce)m 681(the)s 1017(width)s 1606(by)s 1888(\207nding)s
2607(and)s 2999(breaking)s 3877(paragraphs.)s 5077(This)s 5541(second)s
6251(stage)s 6786(is)s 6984(quite)s 7505(routine)s 8226(e)s 3(xcept)k
8894(at)s 220 fnt5 0 756(|)m 240 fnt1 84 759(nodes,)m
736(whose)s 1390(children)s 2216(are)s 2549(the)s 2883(columns)s
3731(of)s 3988(a)s 4141(table.)s 4755(It)s 4946(is)s
5142(necessary)s 6111(to)s 6336(apportion)s 7296(the)s 7630(a)s 4(v)k 6(ailable)k
8524(width)s 0 471(\(minus)m 727(inter)s 4(-column)k 2026(g)s 1(aps\))k
2604(among)s 3321(the)s 3681(columns.)s 4668(Basser)s 5377(Lout)s
5901(lea)s 4(v)k 3(es)k 6554(narro)s 6(w)k
7291(columns)s 8166(unbrok)s 2(en)k 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 14 15
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Bold
%%+ font Symbol
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1579(-)m 5833(14)s
6127(-)s 9066 13419 0 13310 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13256(and)m 404(breaks)s 1079(the)s 1427(remaining)s
2449(columns)s 3311(to)s 3550(equal)s 4123(width,)s 4775(using)s
5347(up)s 5640(all)s 5933(of)s 6204(the)s 6552(a)s 4(v)k 6(ailable)k
7460(space.)s 480 12882(The)m 897(size)s 1313(of)s 1572(an)s
1844(object)s 2476(is)s 2675(not)s 3029(clearly)s 3721(determined)s
4843(when)s 5407(the)s 5744(upw)s 2(ard-mo)k 3(ving)k
7309(size)s 7725(is)s 7923(less)s 8321(than)s 8778(the)s
0 12594(do)m 6(wnw)k 2(ard-mo)k 3(ving)k 1871(a)s 4(v)k 6(ailable)k
2786(space,)s 3431(and)s 3842(the)s 4197(object)s 4849(contains)s
5704(constructs)s 6731(that)s 7156(depend)s 7913(on)s 8218(a)s 4(v)k 6(ailable)k
0 12306(space)m 587(\(e.g.)s 1056(right)s 1567(justi\207cation\).)s 2938(F)s 3(or)k
3327(e)s 3(xample,)k 4241(in)s 220 fnt5 480 11805(2i @Wide { Heading // a |1r)m -8(t b })k
240 fnt1 0 11306(it)m 211(seems)s 865(natural)s 1603(to)s
1861(assign)s 2536(a)s 2721(width)s 3342(of)s 3633(tw)s 2(o)k
4062(inches)s 4744(to)s 5002(the)s 5369(subobject)s 220 fnt5
6366 11303(a |1r)m -8(t b)k 240 fnt1 7124 11306(because)m 7957(of)s
8247(the)s 8615(right)s 0 11018(justi\207cation,)m 1270(b)s 4(ut)k
1667(it)s 1895(w)s 2(ould)k 2585(be)s 2903(equally)s
3696(plausible)s 4650(if)s 4903(the)s 5286(width)s 5924(of)s
220 fnt5 6230 11015(Heading)m 240 fnt1 7129 11018(w)m 2(as)k
7586(assigned)s 8503(to)s 8778(the)s 0 10730(subobject)m 989(instead.)s
1843(The)s 2284(author)s 2968(is)s 3191(conscious)s 4199(of)s
4483(ha)s 4(ving)k 5197(f)s 2(ailed)k 5809(to)s
6061(resolv)s 3(e)k 6817(this)s 7226(matter)s 7908(properly;)s
8843(an)s 0 10442(e)m 3(xtra)k 534(operator)s 1390(for)s
1728(controlling)s 2830(a)s 4(v)k 6(ailable)k 3738(space)s
4325(is)s 4535(probably)s 5440(necessary)s 15(.)k 480 10068(The)m
930(actual)s 1578(paragraph)s 2614(breaking)s 3527(is)s 3759(just)s
4187(a)s 4376(simple)s 5092(transformation)s 6578(on)s 6897(the)s
7268(parse)s 7851(tree;)s 8343(the)s 8714(real)s 0 9780(issue)m
544(is)s 764(ho)s 6(w)k 1235(to)s 1484(describe)s
2346(the)s 2704(v)s 6(arious)k 3463(styles:)s 4183(ragged)s
4902(right,)s 5470(adjusted,)s 6384(outdented,)s 7445(and)s 7859(so)s
8135(on.)s 8549(Their)s 0 9492(di)m 6(v)k 3(ersity)k
874(suggests)s 1729(that)s 2140(the)s 3(y)k 2596(should)s
3286(someho)s 6(w)k 4245(be)s 4519(de\207ned)s 5275(using)s
5840(more)s 6380(basic)s 6917(features;)s 7777(b)s 4(ut)k
8132(then)s 8593(there)s 0 9204(are)m 367(algorithms)s 1461(for)s
1820(high-quality)s 3064(paragraph)s 4098(breaking,)s 5063(which)s 5726(presumably)s
6917(must)s 7463(be)s 7766(b)s 4(uilt-in.)k 8650(This)s
0 8916(dilemma)m 915(w)s 2(as)k 1355(not)s 1741(clearly)s
2463(grasped)s 3285(by)s 3598(the)s 3966(author)s 4656(in)s
4919(1985,)s 5525(and)s 5949(he)s 6250(included)s 7152(a)s
7337(b)s 4(uilt-in)k 8113(paragraph)s 0 8628(break)m 2(er)k 9(,)k
818(with)s 1306(the)s 220 fnt5 1660 8625(@Break)m 240 fnt1
2522 8628(operator)m 3384(selecting)s 4292(from)s 4822(a)s 4995(\207x)s 3(ed)k
5535(set)s 5866(of)s 6143(styles.)s 6857(A)s 7093(much)s
7688(better)s 8298(solution)s 0 8340(based)m 603(on)s 900(g)s 1(alle)k 3(ys)k
1624(will)s 2050(be)s 2332(gi)s 6(v)k 3(en)k
2912(in)s 3155(Section)s 3929(5.5,)s 4336(b)s 4(ut,)k
4745(re)s 3(grettably)k 15(,)k 5868(it)s 6060(is)s
6270(not)s 6636(implemented.)s 240 fnt2 0 7547(3.)m 291(De\207nitions)s

[ /Dest /LOUT18_651_s3_0_1 /DEST pdfmark
240 fnt1 480 7116(The)m 936(need)s 1474(to)s 1741(pro)s 3(vide)k
2554(a)s 2748(means)s 3438(of)s 3737(packaging)s 4803(useful)s
5470(pieces)s 6146(of)s 6445(code)s 6982(for)s 7348(easy)s
7855(repeated)s 8751(use)s 0 6828(w)m 2(as)k 440(recognised)s
1554(in)s 1816(the)s 2184(v)s 3(ery)k 2679(earliest)s
3447(programming)s 4822(languages.)s 5962(This)s 6458(need)s 6987(is)s
7217(e)s 6(v)k 3(en)k 7736(more)s 8303(acute)s
8883(in)s 0 6540(document)m 1004(formatting,)s 2118(if)s 2335(that)s
2752(is)s 2962(possible,)s 3852(because)s 4664(the)s 5012(majority)s
5874(of)s 6145(users)s 6686(are)s 7033(not)s 7398(programmers)s
8722(and)s 0 6252(do)m 293(not)s 659(understand)s 1767(the)s
2115(code)s 2623(the)s 3(y)k 3086(in)s 9(v)k 4(ok)k 2(e.)k
240 fnt2 0 5603(3.1.)m 471(Operators)s 
[ /Dest /LOUToperators /DEST pdfmark
240 fnt1 480 5126(It)m
680(is)s 885(e)s 6(vident)k 1637(from)s 2156(the)s
2498(e)s 3(xample)k 3356(of)s 3621(Eqn)s 4059(that)s
4471(user)s 4(-de\207ned)k 5702(operators)s 6636(are)s 6978(needed)s
7708(that)s 8121(mimic)s 8778(the)s 0 4838(primiti)m 6(v)k 3(e)k
929(ones)s 1426(in)s 1677(taking)s 2335(objects)s 3071(as)s
3328(parameters)s 4434(and)s 4845(returning)s 5781(objects)s 6517(as)s
6774(results.)s 7569(F)s 3(or)k 7965(e)s 3(xample,)k
8887(to)s 0 4550(de\207ne)m 641(a)s 807(superscript)s 1915(operator)s
2771(so)s 3037(that)s 220 fnt5 480 4056(2 sup n)m 240 fnt1
0 3531(appears)m 781(as)s 167 fnt1 1145 3647(n)m 240 fnt4
1031 3525(2)m 240 fnt1 1226 3531(,)m 1333(the)s 1681(follo)s 6(wing)k
2658(operator)s 3514(de\207nition)s 4488(may)s 4954(be)s 5236(used:)s
220 fnt5 480 3032(def sup)m 480 2744(    precedence 50)m 480 2456(    associativity r)m -3(ight)k
480 2168(    left x)m 480 1880(    r)m -3(ight y)k 480 1592({)m 480 1304(    @OneRo)m 3(w {  |  {-2p @F)k 6(ont y}  ^/0.5fk  x  })k
480 1016(})m 240 fnt1 0 520(The)m 220 fnt5 481 517(sup)m
240 fnt1 940 520(operator)m 1850(has)s 2273(precedence)s 3458(50,)s
3858(is)s 4122(right)s 4686(associati)s 6(v)k 3(e,)k
5886(tak)s 2(es)k 6479(tw)s 2(o)k 6943(objects)s
7724(as)s 8028(parameters)s 0 232(passed)m 720(on)s 1041(the)s
1413(left)s 1814(and)s 2242(right,)s 2825(and)s 3253(returns)s
3991(the)s 4363(object)s 5031(between)s 5910(braces)s 6595(as)s
6869(result.)s 7587(This)s 8087(object)s 8756(has)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 15 16
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5709 -1582(-)m 5837(15)s
6123(-)s 9066 13413 0 13304 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13250(the)m 348(structure)s gsave
608 12769 translate
280 fnt3 128 191 0 123 280 288 70 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
128 191 0 123 280 288 70 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
128 191 0 123 280 288 70 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
260 fnt5
0 56(y)m 
grestore

grestore
end end restore
grestore
gsave
480 12634 translate
280 fnt3 128 135 0 67 280 288 70 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
128 135 0 67 280 288 70 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
128 135 0 67 280 288 70 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
260 fnt5 0 0(x)m 
grestore

grestore
end end restore
grestore
0 12183(b)m 4(ut)k
381(with)s 882(the)s 1249(\207rst)s 1699(ro)s 6(w)k
2138(mark)s 2709(hidden)s 3437(by)s 3751(the)s 220 fnt5
4118 12180(@OneRo)m 3(w)k 240 fnt1 5268 12183(operator)m 9(,)k
6181(and)s 220 fnt5 6604 12180(y)m 240 fnt1 6791 12183(tw)m 2(o)k
7220(points)s 7875(smaller)s 8657(than)s 0 11895(it)m 220(w)s 2(ould)k
904(otherwise)s 1917(ha)s 4(v)k 3(e)k 2447(been.)s
3091(The)s 3548(length)s 220 fnt5 4231 11892(0.5f)m 240 fnt1
4683 11895(speci\207es)m 5585(half)s 6057(the)s 6433(current)s 7198(font)s
7671(size;)s 8243(Figure)s 8952(2)s 0 11607(describes)m 936(the)s
220 fnt5 1280 11604(k)m 240 fnt1 1446 11607(g)m 1(ap)k
1840(mode.)s 2532(In)s 2784(the)s 3128(Eq)s 3448(equation)s
4325(formatting)s 5382(package)s 6218([10])s 6651(the)s 6995(equation)s
7872(as)s 8118(a)s 8280(whole)s 8916(is)s 0 11319(set)m
331(in)s 580(italic)s 1116(font,)s 1614(and)s 220 fnt5
2024 11316(2)m 240 fnt1 2203 11319(is)m 2419(an)s 2709(identi\207er)s
3637(whose)s 4311(body)s 4852(contains)s 5706(a)s 5879(font)s
6330(change)s 7070(back)s 7590(to)s 7835(Roman.)s 8698(The)s
0 11031(digits)m 220 fnt5 586 11028(0)m 240 fnt1 765 11031(to)m
220 fnt5 1009 11028(9)m 240 fnt1 1186 11031(are)m 1538(classed)s
2291(as)s 2546(punctuation)s 3737(characters,)s 4816(permitting)s 220 fnt5
5869 11028(234)m 240 fnt1 6293 11031(for)m 6635(e)s 3(xample)k
7503(to)s 7747(be)s 8034(interpreted)s 0 10743(as)m 250(a)s
416(sequence)s 1349(of)s 1620(three)s 2153(identi\207ers.)s 480 10369(These)m
1152(de\207nitions)s 2258(are)s 2650(easily)s 3307(implemented)s 4658(by)s
4997(a)s 5208(standard)s 6122(symbol)s 6927(table)s 7492(and)s
7941(an)s 8270(operator)s 0 10081(precedence)m 1155(parser)s 13(.)k
1914(Algol)s 2539(block)s 3157(structure)s 4073(with)s 4580(the)s
4953(usual)s 5538(scope)s 6164(rules)s 6704(w)s 2(as)k
7150(adopted)s 7991(as)s 8266(a)s 8457(matter)s 0 9793(of)m
271(course.)s 480 9419(Operators)m 1481(are)s 1837(limited)s 2580(to)s
2828(at)s 3069(most)s 3603(tw)s 2(o)k 4022(parameters,)s
5185(left)s 5571(and)s 5984(right,)s 6551(and)s 6964(the)s
7321(parameters)s 8428(cannot)s 0 9131(be)m 282(gi)s 6(v)k 3(en)k
862(def)s 2(ault)k 1583(v)s 6(alues.)k 240 fnt3
2352 9133(Named)m 240 fnt1 3097 9131(parameters)m 4195(solv)s 3(e)k
4753(both)s 5236(problems:)s 220 fnt5 480 8630(def @Pref)m 6(ace)k
480 8342(    named @T)m 26(ag {})k 480 8054(    named @Title { Pref)m 6(ace })k 480 7766(    r)m -3(ight @Body)k
480 7478({)m 480 7190(    Bold @F)m 6(ont @Title)k 480 6902(    //0.3v  @Body)m 480 6614(})m
240 fnt1 0 6120(The)m 452(def)s 2(ault)k 1197(v)s 6(alue)k
1789(appears)s 2594(just)s 3023(after)s 3543(the)s 3915(parameter')s 13(s)k
5103(declaration,)s 6295(between)s 7173(braces.)s 7972(In)s 9(v)k 4(ocations)k
0 5832(ha)m 4(v)k 3(e)k 501(a)s 667(natural)s
1385(syntax:)s 220 fnt5 480 5331(@Pref)m 6(ace)k 480 5043(    @Title { About this book })m
480 4755({)m 480 4467(    F)m 6(e)k 4(w obser)k -6(v)k 5(ers w)k 2(ould ha)k 4(v)k 5(e supposed in 1984, that ...)k
480 4179(})m 240 fnt1 0 3685(with)m 481(the)s 827(actual)s
1450(named)s 2145(parameters)s 3241(follo)s 6(wing)k 4216(directly)s
4998(after)s 5492(the)s 5838(operator)s 9(,)k 6731(before)s
7395(an)s 3(y)k 7790(right)s 8299(parame)s 8998(-)s
0 3397(ter)m 13(.)k 400(In)s 653(this)s 1046(e)s 3(xample,)k
220 fnt5 1958 3394(@T)m 26(ag)k 240 fnt1 2578 3397(will)m
3001(recei)s 6(v)k 3(e)k 3735(its)s 4008(def)s 2(ault)k
4726(v)s 6(alue,)k 5342(and)s 5744(a)s 5907(less)s
6313(e)s 3(xpert)k 6965(user)s 7420(could)s 8007(safely)s
8628(omit)s 0 3109(the)m 220 fnt5 348 3106(@Title)m 240 fnt1
1036 3109(parameter)m 2050(as)s 2300(well.)s 480 2735(Lout)m 1007(permits)s
1790(named)s 2502(parameters)s 3616(to)s 3870(ha)s 4(v)k 3(e)k
4387(parameters,)s 5557(a)s 5739(feature)s 6472(with)s 6970(applications)s
8192(to)s 8447(biblio)s 8998(-)s 0 2447(graphic)m 781(databases,)s
1816(running)s 2626(headers,)s 3475(and)s 3891(other)s 4454(places)s
5114(where)s 5766(a)s 5944(format)s 6652(has)s 7034(to)s
7285(be)s 7579(supplied)s 8460(before)s 0 2159(content)m 760(is)s
965(kno)s 6(wn.)k 1771(One)s 2221(could)s 2806(go)s
3094(further)s 3798(and)s 4197(pro)s 3(vide)k 4976(a)s
5137(complete)s 6064(lambda)s 6823(calculus,)s 7708(with)s 8185(functions)s
0 1871(as)m 250(\207rst-)s 689(class)s 1204(objects,)s 1988(pro)s 3(vided)k
2894(care)s 3347(w)s 2(as)k 3768(tak)s 2(en)k
4341(not)s 4707(to)s 4946(intimidate)s 5970(the)s 6318(non-)s
6746(e)s 3(xpert)k 7400(user)s 13(.)k 240 fnt2
0 1222(3.2.)m 471(Recursion)s 1563(and)s 2004(page)s 2539(lay)s 6(out)k

[ /Dest /LOUTrecursion /DEST pdfmark
240 fnt1 480 745(Design)m 1302(and)s 1794(implementation)s 3439(should)s
4223(proceed)s 5126(together)s 6057(in)s 6387(e)s 3(xploratory)k
7628(projects,)s 8579(since)s 0 457(otherwise)m 988(the)s 1340(design)s
2025(too)s 2388(easily)s 3003(becomes)s 3894(unrealistic.)s 5056(Sometimes)s
6173(the)s 6524(implementation)s 8085(does)s 8579(more)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 16 17
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1581(-)m 5833(16)s
6126(-)s 9066 13414 0 13305 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13251(than)m 469(its)s 745(designer)s 1615(intended.)s
2603(The)s 3031(author)s 3702(wrote)s 4302(the)s 4650(follo)s 6(wing)k
5627(purely)s 6292(as)s 6542(a)s 6708(testing)s 7398(scaf)s 6(fold:)k
220 fnt5 480 12750(def @P)m 8(age r)k -3(ight x)k 480 12462({)m
480 12174(    8i @Wide 11i @High)m 480 11886(    {)m 480 11598(        //1i  ||1i  x  ||1i)m 480 11310(        //1i)m 480 11022(    })m
480 10734(})m 240 fnt1 0 10240(Only)m 518(afterw)s 2(ards)k
1558(did)s 1906(he)s 2172(realize)s 2848(its)s 3108(signi\207cance:)s
4400(the)s 4732(concept)s 5521(of)s 5776(a)s 5926(page)s
6418(had)s 6807(been)s 7300(de\207ned)s 8047(outside)s 8778(the)s
0 9952(implementation,)m 1619(remo)s 3(ving)k 2598(the)s 2959(need)s
3481(for)s 3831(commands)s 4932(for)s 5282(setting)s 5984(page)s
6505(width)s 7119(and)s 7535(height,)s 8253(mar)s 4(gins,)k
0 9664(and)m 404(so)s 670(on.)s 480 9290(De\207ning)m 1393(a)s
1582(sequence)s 2538(of)s 2831(pages)s 3450(is)s 3683(harder)s 9(,)k
4414(since)s 4983(their)s 5503(number)s 6317(is)s 6550(not)s
6938(kno)s 6(wn)k 7665(in)s 7931(adv)s 6(ance.)k
8896(A)s 0 9002(simple)m 693(v)s 3(ersion)k 1451(of)s
1722(this)s 2118(same)s 2665(problem)s 3522(is)s 3732(af)s 6(forded)k
4593(by)s 4887(the)s 5235(leaders)s 5962(found)s 6579(in)s
6822(tables)s 7430(of)s 7701(contents:)s 480 8497(Chapter)m 1297(7)s
1525(..)s 1809(..)s 2093(..)s 2377(..)s 2661(..)s
2945(..)s 3229(..)s 3513(..)s 3797(..)s 4081(..)s
4365(..)s 4649(..)s 4933(..)s 5217(..)s 5501(..)s
5785(..)s 6009(53)s 0 7994(This)m 476(seemed)s 1251(to)s
1490(require)s 2222(recursion,)s 3218(speci\207cally)s 4360(the)s 4708(de\207nition)s
220 fnt5 480 7493(def @Leaders { ..)m 13(   @Leaders })k 240 fnt1 0 6999(Note)m
535(that)s 968(both)s 220 fnt5 1465 6996(..)m 240 fnt1
1643 6999(and)m 220 fnt5 2061 6996(@Leaders)m 240 fnt1 3145 6999(are)m
3506(objects,)s 4305(so)s 4585(the)s 4948(tw)s 2(o)k
5372(spaces)s 6062(separating)s 7111(them)s 7664(are)s 8026(signi\207cant.)s
0 6711(No)m 361(base)s 858(case)s 1341(is)s 1567(gi)s 6(v)k 3(en,)k
2213(and)s 2633(indeed)s 3345(we)s 3696(ha)s 4(v)k 3(e)k
4213(no)s 4522(boolean)s 5353(or)s 5628(conditional)s 6775(operators)s
7731(with)s 8229(which)s 8887(to)s 0 6423(e)m 3(xpress)k
757(it;)s 993(b)s 4(ut)k 1346(we)s 1673(can)s
2053(adopt)s 2637(the)s 2977(implicit)s 3770(base)s 4243(`if)s
4530(space)s 5109(is)s 5311(not)s 5668(suf\207cient,)s 6656(delete)s
220 fnt5 7273 6420(@Leaders)m 240 fnt1 8334 6423(and)m 8729(an)s 3(y)k
0 6135(preceding)m 996(space'.)s 1770(Then)s 2319(the)s 2667(e)s 3(xpression)k
220 fnt5 480 5634(4i @Wide { Chapter 7  @Leaders  53 })m 240 fnt1 0 5138(will)m 417(produce)s
1234(the)s 1572(object)s 2206(sho)s 6(wn)k 2873(abo)s 3(v)k 3(e.)k
3593(It)s 3788(is)s 3988(hard)s 4461(to)s 4691(see)s
5042(ho)s 6(w)k 5493(this)s 5879(base)s 6350(could)s
6930(be)s 7202(made)s 7766(e)s 3(xplicit,)k 8576(with)s
8998(-)s 0 4850(out)m 348(violating)s 1232(the)s 1561(general)s
2301(principle)s 3187(of)s 3439(k)s 2(eeping)k 4230(all)s
4504(size)s 4912(information)s 6079(internal.)s 6953(In)s 7190(the)s
7519(implementation,)s 220 fnt5 0 4559(@Leaders)m 240 fnt1 1071 4562(remains)m
1881(une)s 3(xpanded)k 3097(while)s 3686(sizes)s 4204(are)s
4554(being)s 5142(calculated;)s 6224(then)s 6696(it)s 6891(is)s
7103(treated)s 7813(similarly)s 8718(to)s 8960(a)s 0 4274(recepti)m 6(v)k 3(e)k
922(symbol,)s 1734(with)s 2216(its)s 2492(body)s 3026(as)s
3276(an)s 3559(incoming)s 4516(g)s 1(alle)k 3(y)k
5150(\(Section)s 6003(5.2\).)s 480 3900(W)m 9(ith)k 1014(this)s
1418(settled,)s 2156(it)s 2356(is)s 2574(no)s 6(w)k
3044(clear)s 3575(ho)s 6(w)k 4044(to)s 4291(de\207ne)s
4940(a)s 5115(document)s 6127(which)s 6777(is)s 6995(a)s
7169(numbered)s 8193(sequence)s 0 3612(of)m 271(pages.)s 980(Let)s
220 fnt5 1358 3609(@Ne)m 6(xt)k 240 fnt1 2082 3612(be)m
2364(a)s 2530(pre\207x)s 3143(operator)s 3999(which)s 4641(returns)s
5355(its)s 5631(parameter)s 6645(plus)s 7095(one.)s 7605(Then)s
220 fnt5 480 3111(def @P)m 8(ageList)k 480 2823(    r)m -3(ight @P)k 8(ageNum)k
480 2535({)m 480 2247(    @P)m 8(age {)k 480 1959(          |0.5r)m -8(t - @P)k 8(ageNum -)k
480 1671(          //1v   @T)m 26(e)k 6(xtPlace)k 480 1383(          //1r)m -8(t  @F)k 6(ootSect)k
480 1095(    })m 480 807(    //)m 480 519(    @P)m 8(ageList @Ne)k 6(xt @P)k 8(ageNum)k
480 231(})m 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 17 18
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5708 -1579(-)m 5836(17)s
6124(-)s 9066 13418 0 13418 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13255(when)m 576(in)s 9(v)k 4(ok)k 2(ed)k
1391(in)s 1634(the)s 1982(e)s 3(xpression)k 220 fnt5
3059 13252(@P)m 8(ageList 1)k 240 fnt1 4267 13255(,)m 4374(has)s
4744(for)s 5082(its)s 5358(result)s 5948(the)s 6296(potentially)s
7372(in\207nite)s 8105(object)s 1927 2494 0 2494 240 288 60 480 10421 LoutGr2
0 0 moveto xsize 0 lineto xsize ysize lineto
0 ysize lineto closepath stroke
grestore
160 fnt1 845 2216(-)m 931(1)s
1035(-)s 140 fnt5 170 2000(@T)m 16(e)k 4(xtPlace)k
170 173(@F)m 4(ootSect)k 
grestore
1927 2494 0 2494 240 288 60 480 7927 LoutGr2
0 0 moveto xsize 0 lineto xsize ysize lineto
0 ysize lineto closepath stroke
grestore
160 fnt1 839 2216(-)m 925(2)s
1041(-)s 140 fnt5 170 2000(@T)m 16(e)k 4(xtPlace)k
170 173(@F)m 4(ootSect)k 
grestore
140 fnt5 480 7712(@P)m 5(ageList 3)k
240 fnt1 0 7230(Similarly)m 15(,)k 980(we)s 1315(may)s
1781(de\207ne)s 220 fnt5 2422 7227(@F)m 6(ootSect)k 240 fnt1
3573 7230(lik)m 2(e)k 3985(this:)s 220 fnt5 480 6729(def @F)m 6(ootSect)k
480 6441({)m 480 6153(    def @F)m 6(ootList)k 480 5865(        r)m -3(ight @Num)k
480 5577(    {)m 480 5289(        @F)m 6(ootPlace)k 480 5001(        //1v)m 480 4713(        @F)m 6(ootList @Ne)k 6(xt @Num)k
480 4425(    })m 480 3849(    1i @Wide @HLine)m 480 3561(    //1v)m 480 3273(    @F)m 6(ootList 1)k
480 2985(})m 240 fnt1 0 2491(so)m 266(that)s 684(an)s
967(in)s 9(v)k 4(ocation)k 2021(of)s 220 fnt5
2292 2488(@F)m 6(ootSect)k 240 fnt1 3443 2491(produces)m gsave
480 2151 translate
220 fnt5
1440 0 0 0 220 288 61 LoutGraphic
gsave
0 0 moveto xsize 0 lineto stroke
grestore

grestore
220 fnt5 480 1806(@F)m 6(ootPlace)k 480 1518(@F)m 6(ootPlace)k
480 1230(@F)m 6(ootPlace)k 480 942(...)m 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 18 19
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Bold
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5708 -1579(-)m 5836(18)s
6123(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13253(The)m 476(e)s 3(xpansion)k 1550(process)s
2367(is)s 2626(v)s 3(ery)k 3150(similar)s 3921(to)s
4209(a)s 4424(BNF)s 4997(deri)s 6(v)k 6(ation,)k
6109(and)s 6562(w)s 2(ould)k 7266(be)s 7597(attempted)s
8646(only)s 0 12965(on)m 297(demand.)s 480 12591(Clearly)m 15(,)k
1276(deciding)s 2154(which)s 2797(e)s 3(xpansions)k 3910(to)s
4150(tak)s 2(e)k 4603(and)s 5008(replacing)s 220 fnt5
5951 12588(@T)m 26(e)k 6(xtPlace)k 240 fnt1 7170 12591(and)m
220 fnt5 7575 12588(@F)m 6(ootPlace)k 240 fnt1 8832 12591(by)m
0 12303(the)m 338(appropriate)s 1471(actual)s 2085(te)s 3(xt)k
2489(will)s 2904(not)s 3259(be)s 3530(easy;)s 4056(this)s
4441(is)s 4640(the)s 4977(subject)s 5703(of)s 5963(Section)s
6726(5.1.)s 7179(The)s 7596(important)s 8574(point)s 0 12015(for)m
331(no)s 6(w)k 784(is)s 986(that)s 1397(we)s
1724(ha)s 4(v)k 3(e)k 2217(here)s 2677(a)s
2835(v)s 3(ery)k 3303(simple)s 3989(and)s 4385(\210e)s 3(xible)k
5147(method)s 5916(of)s 6179(specifying)s 7220(the)s 7561(layout)s
8211(of)s 8474(pages,)s 0 11727(which)m 642(requires)s 1462(no)s
1755(specialized)s 2874(language)s 3794(features.)s 240 fnt2 0 11079(3.3.)m
471(Modules)s 
[ /Dest /LOUTmodules /DEST pdfmark
240 fnt1 480 10648(It)m 679(is)s 882(well)s
1342(accepted)s 2229(that)s 2641(the)s 2982(visibility)s 3879(of)s
4143(symbols)s 4986(is)s 5189(not)s 5549(adequately)s 6632(controlled)s
7653(by)s 7940(Algol)s 8533(block)s 0 10360(structure.)m 999(The)s
1427(author)s 2098(is)s 2308(a)s 3(w)k 2(are)k
2929(of)s 3200(se)s 6(v)k 3(eral)k 3922(major)s
4539(problems)s 5480(of)s 5751(this)s 6147(kind)s 6631(in)s
6874(document)s 7878(formatting.)s 480 9986(One)m 976(problem)s 1874(is)s
2126(that)s 2585(some)s 3187(symbols)s 4078(should)s 4816(be)s
5139(visible)s 5874(only)s 6395(within)s 7104(restricted)s 8091(parts)s
8647(of)s 8960(a)s 0 9698(document.)m 1108(F)s 3(or)k
1497(e)s 3(xample,)k 2411(we)s 2746(naturally)s 3649(e)s 3(xpect)k
4330(equation)s 5211(formatting)s 6272(to)s 6511(be)s 6793(accomplished)s
8166(lik)s 2(e)k 8578(this:)s 220 fnt5 480 9201(surrounding te)m 6(xt)k
480 8913(@Eq { {x sup 2  +  1} o)m 3(v)k 5(er 4 })k 480 8625(surrounding te)m 6(xt)k
240 fnt1 0 8126(with)m 482(the)s 830(symbols)s 220 fnt5
1679 8123(sup)m 240 fnt1 2025 8126(,)m 220 fnt5 2132 8123(o)m 3(v)k 5(er)k
240 fnt1 2551 8126(,)m 2658(etc.,)s 3103(visible)s 3796(only)s
4276(within)s 4944(the)s 5292(equation,)s 6223(not)s 6589(in)s
6832(the)s 7180(surrounding)s 8390(te)s 3(xt.)k 480 7752(It)m
695(seems)s 1341(natural)s 2069(to)s 2319(de\207ne)s 2970(these)s
3528(symbols)s 4387(within)s 220 fnt5 5066 7749(@Eq)m 240 fnt1
5544 7752(,)m 5661(since)s 6219(the)s 3(y)k 6692(are)s
7050(local)s 7579(to)s 7829(equations.)s 8921(It)s 0 7464(only)m
494(remains)s 1316(then)s 1799(to)s 2053(decree)s 2746(that)s
3179(symbols)s 4043(local)s 4576(to)s 220 fnt5 4830 7461(@Eq)m
240 fnt1 5382 7464(are)m 5744(to)s 5998(be)s 6294(visible)s
7002(within)s 7684(its)s 7975(actual)s 8615(right)s 0 7176(parameter)m 9(,)k
1052(and)s 1456(this)s 1852(is)s 2062(done)s 2584(by)s
2878(replacing)s 3820(the)s 4168(right)s 4679(formal)s 5370(parameter)s
6384(with)s 6866(a)s 240 fnt3 7032 7178(body)m 240 fnt1
7554 7176(parameter:)m 220 fnt5 480 6690(e)m 6(xpor)k -8(t sup o)k 3(v)k 5(er)k
480 6402(def @Eq)m 480 6114(    body @Body)m 480 5826({)m 480 5538(    def sup ...)m 480 5250(    def o)m 3(v)k 5(er ...)k
480 4674(    Slope @F)m 6(ont @Body)k 480 4386(})m 240 fnt1 0 3892(The)m
220 fnt5 426 3889(e)m 6(xpor)k -8(t)k 240 fnt1
1092 3892(clause)m 1743(lists)s 2176(the)s 2522(identi\207ers)s 3526(which)s
4166(are)s 4511(permitted)s 5482(to)s 5719(be)s 5999(visible)s
6690(outside)s 7435(their)s 7930(usual)s 8488(range,)s 0 3604(the)m
359(body)s 905(of)s 220 fnt5 1188 3601(@Eq)m 240 fnt1
1666 3604(;)m 1790(and)s 2206(the)s 220 fnt5 2566 3601(body)m
240 fnt1 3112 3604(declaration)m 4241(imports)s 5034(them)s 5584(into)s
6021(\(mak)s 2(es)k 6772(them)s 7322(visible)s 8027(within\))s
8778(the)s 0 3316(actual)m 614(right)s 1114(parameter)s 2117(of)s
2376(each)s 2860(in)s 9(v)k 4(ocation)k 3903(of)s
220 fnt5 4162 3313(@Eq)m 240 fnt1 4640 3316(.)m 4793(This)s
5258(arrangement)s 6500(has)s 6859(pro)s 3(v)k 3(en)k
7564(v)s 3(ery)k 8028(con)s 9(v)k 3(enient)k
0 3028(for)m 338(de\207ning)s 1176(a)s 1342(v)s 6(ariety)k
2053(of)s 2324(special-purpose)s 3880(packages.)s 480 2654(Another)m 1361(problem)s
2256(arises)s 2888(when)s 3502(global)s 4193(symbols,)s 5136(such)s
5669(as)s 5957(the)s 6343(ones)s 6871(used)s 7406(for)s
7782(headings)s 8722(and)s 0 2366(paragraph)m 1034(separators,)s 2130(call)s
2550(on)s 2868(v)s 6(alues)k 3545(that)s 3984(the)s
4353(non-e)s 3(xpert)k 5468(user)s 5947(will)s 6394(need)s
6925(to)s 7185(modify)s 15(,)k 7989(such)s 8506(as)s
8778(the)s 0 2078(initial)m 605(font)s 1044(or)s 1297(paragraph)s
2303(indent.)s 3059(These)s 3680(v)s 6(alues)k 4329(are)s
4670(lik)s 2(e)k 5076(parameters)s 6167(of)s 6432(the)s
6774(document)s 7771(as)s 8015(a)s 8175(whole,)s 8860(so)s
0 1790(it)m 192(is)s 402(natural)s 1120(to)s 1359(try)s
1678(this:)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 19 20
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5706 -1579(-)m 5834(19)s
6125(-)s 9066 13414 0 13310 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
220 fnt5 480 13253(e)m 6(xpor)k -8(t @Heading @PP ...)k
480 12965(def @BookLa)m 6(y)k 4(out)k 480 12677(    named @InitialF)m 6(ont { )k 11(Times Base 12p })k
480 12389(    named @InitialBreak { adjust 14p })m 480 12101(    named @ColumnWidth { 6i })m 480 11813(    ...)m 480 11525({)m 480 11237(    def @Heading ...)m
480 10949(    def @PP ...)m 480 10661(})m 240 fnt1 0 10167(No)m 6(w)k
220 fnt5 579 10164(@Heading)m 240 fnt1 1732 10167(and)m 220 fnt5
2202 10164(@PP)m 240 fnt1 2833 10167(may)m 3365(in)s 9(v)k 4(ok)k 2(e)k
220 fnt5 4124 10164(@InitialF)m 6(ont)k 240 fnt1 5411 10167(and)m
5881(the)s 6295(other)s 6911(parameters.)s 8188(T)s 19(o)k
8554(mak)s 2(e)k 220 fnt5 0 9876(@Heading)m 240 fnt1
1100 9879(and)m 220 fnt5 1517 9876(@PP)m 240 fnt1 2096 9879(visible)m
2802(throughout)s 3926(the)s 4287(document,)s 5352(we)s 5700(need)s
6223(only)s 6716(add)s 7133(a)s 7312(body)s 7859(parameter)s
8887(to)s 220 fnt5 0 9588(@BookLa)m 6(y)k 4(out)k
240 fnt1 1428 9591(and)m 1832(present)s 2582(the)s 2930(entire)s
3529(document)s 4533(as)s 220 fnt5 480 9090(@BookLa)m 6(y)k 4(out)k
480 8802(    @InitialF)m 6(ont { Helv)k 5(etica Base 10p })k 480 8514(    @InitialBreak { adjust 12p })m 480 8226({)m
480 7938(    )m 11(The document.)k 480 7650(})m 240 fnt1 0 7156(b)m 4(ut)k
383(for)s 742(practical)s 1639(reasons)s 2429(gi)s 6(v)k 3(en)k
3030(belo)s 6(w)k 3684(we)s 4040(prefer)s 4691(not)s
5078(to)s 5338(enclose)s 6132(the)s 6502(entire)s 7122(document)s
8147(in)s 8412(braces.)s 0 6868(Instead,)m 797(we)s 1132(write)s
220 fnt5 480 6386(@Use { @BookLa)m 6(y)k 4(out)k 480 6098(    @InitialF)m 6(ont { Helv)k 5(etica Base 10p })k
480 5810(    @InitialBreak { adjust 12p })m 480 5522(})m 480 5234(The document.)m 240 fnt1 0 4780(which)m
643(has)s 1015(the)s 1365(same)s 1914(ef)s 6(fect:)k
220 fnt5 2617 4777(@Use)m 240 fnt1 3284 4780(mak)m 2(es)k
3946(the)s 4296(e)s 3(xported)k 5190(symbols)s 6040(of)s
220 fnt5 6313 4777(@BookLa)m 6(y)k 4(out)k 240 fnt1
7743 4780(visible)m 8438(for)s 8778(the)s 0 4492(remainder)m 1028(of)s
1299(the)s 1647(document,)s 2698(and)s 3102(is)s 3312(permitted)s
4285(only)s 4765(at)s 4997(the)s 5345(be)s 3(ginning.)k
480 4118(The)m 925(third)s 1451(feature)s 2187(that)s 2622(af)s 6(fects)k
3319(visibility)s 15(,)k 4278(and)s 4699(which)s 5359(will)s
5802(pro)s 3(v)k 3(e)k 6414(useful)s 7071(for)s
7426(cross)s 7986(referencing)s 0 3830(\(Section)m 851(6.1\),)s 1335(is)s
1543(the)s 220 fnt5 1889 3827(@Open)m 240 fnt1 2693 3830(symbol.)m
3560(It)s 3763(mak)s 2(es)k 4421(the)s 4767(e)s 3(xported)k
5657(symbols)s 6504(of)s 6773(its)s 7047(left)s 7422(parameter)s
8433(visible)s 0 3542(within)m 668(its)s 944(right)s 1455(parameter)s 9(,)k
2507(and)s 2911(is)s 3121(therefore)s 4038(similar)s 4760(to)s
4999(the)s 5347(P)s 3(ascal)k 220 fnt5 6009 3539(with)m
240 fnt1 6444 3542(statement.)m 480 3168(It)m 698(could)s 1301(be)s
1596(ar)s 4(gued)k 2314(that)s 2745(Lout)s 3270(is)s
3493(o)s 3(v)k 3(er)k 4(-supplied)k 4869(with)s
5364(these)s 5924(visibility)s 6840(modifying)s 7903(features:)s 8778(the)s
0 2880(body)m 544(parameter)s 9(,)k 220 fnt5 1606 2877(@Use)m
240 fnt1 2282 2880(and)m 220 fnt5 2696 2877(@Open)m 240 fnt1
3513 2880(do)m 3816(not)s 4193(seem)s 4754(suf\207ciently)s 5894(dif)s 6(ferent)k
6779(from)s 7314(each)s 7819(another)s 13(.)k 8698(The)s
220 fnt5 0 2589(@Open)m 240 fnt1 806 2592(symbol)m 1566(is)s
1776(the)s 2124(most)s 2649(general,)s 3459(being)s 4044(capable)s
4830(of)s 5101(replacing)s 6043(the)s 6391(other)s 6942(tw)s 2(o.)k
7463(F)s 3(or)k 7852(e)s 3(xample,)k 220 fnt5
480 2091(@Use { x })m 480 1803(@Use { y })m 480 1515(Body of document)m 240 fnt1 0 1017(can)m
389(be)s 671(replaced)s 1538(by)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 20 21
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Bold
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5704 -1579(-)m 5832(20)s
6127(-)s 9066 13416 0 13312 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
220 fnt5 480 13255(x @Open {)m 480 12967(y @Open {)m 480 12679(Body of document)m
480 12391(}})m 240 fnt1 0 11897(and,)m 453(taking)s 1104(the)s
220 fnt5 1452 11894(@Eq)m 240 fnt1 1990 11897(symbol)m 2750(abo)s 3(v)k 3(e)k
3372(as)s 3622(e)s 3(xample,)k 4536(we)s 4871(could)s
5461(eliminate)s 6405(its)s 6681(body)s 7215(parameter)s 9(,)k
8267(add)s 220 fnt5 480 11396(def @Body r)m -3(ight x { Slope @F)k 6(ont x })k
240 fnt1 0 10897(to)m 239(the)s 587(e)s 3(xported)k
1479(de\207nitions)s 2540(of)s 220 fnt5 2811 10894(@Eq)m 240 fnt1
3289 10897(,)m 3396(and)s 3800(replace)s 220 fnt5 480 10396(@Eq { object })m
240 fnt1 0 9899(by)m 220 fnt5 480 9398(@Eq @Open { @Body { object } })m 240 fnt1
0 8898(If)m 220 fnt5 232 8895(@Eq)m 240 fnt1 772 8898(is)m
985(a)s 1153(g)s 1(alle)k 3(y)k 1790(\(Section)s
2645(5.1\),)s 220 fnt5 3133 8895(@Body)m 240 fnt1 3917 8898(must)m
4444(tak)s 2(e)k 4899(o)s 3(v)k 3(er)k
5380(that)s 5800(function.)s 6764(But)s 7172(one)s 7577(w)s 2(ould)k
8234(not)s 8603(w)s 2(ant)k 0 8610(to)m 253(write)s
813(these)s 1374(clumsy)s 2133(e)s 3(xpressions)k 3311(in)s
3568(practice,)s 4444(and)s 4862(the)s 5224(enclosure)s 6210(of)s
6495(lar)s 4(ge)k 7038(quantities)s 8032(of)s 8317(input)s
8883(in)s 0 8322(e)m 3(xtra)k 534(braces)s 1195(could)s
1785(cause)s 2372(Basser)s 3069(Lout)s 3581(to)s 3820(run)s
4196(out)s 4562(of)s 4833(memory)s 5684(\(Section)s 6537(5.4\).)s
480 7948(A)m 700(quite)s 1224(separate)s 2052(kind)s 2526(of)s
2786(visibility)s 3679(problem)s 4526(arises)s 5110(when)s 5676(e)s 3(xpert)k
6319(users)s 6851(wish)s 7350(to)s 7579(de\207ne)s 8210(an)s
8482(object)s 0 7660(or)m 259(operator)s 1115(for)s 1453(repeated)s
2320(use)s 2695(within,)s 3413(say)s 15(,)k 3824(equations:)s
220 fnt5 480 7161(def isum { sum from i=1 to n })m 240 fnt1 0 6667(As)m 338(it)s
551(stands)s 1221(this)s 1638(can)s 2048(only)s 2549(be)s
2852(placed)s 3555(within)s 4244(the)s 220 fnt5 4613 6664(@Eq)m
240 fnt1 5172 6667(package)m 6033(itself,)s 6637(where)s 220 fnt5
7298 6664(sum)m 240 fnt1 7780 6667(and)m 8205(the)s 8575(other)s
0 6379(symbols)m 841(are)s 1179(visible,)s 1915(b)s 4(ut)k
2268(it)s 2451(is)s 2653(not)s 3010(desirable)s 3919(to)s
4150(modify)s 4886(the)s 5225(source)s 5897(code)s 6396(of)s
6658(a)s 6816(standard)s 7675(package.)s 8614(Lout)s 0 6091(pro)m 3(vides)k
872(an)s 220 fnt5 1155 6088(impor)m -8(t)k 240 fnt1
1828 6091(clause)m 2481(to)s 2720(solv)s 3(e)k 3278(this)s
3674(problem:)s 220 fnt5 480 5590(impor)m -8(t @Eq)k 480 5302(def isum { sum from i=1 to n })m
240 fnt1 0 4808(may)m 469(appear)s 1169(after)s 220 fnt5
1669 4805(@Eq)m 240 fnt1 2210 4808(is)m 2423(de\207ned,)s 3239(and)s
3646(it)s 3842(will)s 4271(mak)s 2(e)k 4846(the)s
5198(e)s 3(xported)k 6093(symbols)s 6945(of)s 220 fnt5
7220 4805(@Eq)m 240 fnt1 7761 4808(visible)m 8458(within)s 0 4520(the)m
335(body)s 855(of)s 220 fnt5 1112 4517(isum)m 240 fnt1
1561 4520(.)m 1711(This)s 2174(feature)s 2878(complicates)s 4056(the)s
4390(treatment)s 5337(of)s 5595(en)s 9(vironments)k 6925(\(Section)s
7764(3.4\),)s 8236(and)s 8626(e)s 6(v)k 3(en)k
0 4232(introduces)m 1050(an)s 1336(insecurity)s 15(,)k 2373(when)s
220 fnt5 2952 4229(isum)m 240 fnt1 3464 4232(is)m 3677(in)s 9(v)k 4(ok)k 2(ed)k
4495(outside)s 5245(an)s 5531(equation.)s 6522(A)s 6755(simpler)s
7534(approach)s 8471(w)s 2(ould)k 0 3944(be)m 290(to)s
538(allo)s 6(w)k 1126(only)s 1615(one)s 2026(symbol)s
2795(in)s 3047(an)s 220 fnt5 3339 3941(impor)m -8(t)k
240 fnt1 4020 3944(clause,)m 4733(and)s 5146(treat)s 5638(the)s
5995(follo)s 6(wing)k 6981(de\207nition)s 7964(e)s 3(xactly)k
8714(lik)s 2(e)k 0 3656(a)m 174(local)s 702(de\207nition)s
1684(of)s 1964(that)s 2390(symbol;)s 3216(b)s 4(ut)k
3587(then)s 4064(it)s 4265(w)s 2(ould)k 4928(not)s
5303(be)s 5594(possible)s 6442(to)s 6690(de\207ne)s 7339(symbols)s
8197(using)s 8778(the)s 0 3368(resources)m 953(of)s 1224(more)s
1771(than)s 2240(one)s 2642(of)s 2913(the)s 3261(standard)s
4129(packages.)s 240 fnt2 0 2719(3.4.)m 471(Implementation)s 2159(of)s
2431(de\207nitions)s 
[ /Dest /LOUTdefs_impl /DEST pdfmark
240 fnt1 480 2242(Input)m 1089(is)s 1343(processed)s
2388(by)s 2726(a)s 2936(h)s 1(ybrid)k 3663(parser)s
4350(which)s 5036(emplo)s 2(ys)k 5940(operator)s 6840(precedence)s
8015(for)s 8398(objects)s 0 1954(and)m 433(simple)s 1156(recursi)s 6(v)k 3(e)k
2108(descent)s 2915(for)s 3283(the)s 3661(headers)s 4472(of)s
4772(de\207nitions.)s 5976(A)s 6236(symbol)s 7026(table)s 7576(stores)s
8214(the)s 8592(body)s 0 1666(of)m 278(each)s 780(de\207nition)s
1761(as)s 2018(a)s 2191(parse)s 2758(tree,)s 3229(e)s 3(xcept)k
3917(for)s 4263(macros)s 5011(which)s 5660(are)s 6014(lists)s
6456(of)s 6734(tok)s 2(ens,)k 7471(and)s 7882(manages)s
8778(the)s 0 1378(usual)m 564(stack)s 1121(of)s 1397(static)s
1958(scopes,)s 2708(accepting)s 240 fnt3 3682 1380(PushScope)m 240 fnt1
4791 1378(and)m 240 fnt3 5200 1380(P)m 19(opScope)k 240 fnt1
6197 1378(operations)m 7249(as)s 7504(the)s 7857(parser)s 8505(enters)s
0 1090(and)m 447(lea)s 4(v)k 3(es)k 1131(scope)s
1775(re)s 3(gions,)k 2626(including)s 3627(actual)s 4295(body)s
4872(parameters)s 6013(and)s 6461(the)s 6852(right)s 7406(parameter)s
8463(of)s 8778(the)s 220 fnt5 0 799(@Open)m 240 fnt1
806 802(operator)m 13(.)k 480 428(As)m 818(the)s 1187(parse)s
1769(proceeds,)s 2747(a)s 2934(complete)s 3888(call)s 4308(graph)s
4932(is)s 5163(constructed,)s 6393(recording,)s 7438(for)s 7797(each)s
8314(symbol,)s 0 140(which)m 633(symbols)s 1473(are)s 1810(in)s 9(v)k 4(ok)k 2(ed)k
2616(within)s 3274(its)s 3541(body)s 15(.)k 4160(Immediately)s
5412(after)s 5898(the)s 6237(last)s 6618(de\207nition)s 7583(is)s
7783(read,)s 8292(the)s 8630(tran)s 8998(-)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 21 22
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5714 -1579(-)m 5842(21)s
6117(-)s 9066 13419 0 13310 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13256(siti)m 6(v)k 3(e)k 565(closure)s
1312(of)s 1584(the)s 1933(call)s 2334(graph)s 2937(is)s
3148(computed,)s 4200(and)s 4605(used)s 5104(to)s 5344(determine)s
6356(whether)s 7187(each)s 7684(non-)s 8112(parameter)s 0 12968(symbol)m
775(is)s 1001(recursi)s 6(v)k 3(e)k 1939(or)s
2214(recepti)s 6(v)k 3(e)k 3151(\(Section)s 4020(5.1\),)s
4522(and)s 4942(whether)s 5787(each)s 6298(parameter)s 7328(is)s
7554(in)s 9(v)k 4(ok)k 2(ed)k 8385(e)s 3(xactly)k
0 12680(once)m 508(or)s 767(not.)s 480 12306(Purely)m 1188(functional)s
2243(systems)s 3082(may)s 3579(e)s 6(v)k 6(aluate)k
4450(symbol)s 5240(in)s 9(v)k 4(ocations)k 6412(in)s
6686(applicati)s 6(v)k 3(e)k 7812(order)s 8407(\(where)s
0 12018(parameters)m 1092(are)s 1433(e)s 6(v)k 6(aluated)k
2389(before)s 3049(substitution)s 4216(into)s 4635(bodies\),)s 5440(or)s
5693(in)s 5930(normal)s 6656(order)s 7214(\(substitution)s 8460(before)s
0 11730(e)m 6(v)k 6(aluation\),)k 1164(and)s 1562(the)s 3(y)k
2018(may)s 2478(also)s 2909(share)s 3463(the)s 3804(v)s 6(alue)k
4366(of)s 4630(a)s 4790(parameter)s 5798(among)s 6496(all)s
6783(uses)s 7239(of)s 7504(it.)s 7793(But)s 8193(in)s
8429(Basser)s 0 11442(Lout,)m 603(the)s 996(presence)s 1932(of)s
2248(conte)s 3(xt-sensiti)k 6(v)k 3(e)k 3955(style)s
4507(information)s 5736(\(Section)s 6634(2.5\))s 7106(forces)s 7785(normal)s
8562(order)s 0 11154(e)m 6(v)k 6(aluation)k 1041(and)s
1445(pre)s 6(v)k 3(ents)k 2297(sharing)s 3054(of)s
3325(parameter)s 4339(v)s 6(alues.)k 480 10780(T)m 19(o)k
780(e)s 6(v)k 6(aluate)k 1620(an)s 1903(unsized)s
2692(object)s 3336(\(pure)s 3896(parse)s 4456(tree\),)s 4999(its)s
240 fnt3 5275 10782(en)m 9(vir)k 10(onment)k 240 fnt1
6456 10780(,)m 6563(the)s 6911(equi)s 6(v)k 6(alent)k
7955(of)s 8226(the)s 8574(stack)s 0 10492(frames)m 728(in)s
999(Algol-lik)s 2(e)k 2064(languages,)s 3156(must)s 3710(be)s
4020(a)s 4(v)k 6(ailable,)k 5008(containing)s 6099(the)s
6476(actual)s 7129(v)s 6(alues)k 7814(of)s 8113(all)s
8435(formal)s 0 10204(parameters)m 1119(that)s 1558(are)s 1927(visible)s
2641(within)s 3330(the)s 3700(unsized)s 4510(object.)s 5279(En)s 9(vironment)k
6601(handling)s 7513(is)s 7744(a)s 7932(well-kno)s 6(wn)k
0 9916(implementation)m 1557(technique,)s 2594(so)s 2860(it)s 3052(will)s
3478(be)s 3760(discussed)s 4735(only)s 5215(brie\210y)s 5893(here.)s
480 9542(En)m 9(vironments)k 1894(are)s 2272(e)s 3(xtra)k
2837(subtrees)s 3702(hung)s 4265(from)s 4820(the)s 5199(objects)s
5958(the)s 3(y)k 6451(refer)s 6991(to.)s 7372(This)s
7879(or)s 4(g)k 1(anization)k 0 9254(mak)m 2(es)k
668(e)s 3(xcellent)k 1595(use)s 1978(of)s 2257(the)s
2613(ordered)s 3409(dag)s 3816(to)s 4063(permit)s 4754(en)s 9(vironments)k
6106(to)s 6353(be)s 6643(shared,)s 7382(and)s 7794(deleted)s
8550(when)s 0 8966(the)m 339(last)s 721(reference)s 1655(to)s
1885(them)s 2413(is)s 2614(remo)s 3(v)k 3(ed.)k
3600(Se)s 6(v)k 3(eral)k 4353(optimizations)s 5695(ha)s 4(v)k 3(e)k
6187(been)s 6687(implemented.)s 8090(Actual)s 8772(pa)s 8998(-)s
0 8678(rameters)m 860(kno)s 6(wn)k 1552(to)s 1778(be)s
2048(in)s 9(v)k 4(ok)k 2(ed)k 2850(only)s
3318(once)s 3814(are)s 4148(mo)s 3(v)k 3(ed)k
4840(in)s 5070(from)s 5582(the)s 5918(en)s 9(vironment,)k
7212(not)s 7566(copied;)s 8303(cop)s 2(ying)k 0 8390(could)m
581(lead)s 1028(to)s 1258(quadratic)s 2191(time)s 2662(comple)s 3(xity)k 15(.)k
3875(Actual)s 4558(parameters)s 5647(of)s 5909(the)s 6248(form)s
220 fnt5 6763 8387(@Ne)m 6(xt)k 240 fnt3 7478 8392(object)m
240 fnt1 8117 8390(recei)m 6(v)k 3(e)k 8843(an)s
0 8102(applicati)m 6(v)k 3(e)k 1105(pre-)s 1478(e)s 6(v)k 6(aluation)k
2529(which)s 3181(pre)s 6(v)k 3(ents)k 4044(long)s
4533(chains)s 5205(of)s 220 fnt5 5486 8099(@Ne)m 6(xt)k
240 fnt1 6221 8102(symbols)m 7080(from)s 7614(forming)s 8448(during)s
0 7814(the)m 359(generation)s 1437(of)s 1719(lar)s 4(ge)k
2260(page)s 2779(numbers.)s 3779(Some)s 4391(en)s 9(vironments)k
5747(which)s 6400(pro)s 3(v)k 6(ably)k 7308(contrib)s 4(ute)k
8341(nothing)s 0 7526(are)m 344(deleted,)s 1137(most)s 1659(notably)s
2427(when)s 3000(a)s 3162(symbol)s 3918(in)s 9(v)k 4(ocation)k
4969(has)s 5335(no)s 5625(symbols)s 6470(within)s 7135(its)s
7407(actual)s 8028(parameters)s 0 7238(and)m 406(no)s 702(import)s
1402(list,)s 1803(so)s 2071(that)s 2492(only)s 2975(the)s
3326(en)s 9(vironment)k 4589(of)s 4862(its)s 5141(body)s
5678(need)s 6191(be)s 6476(k)s 2(ept;)k 7000(this)s
7399(sa)s 4(v)k 3(es)k 7964(a)s 8133(great)s
8673(deal)s 0 6950(of)m 271(space)s 858(when)s 1434(objects)s
2162(with)s 2644(en)s 9(vironments)k 3988(are)s 4335(written)s
5068(to)s 5307(auxiliary)s 6210(\207les)s 6659(\(Section)s 7512(6.1\).)s
240 fnt2 0 6157(4.)m 291(Implementation)s 1979(of)s 2251(the)s
2625(functional)s 3715(subset)s 
[ /Dest /LOUTfunctional /DEST pdfmark
240 fnt1 480 5680(The)m 941(objects)s
1702(and)s 2139(de\207nitions)s 3233(of)s 3537(Lout)s 4082(are)s
4462(v)s 3(ery)k 4971(similar)s 5726(to)s 5998(those)s
6592(found)s 7242(in)s 7518(other)s 8102(functional)s 0 5392(languages,)m
1085(and)s 1510(the)s 3(y)k 1994(form)s 2539(a)s
2726(natural)s 3465(subset)s 4144(of)s 4436(the)s 4805(language.)s
5854(So)s 6181(we)s 6537(pause)s 7159(here)s 7647(and)s
8072(present)s 8843(an)s 0 5104(o)m 3(v)k 3(ervie)k 6(w)k
932(of)s 1203(the)s 1551(Basser)s 2248(Lout)s 2760(object)s
3404(e)s 6(v)k 6(aluation)k 4445(algorithm.)s 480 4730(The)m
922(problem)s 1794(is)s 2019(to)s 2272(tak)s 2(e)k
2739(an)s 3037(unsized)s 3841(object)s 4499(\(pure)s 5074(parse)s
5649(tree\),)s 6206(its)s 6497(en)s 9(vironment)k 7772(\(Section)s
8640(3.4\),)s 0 4442(and)m 404(its)s 681(style)s 1188(\(Section)s
2042(2.5\),)s 2528(and)s 2933(to)s 3173(produce)s 4000(a)s
4167(PostScript)s 5209(\207le)s 5571(for)s 5910(rendering)s 6879(the)s
7228(object)s 7872(on)s 8170(an)s 8454(output)s 0 4154(de)m 6(vice.)k
786(This)s 1267(\207le)s 1632(is)s 1847(essentially)s 2914(a)s
3084(sequence)s 4022(of)s 4298(instructions)s 5468(to)s 5712(print)s
6227(a)s 6398(gi)s 6(v)k 3(en)k 6983(string)s
7584(of)s 7860(characters)s 8883(in)s 0 3866(a)m 166(gi)s 6(v)k 3(en)k
746(font)s 1191(at)s 1423(a)s 1589(gi)s 6(v)k 3(en)k
2169(point.)s 480 3492(Before)m 1189(the)s 1541(algorithm)s 2534(be)s 3(gins,)k
3266(the)s 3618(parse)s 4182(tree)s 4599(must)s 5127(be)s
5413(obtained,)s 6348(either)s 6955(by)s 7252(parsing)s 8013(input)s
8569(or)s 8832(by)s 0 3204(cop)m 2(ying)k 823(from)s
1347(the)s 1695(symbol)s 2455(table.)s 3082(Afterw)s 2(ards)k
4205(the)s 4553(data)s 5011(structure)s 5901(must)s 6426(be)s
6708(disposed.)s 7710(The)s 8137(algorithm)s 0 2916(proper)m 692(consists)s
1508(of)s 1787(\207v)s 3(e)k 2207(passes,)s 2933(each)s
3437(a)s 3611(recursi)s 6(v)k 3(e)k 4541(tra)s 4(v)k 3(ersal)k
5418(of)s 5697(the)s 6054(structure)s 6953(from)s 7485(the)s
7841(root)s 8294(do)s 6(wn)k 8887(to)s 0 2628(the)m
348(lea)s 4(v)k 3(es)k 989(and)s 1393(back.)s
240 fnt3 0 2174(1.)m 330(Evaluation)s 1490(of)s 1827(unsized)s
2667(objects.)s 240 fnt1 3554 2172(On)m 3960(the)s 4364(w)s 2(ay)k
4871(do)s 6(wn,)k 5561(calculate)s 6521(en)s 9(vironments)k
7921(and)s 8381(replace)s 0 1884(non-recursi)m 6(v)k 3(e,)k
1404(non-recepti)s 6(v)k 3(e)k 2757(symbols)s 3598(by)s
3884(their)s 4373(bodies)s 5041(\(Section)s 5886(3.4\);)s 6369(broadcast)s
7337(fonts)s 7858(to)s 8089(the)s 8429(lea)s 4(v)k 3(es,)k
0 1596(and)m 409(paragraph)s 1427(breaking)s 2322(and)s 2731(spacing)s
3521(styles)s 4121(to)s 4365(the)s 4718(paragraph)s 5736(nodes.)s
6465(On)s 6820(the)s 7173(w)s 2(ay)k 7629(back)s
8147(up,)s 8500(delete)s 240 fnt3 0 1310(FONT)m 240 fnt1
630 1308(,)m 240 fnt3 737 1310(BREAK)m 240 fnt1 1494 1308(,)m
1601(and)s 240 fnt3 2005 1310(SP)m 21(A)k 7(CE)k
240 fnt1 2760 1308(nodes,)m 3426(and)s 3830(insert)s 240 fnt3
4420 1310(SPLIT)m 240 fnt1 5049 1308(,)m 240 fnt3 5156 1310(COL)m
240 fnt1 5622 1308(,)m 5729(and)s 240 fnt3 6133 1310(R)m 9(O)k 12(W)k
240 fnt1 6707 1308(nodes)m 7317(\(Section)s 8170(2.3\).)s 240 fnt3
0 815(2.)m 293(W)s 13(idth)k 925(calculations)s 2169(and)s
2614(br)s 8(eaking)k 3(.)k 240 fnt1 3628 813(Calculate)m
4605(the)s 4973(width)s 5594(of)s 5885(e)s 6(v)k 3(ery)k
6480(subobject)s 7477(from)s 8020(the)s 8388(bottom)s 0 525(up.)m
404(As)s 720(described)s 1693(in)s 1936(Section)s 2709(2.3,)s
240 fnt3 3115 527(WIDE)m 240 fnt1 3777 525(nodes)m 4386(may)s
4851(trigger)s 5547(object)s 6190(breaking)s 7079(sub-tra)s 4(v)k 3(ersals)k
8448(during)s 0 237(this)m 396(pass.)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 22 23
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Times-Bold
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1579(-)m 5833(22)s
6127(-)s 9066 13419 0 13308 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
240 fnt3 0 13256(3.)m 274(Height)s 989(calculations.)s
240 fnt1 2312 13254(Calculate)m 3270(the)s 3618(height)s 4276(of)s
4547(e)s 6(v)k 3(ery)k 5123(subobject,)s 6147(from)s
6671(the)s 7019(bottom)s 7757(up.)s 240 fnt3 0 12751(4.)m
283(Horizontal)s 1389(coor)s 8(dinates.)k 240 fnt1 2674 12749(Calculate)m
3641(the)s 3998(horizontal)s 5032(coordinate)s 6106(of)s 6386(each)s
6890(subobject)s 7876(from)s 8409(the)s 8767(top)s 0 12461(do)m 6(wn,)k
634(and)s 1038(store)s 1558(each)s 2053(leaf)s -13(')k 13(s)k
2633(coordinate)s 3698(in)s 3941(the)s 4289(leaf.)s 240 fnt3
0 11977(5.)m 295(V)s 26(ertical)k 1119(coor)s 8(dinates)k
2317(and)s 2765(P)s 19(ostScript)k 3827(g)s 2(ener)k 3(ation.)k
240 fnt1 5034 11975(Calculate)m 6013(the)s 6383(v)s 3(ertical)k
7171(coordinate)s 8257(of)s 8550(e)s 6(v)k 3(ery)k
0 11687(subobject)m 981(from)s 1509(the)s 1861(top)s 2224(do)s 6(wn,)k
2862(and)s 3270(at)s 3506(each)s 4005(leaf,)s 4473(retrie)s 6(v)k 3(e)k
5252(the)s 5604(character)s 6542(string,)s 7197(font,)s 7693(and)s
8102(horizontal)s 0 11399(coordinate,)m 1116(and)s 1520(print)s 2031(the)s
2379(PostScript)s 3421(instruction)s 4500(for)s 4838(rendering)s 5807(that)s
6225(leaf.)s 0 10896(Figure)m 692(3)s 869(gi)s 6(v)k 3(es)k
1428(the)s 1789(amount)s 2579(of)s 2863(code)s 3383(required)s
4250(for)s 4600(each)s 5168(pass.)s 5756(Symmetry)s 6819(between)s
7685(horizontal)s 8722(and)s 0 10608(v)m 3(ertical)k 764(is)s
971(e)s 3(xploited)k 1913(throughout)s 3021(Basser)s 3715(Lout,)s
4271(and)s 4672(passes)s 5331(2)s 5502(and)s 5903(3,)s
6127(as)s 6374(well)s 6837(as)s 7084(4)s 7255(and)s
7656(5,)s 7880(are)s 8224(e)s 3(x)k 3(ecuted)k
0 10320(on)m 297(shared)s 979(code.)s 480 9946(The)m 929(author)s
1621(can)s 2031(see)s 2413(no)s 2728(simple)s 3442(w)s 2(ay)k
3914(to)s 4174(reduce)s 4888(the)s 5258(number)s 6070(of)s
6362(passes.)s 7158(The)s 7607(introduction)s 8855(of)s 0 9658(horizontal)m
1027(g)s 1(alle)k 3(ys)k 1755(\(Section)s 2612(5.5\))s
3044(w)s 2(ould)k 3703(remo)s 3(v)k 3(e)k
4474(the)s 4826(need)s 5340(for)s 5682(the)s 6034(object)s
6682(breaking)s 7576(transformations)s 0 9370(within)m 700(this)s 1128(algorithm)s
2149(that)s 2599(are)s 2978(the)s 3359(principal)s 4295(obstacles)s
5254(in)s 5529(the)s 5909(w)s 2(ay)k 6393(of)s
6696(the)s 7076(mer)s 4(ging)k 7954(of)s 8257(passes)s
8952(2)s 0 9082(and)m 404(3.)s 240 fnt2 0 8338(5.)m
291(Galleys)s 
[ /Dest /LOUT18_651_s5_0_1 /DEST pdfmark
240 fnt1 480 7861(W)m 9(ith)k 1022(objects)s
1767(and)s 2188(de\207nitions)s 3266(under)s 3888(control,)s 4689(the)s
5053(author)s 5741(f)s 2(aced)k 6331(the)s 6696(problem)s
7570(of)s 7858(getting)s 8592(body)s 0 7573(te)m 3(xt,)k
478(footnotes,)s 1491(\210oating)s 2291(\207gures)s 3009(and)s 3429(tables,)s
4109(references,)s 5213(inde)s 3(x)k 5813(entries,)s 6572(and)s
6992(entries)s 7695(in)s 7954(the)s 8318(table)s 8855(of)s
0 7285(contents)m 844(into)s 1264(their)s 1757(places.)s 2513(The)s
2937(resulting)s 3821(in)s 9(v)k 3(estig)k 1(ation)k
5095(occupied)s 6013(three)s 6541(months)s 7293(of)s 7559(full-time)s
8444(design)s 0 6997(w)m 2(ork,)k 612(and)s 1031(proceeded)s
2088(approximately)s 3538(as)s 3803(described)s 4793(in)s 5051(Section)s
5840(5.1;)s 6268(the)s 6631(implementation)s 8204(occupied)s 0 6709(the)m
348(years)s 903(1987-89.)s 240 fnt2 0 6060(5.1.)m 471(The)s
926(galley)s 1580(abstraction)s 
[ /Dest /LOUTgalleys /DEST pdfmark
240 fnt1 480 5583(Let)m 870(us)s
1147(tak)s 2(e)k 1611(the)s 1972(footnote)s 2838(as)s
3100(a)s 3279(representati)s 6(v)k 3(e)k 4677(e)s 3(xample.)k
5661(At)s 5973(some)s 6546(point)s 7111(in)s 7366(the)s
7727(document,)s 8791(we)s 0 5295(wish)m 509(to)s 748(write)s
220 fnt5 480 4847(preceding te)m 6(xt)k 480 4559(@F)m 6(ootNote { f)k 6(ootnote te)k 6(xt })k
480 4271(f)m 6(ollo)k 3(wing te)k 6(xt)k 240 fnt1
0 3772(and)m 406(we)s 744(e)s 3(xpect)k 1428(the)s
1779(formatter)s 2729(to)s 2971(remo)s 3(v)k 3(e)k
3741(the)s 4092(footnote)s 4947(from)s 5474(this)s 5873(conte)s 3(xt)k
6637(and)s 7044(place)s 7607(it)s 7802(at)s 8037(the)s
8388(bottom)s 0 3484(of)m 281(the)s 639(current)s 1386(page,)s
1955(possibly)s 2817(splitting)s 3664(some)s 4235(or)s 4504(all)s
4808(of)s 5089(it)s 5291(onto)s 5781(a)s 5957(follo)s 6(wing)k
6944(page)s 7463(if)s 7690(space)s 8287(is)s 8508(insuf)s
8998(-)s 0 3196(\207cient.)m 480 2822(An)m 844(object)s 1503(appears)s
2298(in)s 2556(the)s 2918(\207nal)s 3413(document)s 4431(at)s
4678(the)s 5040(point)s 5607(it)s 5813(is)s 6038(in)s 9(v)k 4(ok)k 2(ed,)k
6916(b)s 4(ut)k 7293(this)s 7703(basic)s 8262(property)s
0 2534(does)m 503(not)s 882(hold)s 1379(for)s 1730(footnotes:)s
2799(the)s 3160(point)s 3725(of)s 4009(in)s 9(v)k 4(ocation)k
5076(and)s 5493(the)s 5854(point)s 6419(of)s 6703(appearance)s
7847(are)s 8207(dif)s 6(ferent.)k 0 2246(In)m 254(some)s
813(w)s 2(ay)k 15(,)k 1299(the)s 1645(footnote)s
2496(is)s 2703(attached)s 3555(to)s 3791(the)s 4137(document)s
5139(at)s 5368(both)s 5849(points,)s 6539(introducing)s 7692(a)s
7856(cross)s 8395(linking)s 0 1958(\(Section)m 853(2.1\))s 1281(that)s
1699(cannot)s 2397(be)s 2679(described)s 3653(in)s 3896(purely)s
4561(functional)s 5585(terms.)s 480 1584(Since)m 1069(the)s 1420(interpretation)s
2766(of)s 3040(an)s 3(y)k 3440(object)s 4087(depends)s
4926(on)s 5226(an)s 5512(en)s 9(vironment)k 6775(and)s
7182(style)s 7692(inherited)s 8602(from)s 0 1296(the)m 347(conte)s 3(xt,)k
1153(the)s 1499(\207rst)s 1929(question)s 2795(must)s 3318(be)s
3598(whether)s 4427(the)s 4773(footnote)s 5624(inherits)s 6390(them)s
6926(through)s 7726(the)s 8072(in)s 9(v)k 4(ocation)k
0 1008(point)m 552(or)s 811(through)s 1613(the)s 1961(point\(s\))s
2753(of)s 3024(appearance.)s 480 634(If)m 697(symbols)s 1533(are)s
1867(to)s 2092(be)s 2361(interpreted)s 3440(statically)s 4341(as)s
4578(heretofore,)s 5653(then)s 6108(en)s 9(vironments)k 7439(must)s
7951(be)s 8219(inherited)s 0 346(through)m 829(the)s 1204(in)s 9(v)k 4(ocation)k
2285(point)s 2865(alone.)s 3574(Dynamic)s 4531(inheritance)s 5675(through)s
6505(the)s 6880(point)s 7459(of)s 7757(appearance)s 8916(is)s
0 58(enticing)m 836(in)s 1092(some)s 1666(w)s 2(ays:)k
2335(it)s 2541(might)s 3172(replace)s 3930(the)s 4291(body)s
4838(parameter)s 9(,)k 5904(and)s 6321(it)s 6526(might)s
7157(help)s 7635(with)s 8131(automatic)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 23 24
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5710 -1579(-)m 5838(23)s
6122(-)s 9066 13416 0 13416 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
1659 13218(1.)m 2163(Initialization)s 7172(200)s 1659 12930(2.)m
2163(Memory)s 3041(allocation,)s 4090(ordered)s 4878(dag)s 5277(operations)s
7172(400)s 1659 12642(3.)m 2163(Le)s 3(xical)k 2931(analysis,)s
3808(macros,)s 4605(\207le)s 4966(handling)s 6992(1,350)s 1659 12354(4.)m
2163(P)s 3(arsing)k 2930(of)s 3201(objects)s 3929(and)s
4333(de\207nitions)s 6992(1,150)s 1659 12066(5.)m 2163(Symbol)s 2963(table)s
3483(and)s 3887(call)s 4286(graph)s 7172(600)s 1659 11778(6.)m
2163(Ev)s 6(aluation)k 3250(of)s 3521(pure)s 4002(parse)s
4562(trees)s 6992(1,650)s 1659 11490(7.)m 2163(Reading,)s 3068(storing,)s
3839(and)s 4243(scaling)s 4973(of)s 5244(fonts)s 7172(600)s
1659 11202(8.)m 2163(Cross)s 2759(references)s 3790(and)s 4194(databases)s
6992(1,000)s 1659 10914(9.)m 2163(W)s 9(idth)k 2809(and)s
3213(height)s 3871(calculations,)s 5119(and)s 5523(breaking)s 7172(700)s
1539 10626(10.)m 240 fnt3 2163 10628(Constr)m 3(ained)k 240 fnt1
3410 10626(and)m 240 fnt3 3814 10628(AdjustSize)m 240 fnt1 7172 10626(700)m
1539 10338(11.)m 2163(T)s 8(ransfer)k 3023(of)s 3294(sized)s
3843(objects)s 4571(into)s 4996(g)s 1(alle)k 3(y)k
5630(tree)s 7172(450)s 1539 10050(12.)m 2163(Galle)s 3(y)k
2851(\210ushing)s 3676(algorithm)s 6992(1,500)s 1539 9762(13.)m 2163(Coordinate)s
3282(calculations)s 4474(and)s 4878(PostScript)s 5920(output)s 7172(700)s
1539 9474(14.)m 2163(Deb)s 4(ugging)k 3277(and)s 3681(error)s
4204(handling)s 6992(1,200)s 655 0 0 0 240 288 60 6872 9328 LoutGr2
0.5 pt ltabhs
grestore

grestore
6872 9074(12,200)m 
[ /Dest /LOUTcomponents /DEST pdfmark
200 fnt2 41 8421(Figur)m 3(e)k
649(3.)s 200 fnt1 891 8422(Major)m 1427(components)s 2432(of)s
2658(the)s 2947(Basser)s 3526(Lout)s 3953(interpreter)s 8(,)k
4861(sho)s 5(wing)k 5576(the)s 5865(approximate)s 6906(number)s
7565(of)s 7791(lines)s 8208(of)s 8434(C)s 8611(code.)s
240 fnt1 0 7791(numbering,)m 1163(since)s 1730(the)s 2097(number)s
2908(of)s 3198(a)s 3384(footnote)s 4256(is)s 4486(kno)s 6(wn)k
5209(only)s 5709(at)s 5960(the)s 6328(point)s 6899(of)s
7190(appearance;)s 8396(b)s 4(ut)k 8778(the)s 0 7503(implementation)m
1606(problems)s 2597(are)s 2993(se)s 6(v)k 3(ere,)k
3751(and)s 4204(static)s 4810(inheritance)s 5976(seems)s 6661(much)s
7299(simpler)s 8125(and)s 8579(more)s 0 7215(comprehensible)m 1572(to)s
1814(the)s 2165(user)s 13(.)k 2716(Style,)s 3317(at)s
3552(least)s 4052(its)s 4330(a)s 4(v)k 6(ailable)k
5241(width)s 5846(and)s 6253(height)s 6913(part,)s 7394(must)s
7922(of)s 8196(necessity)s 0 6927(be)m 268(inherited)s 1160(through)s
1947(the)s 2280(point)s 2817(of)s 3073(appearance.)s 4297(F)s 3(or)k
4671(consistenc)s 3(y)k 15(,)k 5861(the)s 6194(entire)s
6778(style)s 7270(should)s 7952(be)s 8219(inherited)s 0 6639(in)m
256(this)s 666(w)s 2(ay)k 15(.)k 1226(There)s
1853(is)s 2077(a)s 2257(suggesti)s 6(v)k 3(e)k
3328(analogy)s 4154(here)s 4635(with)s 5131(actual)s 5770(parameters,)s
6938(which)s 7594(ha)s 4(v)k 3(e)k 8109(a)s
8289(point)s 8855(of)s 0 6351(in)m 9(v)k 4(ocation)k
1060(from)s 1591(which)s 2240(the)s 3(y)k 2710(inherit)s
3400(an)s 3690(en)s 9(vironment,)k 5004(and)s 5414(a)s
5587(point)s 6146(of)s 6424(appearance)s 7562(within)s 8237(the)s
8592(body)s 0 6063(of)m 265(the)s 606(enclosing)s 1569(de\207nition,)s
2587(from)s 3104(which)s 3739(the)s 3(y)k 4196(inherit)s
4872(a)s 5031(style.)s 5639(It)s 5838(may)s 6297(be)s
6572(possible)s 7406(to)s 7638(treat)s 8114(a)s 8273(footnote)s
0 5775(as)m 250(the)s 598(actual)s 1223(parameter)s 2237(of)s
2508(some)s 3069(symbol,)s 3881(therefore,)s 4849(although)s 5744(the)s
6092(details)s 6766(seem)s 7317(v)s 3(ery)k 7793(obscure.)s
480 5401(But)m 881(the)s 1224(most)s 1744(profound)s 2674(consequence)s
3948(of)s 4214(ha)s 4(ving)k 4910(tw)s 2(o)k
5314(types)s 5865(of)s 6131(attachment)s 7234(point)s 7780(is)s
7985(that)s 8398(it)s 8584(leads)s 0 5113(to)m 261(tw)s 2(o)k
693(distincti)s 6(v)k 3(e)k 1757(tree)s 2192(structures.)s
3306(Considering)s 4551(in)s 9(v)k 4(ocation)k 5627(points)s
6285(only)s 6787(leads)s 7351(to)s 7612(static)s 8190(trees)s
8714(lik)s 2(e)k 0 4825(this)m 396(one:)s gsave
480 2539 translate
240 fnt3
3666 1996 170 1715 240 288 60 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
1117 1273 170 993 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 1273 170 993 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 551 170 272 240 288 60 0 721 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(footnote)m 
grestore
(T) lfigpromotelabels
grestore
(L) lfigpromotelabels
grestore
1206 553 170 272 240 288 60 1230 1443 LoutGr2
currentdict end 200 dict begin begin
grestore
1206 553 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(body)m 692(te)s 4(xt)k 
grestore
(T) lfigpromotelabels
grestore
0 0 0 0 240 288 60 2436 1715 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ L@T@CTR L@T@CTR T@CTR lfigangle L@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR L@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1117 1273 0 993 240 288 60 2549 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1001 552 170 272 240 288 60 116 721 LoutGr2
currentdict end 200 dict begin begin
grestore
884 552 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(\207gur)m 8(e)k

grestore
(T) lfigpromotelabels
grestore
1117 551 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 551 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 551 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(footnote)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 60 1117 272 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
(R) lfigpromotelabels
grestore
0 0 0 0 240 288 60 3666 1715 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ R@T@CTR R@T@CTR T@CTR lfigangle R@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR R@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore
0 2088(which)m 663(sho)s 6(ws)k 1329(that)s
1769(the)s 2139(body)s 2695(te)s 3(xt)k 3131(contains)s
4001(a)s 4189(footnote)s 5064(and)s 5490(a)s 5677(\207gure,)s
6364(the)s 6734(latter)s 7305(itself)s 7875(containing)s 8960(a)s
0 1800(footnote.)m 961(Considering)s 2184(points)s 2820(of)s 3091(appearance)s
4222(only)s 4702(gi)s 6(v)k 3(es)k 5249(a)s
5415(completely)s 6531(dif)s 6(ferent,)k 7453(dynamic)s 8330(tree:)s
gsave
480 186 translate
240 fnt3 4663 1274 0 995 240 288 60 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
3382 551 170 272 240 288 60 1281 723 LoutGr2
currentdict end 200 dict begin begin
grestore
2101 551 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(sequence)m 1100(of)s 1381(pa)s 2(g)k 2(es)k

grestore
(T) lfigpromotelabels
grestore
1206 553 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1206 553 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1206 553 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(body)m 692(te)s 4(xt)k 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 60 1206 272 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1117 553 170 272 240 288 60 1319 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 553 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 551 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(footnote)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 60 2436 272 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
884 553 170 272 240 288 60 2549 0 LoutGr2
currentdict end 200 dict begin begin
grestore
884 553 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
884 552 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(\207gur)m 8(e)k

grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 60 3433 272 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
1117 553 170 272 240 288 60 3546 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 553 170 272 240 288 60 0 0 LoutGr2
currentdict end 200 dict begin begin
grestore
1117 551 170 272 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
170 220(footnote)m 
grestore
(T) lfigpromotelabels
grestore
(S) lfigpromotelabels
grestore
0 0 0 0 240 288 60 4663 272 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ S@T@CTR S@T@CTR T@CTR lfigangle S@T@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
T@CTR T@CTR S@T@CTR lfigangle T@CIRCUM lfigpadd lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore

grestore
end end restore
grestore

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 24 25
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1579(-)m 5833(24)s
6127(-)s 9066 13419 0 13419 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13256(The)m 468(tree)s 921(can)s 1351(be)s
1673(deeper)s 9(,)k 2448(for)s 2827(e)s 3(xample)k
3730(with)s 4253(sections)s 5114(appearing)s 6150(within)s 6859(chapters)s
7746(which)s 8429(appear)s 0 12968(within)m 680(the)s 1041(body)s
1587(te)s 3(xt,)k 2062(which)s 2717(appears)s 3510(within)s
4191(the)s 4551(\207nal)s 5044(sequence)s 5990(of)s 6273(pages.)s
6995(Document)s 8065(formatting)s 0 12680(languages)m 1024(generally)s 1984(shirk)s
2540(the)s 2905(issues)s 3544(raised)s 4189(by)s 4500(this)s
4912(dual)s 5396(tree)s 5826(structure,)s 6785(by)s 7096(making)s
7884(the)s 8249(dynamic)s 0 12392(tree)m 421(b)s 4(uilt-in,)k
1235(by)s 1537(limiting)s 2354(one)s 2764(or)s 3032(both)s
3523(trees)s 4032(to)s 4279(tw)s 2(o)k 4697(le)s 6(v)k 3(els,)k
5360(and)s 5773(so)s 6047(on,)s 6402(pro)s 3(viding)k
7391(a)s 7565(classic)s 8263(e)s 3(xample)k 0 12104(of)m
295(the)s 667(impo)s 3(v)k 3(erishing)k 2120(ef)s 6(fect)k
2740(of)s 3035(f)s 2(ailing)k 3733(to)s 3997(permit)s
4704(language)s 5648(features)s 6478(to)s 6741(attain)s 7352(their)s
7873(natural)s 8616(le)s 6(v)k 3(el)k 0 11816(of)m
271(generality)s 15(.)k 480 11442(W)m 19(e)k 854(are)s
1206(thus)s 1662(led)s 2017(to)s 2261(propose)s 3081(a)s
3252(second)s 3980(abstraction)s 5091(for)s 5434(document)s 6443(formatting,)s
7564(which)s 8211(we)s 8552(name)s 0 11154(the)m 240 fnt3
371 11156(galle)m 7(y)k 240 fnt1 1028 11154(in)m 1294(recognition)s
2464(of)s 2759(its)s 3058(similarity)s 4050(to)s 4312(the)s
4684(g)s 1(alle)k 3(ys)k 5432(used)s 5952(in)s
6219(manual)s 7001(typesetting.)s 8238(A)s 8492(g)s 1(alle)k 3(y)k
0 10866(consists)m 817(of)s 1098(an)s 1391(object)s 2045(\(such)s
2630(as)s 2890(a)s 3066(footnote\))s 4001(together)s 4854(with)s
5346(a)s 5522(sequence)s 6465(of)s 6746(places)s 7404(where)s
8054(that)s 8482(object)s 0 10578(may)m 491(appear)s 1214(\(such)s
1814(as)s 2090(the)s 2464(bottoms)s 3311(of)s 3608(the)s
3982(current)s 4743(and)s 5173(follo)s 6(wing)k 6176(pages\).)s
6989(Splitting)s 7891(occurs)s 8592(quite)s 0 10290(naturally)m 903(when)s
1479(space)s 2066(at)s 2298(an)s 3(y)k 2695(place)s
3255(is)s 3465(insuf\207cient)s 4600(to)s 4839(hold)s 5323(the)s
5671(entire)s 6270(object.)s 480 9916(In)m 736(Lout,)s 1295(a)s
1461(footnote)s 2314(g)s 1(alle)k 3(y)k 2948(and)s
3352(its)s 3628(place)s 4188(of)s 4459(appearance)s 5590(are)s
5937(de\207ned)s 6700(as)s 6950(follo)s 6(ws:)k 220 fnt5
480 9415(def @F)m 6(ootPlace { @Galle)k 4(y })k 480 8839(def @F)m 6(ootNote into { @F)k 6(ootPlace&&f)k 6(ollo)k 3(wing })k
480 8551(    r)m -3(ight x)k 480 8263({ x })m 240 fnt1 0 7769(The)m
220 fnt5 445 7766(@F)m 6(ootPlace)k 240 fnt1 1719 7769(symbol)m
2496(contains)s 3362(the)s 3727(special)s 4463(symbol)s 220 fnt5
5240 7766(@Galle)m 4(y)k 240 fnt1 6078 7769(,)m 6203(indicating)s
7229(that)s 7665(it)s 7874(is)s 8102(a)s 8285(point)s
8855(of)s 0 7481(appearance)m 1143(for)s 1493(a)s 1672(g)s 1(alle)k 3(y)k 15(.)k
2413(By)s 2759(placing)s 3529(in)s 9(v)k 4(ocations)k
4682(of)s 220 fnt5 4965 7478(@F)m 6(ootPlace)k 240 fnt1
6234 7481(at)m 6478(the)s 6838(bottoms)s 7673(of)s 7956(pages,)s
8620(as)s 8883(in)s 0 7193(Section)m 801(3.2,)s 1235(we)s
1597(de\207ne)s 2265(the)s 2640(desired)s 3415(points)s 4078(of)s
4376(appearance)s 5534(for)s 5899(footnotes.)s 6980(Symbols)s 7896(whose)s
8592(body)s 0 6905(contains)m 220 fnt5 863 6902(@Galle)m 4(y)k
240 fnt1 1776 6905(either)m 2394(directly)s 3192(or)s 3466(indirectly)s
4450(are)s 4812(called)s 5455(recepti)s 6(v)k 3(e)k
6392(symbols,)s 7312(meaning)s 8204(recepti)s 6(v)k 3(e)k
0 6617(to)m 239(g)s 1(alle)k 3(ys,)k 1019(and)s
1423(the)s 3(y)k 1886(are)s 2233(e)s 3(xpanded)k
3207(only)s 3687(on)s 3984(demand.)s 4906(The)s 5334(ef)s 6(fect)k
5930(of)s 6202(the)s 220 fnt5 6550 6614(into)m 240 fnt1
6956 6617(clause)m 7609(is)s 7819(to)s 8058(mak)s 2(e)k
8631(each)s 0 6329(in)m 9(v)k 4(ocation)k 1057(of)s
220 fnt5 1332 6326(@F)m 6(ootNote)k 240 fnt1 2506 6329(a)m
2676(g)s 1(alle)k 3(y)k 3313(whose)s 3985(object)s
4632(is)s 4846(the)s 5198(result)s 5791(of)s 6066(the)s
6417(in)s 9(v)k 4(ocation)k 7475(in)s 7721(the)s
8073(usual)s 8637(w)s 2(ay)k 15(,)k 0 6041(and)m
406(whose)s 1076(sequence)s 2011(of)s 2285(points)s 2923(of)s
3196(appearance)s 4329(is)s 4542(speci\207ed)s 5452(by)s 5748(the)s
220 fnt5 6098 6038(into)m 240 fnt1 6507 6041(clause;)m 7218(in)s
7463(this)s 7861(e)s 3(xample,)k 8778(the)s 0 5753(sequence)m
933(of)s 1204(all)s 220 fnt5 1497 5750(@F)m 6(ootPlace)k
240 fnt1 2753 5753(symbols)m 3602(follo)s 6(wing)k 4579(the)s
4927(in)s 9(v)k 4(ocation)k 5981(point.)s 480 5379(Lout)m
995(permits)s 1766(g)s 1(alle)k 3(ys)k 2494(to)s
2737(be)s 3023(in)s 9(v)k 4(ok)k 2(ed)k
3842(within)s 4514(other)s 5069(g)s 1(alle)k 3(ys)k
5797(to)s 6040(arbitrary)s 6919(depth,)s 7562(so)s 7832(that)s
8254(one)s 8660(may)s 0 5091(ha)m 4(v)k 3(e)k
514(footnotes)s 1468(within)s 2149(\207gures)s 2864(within)s 3546(the)s
3907(body)s 4454(te)s 3(xt)k 4882(g)s 1(alle)k 3(y)k 15(,)k
5568(for)s 5919(e)s 3(xample,)k 6846(creating)s 7681(arbitrary)s
8570(static)s 0 4803(trees.)m 649(Recepti)s 6(v)k 3(e)k
1688(symbols)s 2573(lik)s 2(e)k 220 fnt5 3021 4800(@F)m 6(ootPlace)k
240 fnt1 4313 4803(may)m 4815(appear)s 5548(within)s 6252(an)s 3(y)k
6685(g)s 1(alle)k 3(y)k 15(,)k 7393(creating)s
8251(arbitrary)s 0 4515(dynamic)m 912(trees)s 1449(as)s 1734(well.)s
2345(The)s 2808(root)s 3289(of)s 3595(the)s 3979(dynamic)s
4891(tree,)s 5391(which)s 6068(w)s 2(ould)k 6759(normally)s
7711(consist)s 8471(of)s 8778(the)s 0 4227(sequence)m 959(of)s
1257(pages)s 1880(of)s 2178(the)s 2553(complete)s 3512(assembled)s
4593(document,)s 5671(is)s 5908(considered)s 7029(to)s 7295(be)s
7604(a)s 7797(g)s 1(alle)k 3(y)k 8458(whose)s
0 3939(point)m 563(of)s 845(appearance)s 1987(is)s 2208(the)s
2567(output)s 3250(\207le.)s 3730(Points)s 4390(of)s 4672(appearance)s
5814(may)s 6291(be)s 220 fnt5 6584 3936(preceding)m 240 fnt1
7606 3939(or)m 220 fnt5 7876 3936(f)m 6(ollo)k 3(wing)k
240 fnt1 8778 3939(the)m 0 3651(in)m 9(v)k 4(ocation)k
1054(point;)s 1658(entries)s 2345(in)s 2588(tables)s 3196(of)s
3467(contents)s 4315(are)s 4662(the)s 5010(main)s 5545(users)s
6087(of)s 220 fnt5 6358 3648(preceding)m 240 fnt1 7309 3651(.)m
480 3277(The)m 913(g)s 1(alle)k 3(y)k 1552(abstraction)s
2662(is)s 2877(adequate)s 3788(for)s 4131(all)s 4429(of)s
4706(the)s 5059(applications)s 6270(listed)s 6850(at)s 7087(the)s
7440(be)s 3(ginning)k 8453(of)s 8730(this)s 0 2989(section,)m
808(e)s 3(xcept)k 1514(that)s 1957(there)s 2515(is)s
2749(no)s 3067(pro)s 3(vision)k 4050(for)s 4413(sorting)s
5155(inde)s 3(x)k 5763(entries)s 6475(and)s 6904(references.)s
8073(Sorting)s 8855(of)s 0 2701(g)m 1(alle)k 3(ys)k
715(has)s 1075(been)s 1574(added)s 2194(to)s 2423(Lout)s
2925(as)s 3165(a)s 3321(b)s 4(uilt-in)k 4068(feature,)s
4827(in)s 9(v)k 4(ok)k 2(ed)k 5632(by)s
5916(adding)s 6611(a)s 6767(special)s 220 fnt5 7475 2698(@K)m 8(e)k 4(y)k
240 fnt1 8112 2701(parameter)m 0 2413(to)m 227(the)s 563(g)s 1(alle)k 3(ys,)k
1330(and)s 1722(using)s 2281(its)s 2545(v)s 6(alue)k
3100(as)s 3338(the)s 3673(sort)s 4079(k)s 2(e)k 3(y)k 15(.)k
4556(The)s 4972(author)s 5631(w)s 2(as)k 6039(at)s
6259(a)s 6412(loss)s 6823(to)s 7049(\207nd)s 7468(an)s 3(y)k
7852(other)s 8391(w)s 2(ay)k 15(,)k 8867(or)s
0 2125(an)m 3(y)k 397(useful)s 1036(generalization)s 2446(of)s
2717(this)s 3113(feature.)s 3939(Its)s 4228(implementation)s 5785(will)s
6211(be)s 6493(discussed)s 7468(in)s 7711(Section)s 8485(6.2.)s
240 fnt2 0 1476(5.2.)m 471(The)s 926(galley)s 1580(\210ushing)s
2447(algorithm)s 
[ /Dest /LOUTflushing /DEST pdfmark
240 fnt1 480 999(Galle)m 3(y)k 1177(components)s
2395(are)s 2751(promoted)s 3736(one)s 4148(by)s 4451(one)s
4863(into)s 5298(the)s 5655(point)s 6217(of)s 6498(appearance)s
7638(in)s 7891(the)s 8249(dynamic)s 0 711(parent)m 672(g)s 1(alle)k 3(y)k 15(,)k
1359(then)s 1843(carried)s 2579(along)s 3179(with)s 3676(it,)s
3931(ultimately)s 4968(to)s 5222(the)s 5586(root)s 6046(g)s 1(alle)k 3(y)k
6695(and)s 7115(the)s 7478(output)s 8165(\207le.)s 8650(This)s
0 423(process)m 800(is)s 1042(called)s 240 fnt3 1703 425(galle)m 7(y)k
2368(\210ushing)s 240 fnt1 3121 423(:)m 3259(the)s 3640(g)s 1(alle)k 3(ys)k
4396(are)s 4775(ri)s 6(v)k 3(ers)k 5393(running)s
6223(together)s 7098(to)s 7370(the)s 7750(sea,)s 8194(and)s
8631(each)s 0 135(component)m 1124(is)s 1334(a)s 1500(drop)s
1992(of)s 2263(w)s 2(ater)k 13(.)k 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 25 26
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5709 -1582(-)m 5837(25)s
6123(-)s 9066 13413 0 13304 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
480 13250(Here)m 1057(is)s 1324(a)s 1547(snapshot)s
2502(of)s 2830(a)s 3053(small)s 3682(dynamic)s 4616(tree,)s
5137(based)s 5797(on)s 6151(the)s 220 fnt5 6556 13247(@P)m 8(ageList)k
240 fnt1 7737 13250(de\207nitions)m 8855(of)s 0 12962(Section)m 774(3.2:)s
6982 3257 0 3257 240 288 60 480 9414 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
200 fnt3 0 3121(output)m 563(\207le)s gsave
860 0 translate
240 fnt1 0 3257 0 3165 240 288 60 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
0 0 0 0 240 288 60 0 3165 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(A) lfigpromotelabels
grestore
1994(r)s 9(oot)k
2370(galle)s 6(y)k gsave
1994 2967 translate
240 fnt1 1927 0 0 0 240 288 60 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
0 0 0 0 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(B) lfigpromotelabels
grestore
gsave
1994 473 translate
240 fnt1 1927 2494 0 2494 240 288 60 LoutGraphic
gsave
0 0 moveto xsize 0 lineto xsize ysize lineto
0 ysize lineto closepath stroke
grestore
160 fnt1
845 2216(-)m 931(1)s 1035(-)s 410 2000(A)m 563(small)s
140 fnt5 170 1784(@Galle)m 2(y)k 160 fnt1 743(*)s
904 1617 5 1545 160 180 40 853 275 LoutGr2
currentdict end 200 dict begin begin
grestore
10 10 5 5 160 180 40 0 1540 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(C) lfigpromotelabels
grestore
140 fnt5 170 173(@F)m 4(ootSect)k 
grestore
gsave
1994 0 translate
240 fnt1 1927 473 170 237 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
140 fnt5
170 201(@P)m 5(ageList 2)k 
grestore
5055 2611(body)m 5490(te)s 4(xt)k
gsave
5055 1974 translate
240 fnt1 1927 483 170 240 240 288 60 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
1927 483 170 240 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
160 fnt1 170 204(paragraph)m 
grestore
(D) lfigpromotelabels
grestore
gsave
5055 1524 translate
240 fnt1 1927 450 170 207 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
160 fnt1
170 171(of)m 351(te)s 2(xt.)k 
grestore
gsave
5055 1034 translate
240 fnt1 1927 490 170 244 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
160 fnt5
170 203(@Input)m 
grestore
gsave
0 0 translate
240 fnt1 0 0 0 0 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ B@W lfigprevious /FROM lfigpointdef
A@E lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
gsave
0 0 translate
240 fnt1 0 0 0 0 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ D@W lfigprevious /FROM lfigpointdef
C@E lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
end end restore
grestore
0 8963(The)m 472(components)s
1724(of)s 2039(the)s 2431(body)s 3009(te)s 3(xt)k
3468(g)s 1(alle)k 3(y)k 4146(are)s 4537(lines,)s
5139(e)s 3(xcept)k 5864(for)s 6246(the)s 6638(special)s
7400(recepti)s 6(v)k 3(e)k 8366(symbol)s 220 fnt5
0 8672(@Input)m 240 fnt1 759 8675(which)m 1393(is)s 1595(a)s
1753(placeholder)s 2920(for)s 3249(as)s 3491(yet)s 3835(unread)s
4536(input)s 5080(\(Section)s 5924(5.4\).)s 6459(The)s 6879(components)s
8079(of)s 8342(the)s 8681(root)s 0 8387(g)m 1(alle)k 3(y)k
646(are)s 1006(pages,)s 1671(e)s 3(xcept)k 2364(for)s
2715(the)s 3076(concluding)s 4205(une)s 3(xpanded)k 5431(in)s 9(v)k 4(ocation)k
6498(of)s 220 fnt5 6781 8384(@P)m 8(ageList)k 240 fnt1
7845 8387(,)m 7965(which)s 8620(is)s 8843(an)s 0 8099(ine)m 3(xhaustible)k
1328(source)s 2008(of)s 2279(more)s 2826(pages,)s 3478(e)s 3(xpanded)k
4451(on)s 4748(demand.)s 480 7725(The)m 923(concrete)s 1804(data)s
2277(structure)s 3184(used)s 3696(by)s 4006(Basser)s 4718(Lout)s
5246(permits)s 6028(the)s 6392(g)s 1(alle)k 3(y)k
7041(\210ushing)s 7882(algorithm)s 8887(to)s 0 7437(na)m 4(vig)k 1(ate)k
861(the)s 1209(dynamic)s 2086(tree)s 2499(and)s 2903(\207nd)s
3334(signi\207cant)s 4390(features)s 5196(quickly:)s gsave
480 78 translate
200 fnt1 8081 7019 226 7019 200 288 50 LoutGraphic
gsave
grestore save gsave 100 dict begin lfigdict begin
grestore
980 7019 226 6704 200 288 50 0 0 LoutGr2
currentdict end 100 dict begin begin
grestore
980 585 226 270 200 288 50 0 6434 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3
226 226(HEAD)m 
grestore
(A) lfigpromotelabels
grestore
1927 588 226 273 200 288 50 1830 6431 LoutGr2
currentdict end 100 dict begin begin
grestore
1631 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3 226 229(RECEIVING)m 1306(*)s 
grestore
(B) lfigpromotelabels
grestore
0 0 0 0 200 288 50 1830 6431 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
B@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 588 226 273 200 288 50 1830 5503 LoutGr2
currentdict end 100 dict begin begin
grestore
1498 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3
226 229(RECEPTIVE)m 
grestore
(C) lfigpromotelabels
grestore
0 0 0 0 200 288 50 1830 5503 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR C@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
C@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 0 0 0 200 288 50 1830 5163 LoutGr2
currentdict end 100 dict begin begin
grestore
0 0 0 0 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore

grestore
(D) lfigpromotelabels
grestore
0 0 0 0 200 288 50 1830 5163 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR D@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
D@NW lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 2494 0 2494 200 288 50 1830 2669 LoutGr2
0 0 moveto xsize 0 lineto xsize ysize lineto
0 ysize lineto closepath stroke
grestore
160 fnt1 845 2216(-)m 931(1)s 1035(-)s
410 2000(A)m 563(small)s 1587 1611 0 1545 160 180 40 170 275 LoutGr2
currentdict end 100 dict begin begin
grestore
572 132 0 66 160 180 40 0 1479 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
140 fnt5 0 30(@Galle)m 2(y )k

grestore
(E) lfigpromotelabels
grestore
1587 105 0 39 160 180 40 170 170 LoutGr2
currentdict end 100 dict begin begin
grestore
731 105 0 39 160 180 40 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
140 fnt5 0 3(@F)m 4(ootSect )k 
grestore
(F) lfigpromotelabels
grestore

grestore
0 0 0 0 200 288 50 1830 2669 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ B@E B@E 0 B@E E@E lfigydistance lfigpadd E@E ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
0 0 0 0 200 288 50 1830 2669 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ C@E C@E 0 C@E F@E lfigydistance lfigpadd F@E ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 588 226 273 200 288 50 1830 1741 LoutGr2
currentdict end 100 dict begin begin
grestore
839 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3 226 229(GAP)m

grestore
(C) lfigpromotelabels
grestore
0 0 0 0 200 288 50 1830 1741 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR C@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
C@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 588 226 273 200 288 50 1830 813 LoutGr2
currentdict end 100 dict begin begin
grestore
1498 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3 226 229(RECEPTIVE)m 
grestore
(C) lfigpromotelabels
grestore
0 0 0 0 200 288 50 1830 813 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR C@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
C@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 473 170 237 200 288 50 1830 0 LoutGr2
currentdict end 100 dict begin begin
grestore
1927 473 170 237 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
140 fnt5 170 201(@P)m 5(ageList 2)k

grestore
(D) lfigpromotelabels
grestore
0 0 0 0 200 288 50 1830 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR D@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
D@NW lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
0 0 0 0 200 288 50 1830 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ C@E C@E 0 C@E D@W 1.8 cm 0 lfigpadd lfigydistance lfigpadd D@W 1.8 cm 0 lfigpadd ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
980 7019 226 6704 200 288 50 4324 0 LoutGr2
currentdict end 100 dict begin begin
grestore
980 585 226 270 200 288 50 0 6434 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3 226 226(HEAD)m 
grestore
(A) lfigpromotelabels
grestore
0 0 0 0 200 288 50 5304 6704 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ B@E lfigprevious /FROM lfigpointdef
A@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 483 170 240 200 288 50 6154 6536 LoutGr2
currentdict end 100 dict begin begin
grestore
1927 483 170 240 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
160 fnt1 170 204(paragraph)m 
grestore
(B) lfigpromotelabels
grestore
0 0 0 0 200 288 50 6154 6536 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
B@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 588 226 273 200 288 50 6154 5608 LoutGr2
currentdict end 100 dict begin begin
grestore
839 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3
226 229(GAP)m 
grestore
(B) lfigpromotelabels
grestore
0 0 0 0 200 288 50 6154 5608 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
B@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 450 170 207 200 288 50 6154 4818 LoutGr2
currentdict end 100 dict begin begin
grestore
1927 450 170 207 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
160 fnt1 170 171(of)m 351(te)s 2(xt.)k

grestore
(B) lfigpromotelabels
grestore
0 0 0 0 200 288 50 6154 4818 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR B@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
B@NW lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 588 226 273 200 288 50 6154 3890 LoutGr2
currentdict end 100 dict begin begin
grestore
839 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3 226 229(GAP)m 
grestore
(B) lfigpromotelabels
grestore
0 0 0 0 200 288 50 6154 3890 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
B@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 588 226 273 200 288 50 6154 2962 LoutGr2
currentdict end 100 dict begin begin
grestore
1498 588 226 273 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigellipse ] lfigdopath
pop pop
grestore
200 fnt3 226 229(RECEPTIVE)m 
grestore
(B) lfigpromotelabels
grestore
0 0 0 0 200 288 50 6154 2962 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR B@W lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
B@W lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
1927 471 170 235 200 288 50 6154 2151 LoutGr2
currentdict end 100 dict begin begin
grestore
1927 471 170 235 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
140 fnt5
170 199(@Input)m 
grestore
(C) lfigpromotelabels
grestore
0 0 0 0 200 288 50 6154 2151 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@CTR A@CTR C@NW lfigangle A@CIRCUM lfigpadd lfigprevious /FROM lfigpointdef
C@NW lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
0 0 0 0 200 288 50 6154 2151 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ B@E B@E 0 B@E C@W 1.2 cm 0 lfigpadd lfigydistance lfigpadd C@W 1.2 cm 0 lfigpadd ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
end end restore
grestore

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 26 27
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1581(-)m 5833(26)s
6126(-)s 9066 13414 0 13414 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13251(Each)m 521(g)s 1(alle)k 3(y)k
1140(has)s 1495(a)s 240 fnt3 1647 13253(HEAD)m 240 fnt1
2325 13251(node)m 2832(whose)s 3485(children)s 4311(are)s 4643(its)s
4904(component)s 6013(objects,)s 6783(separated)s 7728(by)s 240 fnt3
8007 13253(GAP)m 240 fnt1 8516 13251(nodes)m 0 12963(recording)m 969(the)s
1317(inter)s 4(-component)k 2953(g)s 1(aps.)k 480 12589(Each)m
1026(component)s 2161(is)s 2383(preceded)s 3315(by)s 3621(zero)s
4096(or)s 4367(more)s 240 fnt3 4925 12591(galle)m 7(y)k
5569(inde)s 4(x)k 6155(nodes)s 240 fnt1 6780 12589(of)m
7063(v)s 6(arious)k 7823(types.)s 8504(Ev)s 3(ery)k
0 12301(recepti)m 6(v)k 3(e)k 922(symbol)s 1681(has)s
2051(a)s 240 fnt3 2216 12303(RECEPTIVE)m 240 fnt1 3529 12301(inde)m 3(x)k
4112(pointing)s 4963(to)s 5201(it,)s 5440(so)s 5705(that)s
6123(it)s 6314(can)s 6703(be)s 6984(found)s 7601(without)s
8391(search)s 8998(-)s 0 12013(ing)m 355(through)s 1152(its)s
1423(component.)s 2646(If)s 2871(the)s 3215(symbol)s 3970(is)s
4175(currently)s 5086(the)s 5429(tar)s 4(get)k 6023(of)s
6290(a)s 6451(g)s 1(alle)k 3(y)k 15(,)k
7118(it)s 7305(has)s 7670(a)s 240 fnt3 7831 12015(RECEIVING)m
240 fnt1 0 11725(inde)m 3(x)k 595(instead)s 1342(which)s
1995(is)s 2217(also)s 2667(link)s 2(ed)k 3332(to)s
3583(the)s 3942(incoming)s 4911(g)s 1(alle)k 3(y)k 15(.)k
5652(Galle)s 3(ys)k 6441(that)s 6871(are)s 7229(currently)s
8157(without)s 8960(a)s 0 11437(tar)m 4(get)k 586(are)s
920(link)s 2(ed)k 1560(to)s 1786(the)s 2120(dynamic)s
2984(tree)s 3383(by)s 240 fnt3 3664 11439(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k
240 fnt1 5215 11437(g)m 1(alle)k 3(y)k 5836(inde)s 3(x)k 3(es,)k
6654(either)s 7244(just)s 7635(after)s 8118(their)s 8601(most)s
0 11149(recent)m 643(tar)s 4(get)k 1242(if)s 1459(there)s
1992(has)s 2362(been)s 2871(one,)s 3324(or)s 3583(else)s
4010(at)s 4242(their)s 4739(point)s 5291(of)s 5562(in)s 9(v)k 4(ocation.)k
480 10775(Each)m 1041(g)s 1(alle)k 3(y)k 1701(should)s
2424(be)s 2732(thought)s 3550(of)s 3847(as)s 4123(a)s
4315(concurrent)s 5423(process,)s 6273(although)s 7194(the)s 7569(implementation)s
0 10487(in)m 268(C)s 506(uses)s 995(coroutines)s 2067(implemented)s
3399(by)s 3719(procedures.)s 4957(A)s 5213(g)s 1(alle)k 3(y)k
5873(may)s 6364(promote)s 7243(its)s 7545(\207rst)s 8002(component)s
0 10199(only)m 499(if)s 735(it)s 946(has)s 1335(a)s
1520(tar)s 4(get,)k 2185(suf\207cient)s 3153(space)s 3759(is)s
3988(a)s 4(v)k 6(ailable)k 4915(at)s 5166(the)s
5533(tar)s 4(get)k 6151(to)s 6409(recei)s 6(v)k 3(e)k
7164(the)s 7531(component,)s 8722(and)s 0 9911(the)m 349(component)s
1475(contains)s 2325(no)s 2620(recepti)s 6(v)k 3(e)k
3544(symbols.)s 4508(This)s 4986(last)s 5379(condition)s 6342(seems)s
6979(to)s 7220(be)s 7504(the)s 7854(k)s 2(e)k 3(y)k
8251(to)s 8492(g)s 1(alle)k 3(y)k 0 9623(synchronization:)m
1722(it)s 1943(forces)s 2606(a)s 2801(bottom-up)s 3880(promotion)s
4963(re)s 3(gime,)k 5759(pre)s 6(v)k 3(enting)k
6855(pages)s 7480(from)s 8033(\210ushing)s 8887(to)s 0 9335(output)m
672(before)s 1338(te)s 3(xt)k 1753(\210ushes)s 2469(into)s
2894(them,)s 3479(for)s 3817(e)s 3(xample.)k 480 8961(Each)m
1022(g)s 1(alle)k 3(y)k 1663(contains)s 2519(a)s
2692(number)s 3490(of)s 3769(binary)s 4441(semaphores,)s 5685(sho)s 6(wn)k
6369(as)s 6626(asterisks)s 7507(in)s 7757(our)s 8144(snapshots)s
0 8673(when)m 583(set.)s 1019(At)s 1325(an)s 3(y)k
1730(gi)s 6(v)k 3(en)k 2317(moment,)s 3215(a)s
3389(g)s 1(alle)k 3(y)k 4030(process)s 4805(is)s
5022(either)s 5633(running)s 6438(or)s 6704(else)s 7139(is)s
7356(suspended)s 8419(on)s 8724(one)s 0 8385(of)m 269(its)s
543(o)s 6(wn)k 1005(semaphores.)s 2296(The)s 240 fnt3
2722 8387(HEAD)m 240 fnt1 3413 8385(node)m 3933(contains)s 4779(a)s
4943(semaphore)s 6033(which)s 6673(is)s 6881(set)s 7204(when)s
7778(the)s 8124(g)s 1(alle)k 3(y)k 8756(has)s
0 8097(tried)m 499(to)s 742(\207nd)s 1177(a)s 1347(tar)s 4(get)k
1950(and)s 2359(f)s 2(ailed.)k 3068(Each)s 3607(recepti)s 6(v)k 3(e)k
4533(symbol)s 5297(has)s 5671(a)s 5842(semaphore)s 6938(which)s
7584(is)s 7798(set)s 8127(when)s 8708(that)s 0 7809(symbol)m
760(is)s 970(pre)s 6(v)k 3(enting)k 2037(the)s
2385(\207rst)s 2816(component)s 3940(from)s 4464(being)s 5049(promoted.)s
480 7435(F)m 3(or)k 859(e)s 3(xample,)k 1762(in)s
1994(the)s 2331(snapshot)s 3218(at)s 3439(the)s 3776(be)s 3(ginning)k
4773(of)s 5033(this)s 5418(section,)s 6191(the)s 6528(root)s
6962(g)s 1(alle)k 3(y)k 7585(is)s 7784(suspended)s
8829(on)s 0 7147(the)m 220 fnt5 351 7144(@Galle)m 4(y)k
240 fnt1 1253 7147(symbol,)m 2069(b)s 4(ut)k 2435(the)s
2787(te)s 3(xt)k 3205(g)s 1(alle)k 3(y)k
3843(is)s 4057(running.)s 4970(It)s 5179(will)s 5608(suspend)s
6442(on)s 6743(the)s 220 fnt5 7095 7144(@Input)m 240 fnt1
7866 7147(symbol)m 8630(after)s 0 6859(the)m 348(\207rst)s 779(tw)s 2(o)k
1189(components)s 2397(are)s 2744(promoted.)s 480 6485(Ev)m 3(ery)k
1145(g)s 1(alle)k 3(y)k 240 fnt3 1822 6487(G)m
240 fnt1 1995 6485(,)m 2145(be)s 2470(it)s 2705(a)s
2914(list)s 3308(of)s 3623(pages,)s 4318(body)s 4895(te)s 3(xt,)k
5400(a)s 5609(footnote,)s 6556(or)s 6858(whate)s 6(v)k 3(er)k 9(,)k
7866(e)s 3(x)k 3(ecutes)k 8778(the)s 0 6197(follo)m 6(wing)k
977(algorithm)s 1966(in)s 2209(parallel)s 2979(with)s 3461(e)s 6(v)k 3(ery)k
4037(other)s 4588(g)s 1(alle)k 3(y:)k 0 5694(1.)m
303(Initially)s 240 fnt3 1132 5696(G)m 240 fnt1 1384 5694(is)m
1614(unattached.)s 2834(Search)s 3560(forw)s 2(ards)k 4478(or)s
4756(backw)s 2(ards)k 5848(from)s 6392(its)s 240 fnt3
6687 5696(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k
240 fnt1 8272 5694(inde)m 3(x)k 8876(as)s 0 5406(required,)m
903(to)s 1142(\207nd)s 1573(a)s 1739(recepti)s 6(v)k 3(e)k
2661(symbol)s 240 fnt3 3421 5408(S)m 240 fnt1 3602 5406(which)m
4244(can)s 4633(e)s 3(xpand)k 5380(to)s 5619(re)s 6(v)k 3(eal)k
6248(a)s 6414(tar)s 4(get)k 7013(for)s 240 fnt3
7351 5408(G)m 240 fnt1 7524 5406(.)m 0 4903(2.)m 284(If)s
514(no)s 240 fnt3 807 4905(S)m 240 fnt1 988 4903(can)m
1377(be)s 1659(found,)s 2325(suspend)s 3155(on)s 3452(the)s
3800(attachment)s 4908(semaphore.)s 6108(Resume)s 6935(later)s 7418(from)s
7942(step)s 8380(1.)s 0 4400(3.)m 281(Expand)s 240 fnt3
1068 4402(S)m 240 fnt1 1246 4400(to)m 1482(re)s 6(v)k 3(eal)k
2107(the)s 2452(tar)s 4(get)k 3048(of)s 240 fnt3
3316 4402(G)m 240 fnt1 3489 4400(.)m 3649(Preserv)s 3(e)k
240 fnt3 4521 4402(S)m 240 fnt1 4642 4400(')m 13(s)k
4849(semaphore)s 5938(by)s 6229(mo)s 3(ving)k 7007(it)s
7196(to)s 7432(the)s 7777(\207rst)s 8204(recepti)s 6(v)k 3(e)k
0 4112(symbol)m 760(within)s 1428(the)s 1776(e)s 3(xpansion)k
2801(of)s 240 fnt3 3072 4114(S)m 240 fnt1 3193 4112(.)m
0 3609(4.)m 295(Calculate)s 1264(the)s 1624(a)s 4(v)k 6(ailable)k
2543(width)s 3156(and)s 3572(height)s 4241(at)s 4484(the)s
4844(tar)s 4(get,)k 5501(and)s 5917(if)s 240 fnt3
6145 3611(G)m 240 fnt1 6389 3609(is)m 6611(still)s 7034(a)s
7211(pure)s 7704(parse)s 8275(tree,)s 8751(use)s 0 3321(the)m
377(en)s 9(vironment)k 1667(attached)s 2550(to)s 240 fnt3
2819 3323(G)m 240 fnt1 3081 3321(and)m 3515(the)s 3892(style)s
4429(information)s 5643(from)s 6197(the)s 6574(tar)s 4(get)k
7203(to)s 7471(e)s 6(v)k 6(aluate)k 240 fnt3
8341 3323(G)m 240 fnt1 8603 3321(as)m 8883(in)s 0 3033(Section)m
774(4.)s 0 2577(5.)m 284(Examine)s 1190(the)s 1538(components)s
2746(of)s 240 fnt3 3017 2579(G)m 240 fnt1 3250 2577(one)m
3652(by)s 3946(one.)s 4456(F)s 3(or)k 4845(each)s
5340(component)s 6464(there)s 6997(are)s 7344(three)s 7877(possibilities:)s
240 fnt3 480 2205(A)m 7(CCEPT)k 17(.)k 240 fnt1
1513 2203(If)m 1756(the)s 2116(component)s 3253(\207ts)s 3609(into)s
4046(the)s 4407(a)s 4(v)k 6(ailable)k 5328(space,)s
5978(and)s 6395(has)s 6778(no)s 7083(other)s 7647(problems,)s
8657(then)s 0 1915(promote)m 875(it)s 1090(into)s 1538(the)s
1909(tar)s 4(get.)k 2635(If)s 2888(this)s 3306(is)s
3539(the)s 3910(\207rst)s 4364(component)s 5511(promoted)s 6509(into)s
6956(this)s 7375(tar)s 4(get,)k 8044(and)s 240 fnt3
8471 1917(G)m 240 fnt1 8727 1915(is)m 8960(a)s 0 1627(forcing)m
768(g)s 1(alle)k 3(y)k 1428(\(Section)s 2307(5.4\),)s
2819(delete)s 3470(e)s 6(v)k 3(ery)k 4072(recepti)s 6(v)k 3(e)k
5020(symbol)s 5806(preceding)s 6827(the)s 7201(tar)s 4(get)k
7826(in)s 8095(the)s 8469(parent)s 0 1339(g)m 1(alle)k 3(y)k 15(.)k
729(If)s 240 fnt3 959 1341(G)m 240 fnt1 1192 1339(is)m
1402(the)s 1750(root)s 2195(g)s 1(alle)k 3(y)k 15(,)k
2867(render)s 3537(the)s 3885(component)s 5009(on)s 5306(the)s
5654(output)s 6326(\207le)s 6687(and)s 7091(dispose)s 7865(it;)s
240 fnt3 480 967(REJECT)m 17(.)k 240 fnt1 1490 965(If)m
1756(the)s 2140(component)s 3300(is)s 3546(too)s 3941(lar)s 4(ge)k
4506(for)s 4880(the)s 5264(a)s 4(v)k 6(ailable)k
6208(space,)s 6882(or)s 7177(a)s 240 fnt3 7379 967(FOLLO)m 12(WS)k
240 fnt1 8542 965(inde)m 3(x)k 0 677(\(described)m 1043(belo)s 6(w\))k
1740(forbids)s 2458(its)s 2723(promotion)s 3767(into)s 4182(this)s
4568(tar)s 4(get,)k 5203(then)s 5662(detach)s 240 fnt3
6333 679(G)m 240 fnt1 6556 677(from)m 7069(the)s 7407(tar)s 4(get.)k
8100(If)s 8320(this)s 8705(w)s 2(as)k 0 389(the)m
338(\207rst)s 758(component)s 1872(at)s 2093(this)s 2479(tar)s 4(get,)k
240 fnt3 3114 391(S)m 240 fnt1 3284 389(has)m 3644(been)s
4142(a)s 4298(complete)s 5219(f)s 2(ailure,)k 5936(so)s
6191(undo)s 6713(step)s 7141(3)s 7294(\(Basser)s 8060(Lout)s
8561(is)s 8760(not)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 27 28
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5708 -1579(-)m 5836(27)s
6124(-)s 9066 13418 0 13309 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13255(able)m 454(to)s 693(undo)s 1226(step)s
1664(4\);)s 1975(otherwise)s 2960(delete)s 3586(the)s 3934(tar)s 4(get.)k
4637(Return)s 5345(to)s 5584(step)s 6022(1)s 6177(and)s
6581(continue)s 7461(immediately;)s 240 fnt3 480 12883(SUSPEND.)m 240 fnt1
1685 12881(If)m 1928(the)s 2289(component)s 3426(contains)s 4287(a)s
4466(recepti)s 6(v)k 3(e)k 5402(symbol,)s 6227(it)s
6432(cannot)s 7143(be)s 7438(promoted)s 8426(yet.)s 8896(If)s
0 12593(this)m 392(symbol)s 1148(is)s 1354(the)s 1697(tar)s 4(get)k
2292(of)s 2559(a)s 2720(g)s 1(alle)k 3(y)k
3350(that)s 3764(w)s 2(as)k 4180(written)s 4909(to)s
5144(an)s 5423(auxiliary)s 6321(\207le)s 6678(on)s 6971(a)s
7132(pre)s 6(vious)k 7997(run,)s 8419(read)s 8883(in)s
0 12305(that)m 427(g)s 1(alle)k 3(y)k 1071(and)s
1484(\210ush)s 2017(it.)s 2322(Otherwise)s 3370(suspend)s 4209(on)s
4516(the)s 4873(recepti)s 6(v)k 3(e)k 5805(symbol')s 13(s)k
6729(semaphore;)s 7887(resume)s 8643(later)s 0 12017(from)m 524(step)s
962(4.)s 0 11513(6.)m 284(T)s 16(erminate)k 1305(when)s
1881(the)s 2229(g)s 1(alle)k 3(y)k 2863(is)s
3073(empty)s 15(.)k 0 11010(At)m 354(v)s 6(arious)k
1158(points)s 1850(in)s 2148(this)s 2599(algorithm,)s 3691(recepti)s 6(v)k 3(e)k
4668(symbols)s 5572(\(and)s 6111(their)s 6663(semaphores\))s 7975(are)s
8378(deleted)s 0 10722(in)m 273(the)s 652(dynamic)s 1560(parent)s
2247(g)s 1(alle)k 3(y)k 15(,)k 2950(possibly)s
3833(permitting)s 4911(it)s 5134(to)s 5404(resume)s 6180(\210ushing.)s
7147(When)s 7807(this)s 8234(happens,)s 0 10434(Basser)m 701(Lout)s
1218(resumes)s 2057(the)s 2410(parent)s 3071(immediately)s 4324(after)s
240 fnt3 4825 10436(G)m 240 fnt1 5063 10434(suspends)m 5983(or)s
6247(terminates.)s 7410(Also,)s 7974(whene)s 6(v)k 3(er)k
8960(a)s 0 10146(component)m 1140(is)s 1366(promoted,)s 2406(an)s 3(y)k
2819(child)s 3371(g)s 1(alle)k 3(ys)k 4111(connected)s
5156(to)s 5411(it)s 5619(by)s 240 fnt3 5929 10148(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k
240 fnt1 7510 10146(inde)m 3(x)k 3(es)k 8302(must)s
8844(be)s 0 9858(resumed,)m 918(since)s 1466(these)s 2014(g)s 1(alle)k 3(ys)k
2739(may)s 3206(be)s 3490(able)s 3945(to)s 4185(\207nd)s
4617(a)s 4784(tar)s 4(get)k 5384(no)s 6(w)k 15(.)k
5942(A)s 6173(good)s 6712(e)s 3(xample)k 7576(of)s
7848(this)s 8246(situation)s 0 9570(occurs)m 664(when)s 1228(a)s
1382(line)s 1785(of)s 2044(body)s 2566(te)s 3(xt)k
2969(with)s 3440(one)s 3830(or)s 4077(more)s 4613(footnotes)s
5542(is)s 5740(promoted)s 6703(onto)s 7171(a)s 7325(page.)s
7929(Basser)s 8614(Lout)s 0 9282(gi)m 6(v)k 3(es)k
547(priority)s 1317(to)s 1556(such)s 2052(children,)s 2942(suspending)s
240 fnt3 4073 9284(G)m 240 fnt1 4306 9282(while)m 4893(each)s
5388(is)s 5598(gi)s 6(v)k 3(en)k 6178(a)s
6344(chance)s 7064(to)s 7303(\210ush.)s 480 8908(Basser)m 1211(Lout)s
1758(searches)s 2653(for)s 3025(the)s 3408(\207rst)s 3874(tar)s 4(get)k
4507(of)s 240 fnt3 4813 8910(G)m 240 fnt1 5081 8908(only)m
5595(in)s 5873(re)s 3(gions)k 6660(of)s 6965(the)s
7348(dynamic)s 8260(tree)s 8708(that)s 0 8620(will)m 437(clearly)s
1152(precede)s 1963(or)s 2233(follo)s 6(w)k 240 fnt3
2917 8622(G)m 240 fnt1 3090 8620(')m 13(s)k 3312(in)s 9(v)k 4(ocation)k
4378(point)s 4941(in)s 5196(the)s 5556(\207nal)s 6047(printed)s
6794(document,)s 7857(whiche)s 6(v)k 3(er)k 8916(is)s
0 8332(speci\207ed)m 904(in)s 1142(the)s 220 fnt5 1486 8329(into)m
240 fnt1 1887 8332(clause;)m 2591(subsequent)s 3711(tar)s 4(gets)k
4389(are)s 4731(sought)s 5426(later)s 5904(in)s 6142(the)s
6486(same)s 7028(g)s 1(alle)k 3(y)k 7657(as)s
7903(the)s 8246(\207rst.)s 8776(An)s 0 8044(e)m 3(xception)k
982(to)s 1219(this)s 1613(rule,)s 2089(whose)s 2755(necessity)s
3683(will)s 4107(be)s 4387(made)s 4959(clear)s 5480(later)s 9(,)k
5999(is)s 6207(that)s 6623(a)s 6787(\207rst)s 220 fnt5
7216 8041(f)m 6(ollo)k 3(wing)k 240 fnt1 8104 8044(tar)m 4(get)k
8700(will)s 0 7756(be)m 282(sought)s 981(within)s 1649(a)s
1815(dynamic)s 2692(sibling)s 3396(g)s 1(alle)k 3(y)k
4030(preceding)s 240 fnt3 5026 7758(G)m 240 fnt1 5199 7756(')m 13(s)k
5409(in)s 9(v)k 4(ocation)k 6463(point:)s gsave
480 2770 translate
200 fnt1
5379 4646 0 4646 200 288 50 LoutGraphic
gsave
grestore save gsave 200 dict begin lfigdict begin
grestore
200 fnt3 0 4510(dynamic)m 722(par)s 7(ent)k gsave
0 1353 translate
200 fnt1
2039 3003 226 2777 200 288 50 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1587 171 0 86 200 288 50 226 2323 LoutGr2
currentdict end 200 dict begin begin
grestore
796 171 0 86 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
180 fnt5 0 40(@XT)m 21(arget)k 
grestore
(A) lfigpromotelabels
grestore
1587 136 0 47 200 288 50 226 1620 LoutGr2
currentdict end 200 dict begin begin
grestore
1254 136 0 47 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
200 fnt3 0 3(UN)m 5(A)k 7(TT)k 10(A)k 6(CHED)k

grestore
(C) lfigpromotelabels
grestore
180 fnt5 226 752(@XT)m 21(arget)k 
grestore
gsave
2889 4135 translate
200 fnt1 2490 171 0 86 200 288 50 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
2450 171 0 86 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
180 fnt5
0 40(X into { @XT)m 21(arget&&f)k 5(ollo)k 2(wing })k 
grestore
(B) lfigpromotelabels
grestore
gsave
2889 2720 translate
200 fnt1
2039 1302 226 1076 200 288 50 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
180 fnt5 226 492(@GT)m 21(arget)k 
grestore
gsave
2889 1982 translate
200 fnt1 2490 171 0 86 200 288 50 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
2490 171 0 86 200 288 50 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
180 fnt5
0 40(G into { @GT)m 21(arget&&f)k 5(ollo)k 2(wing })k 
grestore
(D) lfigpromotelabels
grestore
gsave
2889 0 translate
200 fnt1
2039 1869 226 1643 200 288 50 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore

grestore
gsave
0 0 translate
200 fnt1 0 0 0 0 200 288 50 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef
0.2 cm 0 B@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
gsave
0 0 translate
200 fnt1 0 0 0 0 200 288 50 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ C@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef
0.2 cm 0 D@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
end end restore
grestore
0 2319(Here)m 240 fnt3 524 2321(G)m
240 fnt1 762 2319(will)m 1193(\207nd)s 1629(the)s 220 fnt5
1982 2316(@GT)m 26(arget)k 240 fnt1 3045 2319(tar)m 4(get)k
3649(within)s 240 fnt3 4322 2321(X)m 240 fnt1 4478 2319(.)m
4647(This)s 5128(is)s 5343(dangerous,)s 6439(since)s 6991(if)s
7213(the)s 7566(\207rst)s 8002(component)s 0 2031(of)m 240 fnt3
303 2033(G)m 240 fnt1 568 2031(is)m 811(then)s 1312(promoted)s
2320(via)s 240 fnt3 2704 2033(X)m 240 fnt1 2952 2031(into)m
3410(the)s 3790(\207rst)s 220 fnt5 4254 2028(@XT)m 26(arget)k
240 fnt1 5319 2031(rather)m 5967(than)s 6469(into)s 6926(the)s
7307(second,)s 240 fnt3 8111 2033(G)m 240 fnt1 8284 2031(')m 13(s)k
8527(tar)s 4(get)k 0 1743(will)m 438(not)s 817(appear)s
1526(later)s 2022(in)s 2277(the)s 2638(\207nal)s 3130(printed)s
3878(document)s 4894(than)s 5376(its)s 5664(in)s 9(v)k 4(ocation)k
6731(point,)s 7342(as)s 7605(required)s 8471(by)s 8778(the)s
220 fnt5 0 1452(into)m 240 fnt1 406 1455(clause.)m 480 1081(Accordingly)m 15(,)k
1753(when)s 2313(such)s 2794(a)s 2944(tar)s 4(get)k
3528(is)s 3722(chosen,)s 4478(tw)s 2(o)k 4873(special)s
5575(g)s 1(alle)k 3(y)k 6194(inde)s 3(x)k 3(es)k
6954(are)s 7286(inserted)s 8084(and)s 8472(link)s 2(ed)k
0 793(together:)m 898(a)s 240 fnt3 1074 795(PRECEDES)m 240 fnt1
2327 793(inde)m 3(x)k 2921(at)s 240 fnt3 3163 795(G)m
240 fnt1 3336 793(')m 13(s)k 3555(in)s 9(v)k 4(ocation)k
4619(point,)s 5227(and)s 5641(a)s 240 fnt3 5817 795(FOLLO)m 12(WS)k
240 fnt1 6952 793(inde)m 3(x)k 7546(at)s 7787(the)s
8145(\207rst)s 8586(com)s 8998(-)s 0 505(ponent)m 720(of)s
240 fnt3 1000 507(G)m 240 fnt1 1173 505(.)m 1346(The)s
1783(algorithm)s 2781(checks)s 3492(before)s 4167(promoting)s 5226(an)s 3(y)k
240 fnt3 5632 507(FOLLO)m 12(WS)k 240 fnt1 6767 505(inde)m 3(x)k
7360(that)s 7787(its)s 8072(promotion)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 28 29
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
%%+ font Symbol
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5708 -1579(-)m 5836(28)s
6123(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13253(w)m 2(ould)k 661(not)s 1033(place)s
1600(it)s 1798(earlier)s 2472(than)s 2948(the)s 3302(corresponding)s
240 fnt3 4730 13255(PRECEDES)m 240 fnt1 5981 13253(inde)m 3(x)k
6571(in)s 6820(the)s 7175(same)s 7728(g)s 1(alle)k 3(y)k 15(,)k
8406(and)s 8817(re)s 8998(-)s 0 12965(jects)m 486(the)s
831(component)s 1952(if)s 2166(it)s 2355(w)s 2(ould.)k
3113(Since)s 240 fnt3 3697 12967(PRECEDES)m 240 fnt1 4939 12965(and)m
240 fnt3 5340 12967(FOLLO)m 12(WS)k 240 fnt1 6463 12965(inde)m 3(x)k 3(es)k
7236(are)s 7580(rarely)s 8187(used,)s 8730(this)s 0 12677(check)m
619(can)s 1008(be)s 1290(implemented)s 2596(by)s 2890(linear)s
3493(search.)s 480 12303(When)m 1114(tw)s 2(o)k 1529(components)s
2742(are)s 3094(separated)s 4060(by)s 220 fnt5 4359 12300(/)m
240 fnt1 4423 12303(,)m 4535(as)s 4790(opposed)s 5652(to)s
5897(the)s 6250(more)s 6802(usual)s 220 fnt5 7367 12300(//)m
240 fnt1 7492 12303(,)m 7604(each)s 8105(in\210uences)s 0 12015(the)m
358(horizontal)s 1393(position)s 2232(of)s 2514(the)s 2872(other)s 13(.)k
3525(Because)s 4389(of)s 4671(this,)s 5133(the)s 240 fnt3
5492 12017(SUSPEND)m 240 fnt1 6596 12015(action)m 7248(is)s 7468(in)s
7722(f)s 2(act)k 8148(tak)s 2(en)k 8732(if)s
8960(a)s 0 11727(recepti)m 6(v)k 3(e)k 930(symbol)s
1698(occurs)s 2382(in)s 2633(an)s 3(y)k 3039(component)s
4171(separated)s 5140(from)s 5672(the)s 6028(\207rst)s 6468(by)s
220 fnt5 6770 11724(/)m 240 fnt1 6903 11727(operators)m 7851(only)s 15(.)k
8435(Ag)s 1(ain,)k 0 11439(linear)m 603(search)s 1270(forw)s 2(ards)k
2168(to)s 2407(the)s 2755(\207rst)s 220 fnt5 3186 11436(//)m
240 fnt1 3371 11439(suf\207ces)m 4152(for)s 4490(this)s 4886(check.)s
480 11065(A)m 740(good)s 1308(illustration)s 2430(of)s 2731(these)s
3308(unusual)s 4139(cases)s 4724(is)s 4964(af)s 6(forded)k
5856(by)s 6180(the)s 220 fnt5 6558 11062(@Align)m 240 fnt1
7344 11065(symbols)m 8223(from)s 8778(the)s 0 10777(standard)m 867(DocumentLayout)s
2600(package.)s 3546(These)s 4171(are)s 4516(used)s 5012(to)s
5249(produce)s 6074(displayed)s 7047(equations,)s 8069(aligned)s 8829(on)s
0 10489(their)m 497(equals)s 1159(signs)s 1702(despite)s 2435(being)s
3020(separated)s 3980(by)s 4274(arbitrary)s 5149(body)s 5683(te)s 3(xt.)k
480 10115(The)m 220 fnt5 921 10112(@Align)m 240 fnt1 1689 10115(symbols)m
2551(are)s 2911(packaged)s 3886(neatly)s 4537(for)s 4889(the)s
5250(con)s 9(v)k 3(enience)k 6503(of)s 6787(the)s
7148(non-e)s 3(xpert)k 8254(user)s 9(,)k 8764(b)s 4(ut)k
0 9827(we)m 335(will)s 761(sho)s 6(w)k 1315(just)s
1720(the)s 2067(essence)s 2853(of)s 3124(the)s 3472(implementation)s
5029(here.)s 5603(First,)s 6147(an)s 220 fnt5 6430 9824(@AlignList)m
240 fnt1 7536 9827(g)m 1(alle)k 3(y)k 8170(is)s
8379(created)s 0 9539(which)m 642(contains)s 1490(an)s 1773(in\207nite)s
2506(supply)s 3199(of)s 220 fnt5 3470 9536(@AlignPlace)m 240 fnt1
4779 9539(recepti)m 6(v)k 3(e)k 5701(symbols)s 6550(separated)s
7510(by)s 220 fnt5 7804 9536(/)m 240 fnt1 7928 9539(operators:)m
4777 3207 0 3207 240 288 60 480 5992 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
240 fnt3 0 3044(body)m 522(te)s 4(xt)k 926(galle)s 7(y)k
gsave
0 161 translate
240 fnt1 2039 2720 226 2494 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1587 1418 0 1314 240 288 60 226 226 LoutGr2
currentdict end 200 dict begin begin
grestore
838 208 0 104 240 288 60 0 1210 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
220 fnt5 0 47(@Galle)m 4(y)k 
grestore
(A) lfigpromotelabels
grestore

grestore
gsave
2889 1638 translate
240 fnt1
1888 209 0 105 240 288 60 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
1046 209 0 105 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
220 fnt5 0 48(@AlignList)m 
grestore
(B) lfigpromotelabels
grestore
gsave
2889 0 translate
240 fnt1 1888 1525 226 1195 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
220 fnt5 226 1138(@AlignPlace)m
226 850(@AlignPlace)m 226 562(...)m 226 274(@EndAlignList)m 
grestore
gsave
0 0 translate
240 fnt1 0 0 0 0 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef
0.2 cm 0 B@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
end end restore
grestore
0 5541(Then)m
549(equations)s 1517(lik)s 2(e)k 1471 214 393 105 240 288 60 480 4987 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
1471 214 393 105 240 288 60 0 0 LoutGr2
/lfiglightgrey [ lfigbox ] gsave lfigpaintpath grestore
0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1471 214 393 105 240 288 60 0 0 LoutGr2

0.015 cm setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ -0.3 cm ymark xsize ymark 0.3 cm 0 lfigpadd
[]
xmark -0.3 cm xmark ysize 0 0.3 cm lfigpadd ] lfigdopath
pop pop
grestore
240 fnt3 0 53(f)m
240 fnt4 113 45(\()m 240 fnt3 197 53(x)m 240 fnt4
315 45(\))m 477(=)s 240 fnt3 690 53(g)m 240 fnt4
816 45(\()m 240 fnt3 900 53(x)m 240 fnt4 1018 45(\))m
1156(+)s 1357(2)s 
grestore

grestore
end end restore
grestore
0 4536(are)m 358(created)s 1117(and)s
1532(sent)s 1989(to)s 220 fnt5 2239 4533(@AlignPlace&&f)m 6(ollo)k 3(wing)k
240 fnt1 4690 4536(tar)m 4(gets.)k 5498(The)s 3(y)k
6052(collect)s 6760(in)s 7014(the)s 220 fnt5 7374 4533(@AlignList)m
240 fnt1 8492 4536(g)m 1(alle)k 3(y)k 0 4248(and)m
404(are)s 751(aligned)s 1513(there:)s 5836 3212 0 3212 240 288 60 480 696 LoutGr2
grestore save gsave 200 dict begin lfigdict begin
grestore
240 fnt3 0 3049(body)m
522(te)s 4(xt)k 926(galle)s 7(y)k gsave
0 166 translate
240 fnt1
2039 2720 226 2494 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
1587 1418 0 1314 240 288 60 226 226 LoutGr2
currentdict end 200 dict begin begin
grestore
838 208 0 104 240 288 60 0 1210 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
220 fnt5 0 47(@Galle)m 4(y)k 
grestore
(A) lfigpromotelabels
grestore

grestore
gsave
2889 1643 translate
240 fnt1 2947 209 0 105 240 288 60 LoutGraphic
gsave
currentdict end 200 dict begin begin
grestore
1046 209 0 105 240 288 60 0 0 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfignoline [ lfigbox ] lfigdopath
pop pop
grestore
220 fnt5
0 48(@AlignList)m 
grestore
(B) lfigpromotelabels
grestore
gsave
2889 0 translate
240 fnt1 2947 1530 1285 1195 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ lfigbox ] lfigdopath
pop pop
grestore
2495 1078 1059 969 240 288 60 226 226 LoutGr2

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigdashed [ xmark ysize lfigprevious /FROM lfigpointdef
xmark 0 lfigprevious /TO lfigpointdef ] lfigdopath
pop pop
grestore
240 fnt3 666 917(f)m 240 fnt4
779 909(\()m 240 fnt3 863 917(x)m 240 fnt4 981 909(\))m
1143(=)s 240 fnt3 1356 917(g)m 240 fnt4 1482 909(\()m
240 fnt3 1566 917(x)m 240 fnt4 1684 909(\))m 1822(+)s
2023(2)s 240 fnt3 0 629(f)m 240 fnt4 113 621(\()m
240 fnt3 197 629(x)m 240 fnt4 315 621(\))m 453(-)s
240 fnt3 653 629(g)m 240 fnt4 779 621(\()m 240 fnt3
863 629(x)m 240 fnt4 981 621(\))m 1143(=)s 1356(2)s
220 fnt5 1059 336(...)m 1059 48(@EndAlignList)m 
grestore

grestore
gsave
0 0 translate
240 fnt1 0 0 0 0 240 288 60 LoutGraphic
gsave

0.5 pt setlinewidth lfiground setlinecap
0.15 cm /lfigsolid [ A@E 0.2 cm 0 lfigpadd lfigprevious /FROM lfigpointdef
0.2 cm 0 B@W lfigpsub lfigprevious /TO lfigpointdef ] lfigdopath
0.15 cm /lfigsolid /lfigblack
lfigopen
0.15 cm 0.05 cm lfigforward
grestore

grestore
end end restore
grestore

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 29 30
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
%%+ font Times-Bold
%%+ font Symbol
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5706 -1579(-)m 5834(29)s
6125(-)s 9066 13414 0 13305 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13251(The)m 220 fnt5 450 13248(@AlignList)m 240 fnt1
1579 13251(g)m 1(alle)k 3(y)k 2236(does)s 2749(not)s
3138(\210ush,)s 3734(because)s 4570(its)s 4868(\207rst)s 5322(component)s
6469(is)s 6702(connected)s 7753(to)s 8015(a)s 8204(recepti)s 6(v)k 3(e)k
0 12963(symbol)m 760(by)s 220 fnt5 1054 12960(/)m 240 fnt1
1178 12963(operators.)m 480 12589(After)m 1048(the)s 1402(last)s 1799(equation,)s
2736(an)s 3025(empty)s 3683(forcing)s 4432(g)s 1(alle)k 3(y)k
5072(is)s 5288(sent)s 5739(to)s 220 fnt5 5984 12586(@EndAlignList)m
240 fnt1 7420 12589(,)m 7533(deleting)s 8362(the)s 8716(tw)s 2(o)k
0 12301(remaining)m 1028(recepti)s 6(v)k 3(e)k 1957(symbols)s
2813(from)s 3344(the)s 220 fnt5 3699 12298(@AlignList)m 240 fnt1
4812 12301(g)m 1(alle)k 3(y)k 5452(and)s 5863(permitting)s
6918(it)s 7117(to)s 7363(\210ush.)s 240 fnt3 8000 12303(FOLLO)m 12(WS)k
240 fnt1 0 12013(inde)m 3(x)k 3(es)k 797(ensure)s
1499(that)s 1939(each)s 2456(equation)s 3359(\207nds)s 3898(a)s
4086(tar)s 4(get)k 4707(placed)s 5410(in)s 5675(the)s
6045(body)s 6601(te)s 3(xt)k 7038(just)s 7465(after)s
7983(its)s 8281(point)s 8855(of)s 0 11725(in)m 9(v)k 4(ocation,)k
1090(so)s 1341(the)s 1675(equations)s 2628(return,)s 3290(aligned,)s
4087(to)s 4311(approximately)s 5732(the)s 6065(points)s 6686(where)s
7312(the)s 3(y)k 7760(were)s 8265(in)s 9(v)k 4(ok)k 2(ed.)k
0 11437(Notice)m 703(that)s 1131(the)s 1489(\210ushing)s 2324(of)s
2605(body)s 3149(te)s 3(xt)k 3574(is)s 3794(suspended)s
4860(until)s 5363(the)s 5721(list)s 6082(of)s 6363(equations)s
7341(is)s 7561(completed,)s 8674(as)s 8934(it)s 0 11149(must)m
513(be,)s 833(since)s 1367(the)s 1702(horizontal)s 2713(position)s
3528(of)s 3786(the)s 4121(\207rst)s 4539(equation)s 5407(cannot)s
6092(be)s 6361(kno)s 6(wn)k 7052(until)s 7532(the)s
7867(last)s 8245(equation)s 0 10861(is)m 210(added)s 840(to)s
1079(the)s 1427(list.)s 480 10487(Layout)m 1262(quality)s 2025(can)s
2459(occasionally)s 3753(be)s 4080(impro)s 3(v)k 3(ed)k
5094(by)s 5433(rejecting)s 6366(a)s 6577(component)s 7746(that)s
8209(could)s 8844(be)s 0 10199(promoted)m 978(\211)s 1161(for)s
1502(e)s 3(xample,)k 2419(a)s 2588(component)s 3715(of)s
3989(body)s 4526(te)s 3(xt)k 4944(that)s 5365(carries)s
6054(a)s 6223(footnote)s 7079(too)s 7441(lar)s 4(ge)k
7973(to)s 8215(\207t)s 8477(on)s 8778(the)s 0 9911(current)m
747(page.)s 1374(Since)s 1972(Lout)s 2496(does)s 2997(not)s
3374(specify)s 4130(ho)s 6(w)k 4602(breaking)s 5503(decisions)s
6455(are)s 6814(made,)s 7450(be)s 3(yond)k 8222(the)s
8582(basic)s 0 9623(constraints)m 1089(imposed)s 1961(by)s 2258(a)s 4(v)k 6(ailable)k
3169(space)s 3759(and)s 220 fnt5 4166 9620(into)m 240 fnt1
4575 9623(clauses,)m 5375(in)s 5621(principle)s 6529(such)s 7028(high)s
7514(quality)s 8236(breaking)s 0 9335(could)m 592(be)s 877(added)s
1510(to)s 1752(the)s 2102(implementation)s 3662(with)s 4147(no)s
4443(change)s 5180(to)s 5421(the)s 5772(language.)s 6803(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k
7766(the)s 8117(generality)s 0 9047(of)m 280(the)s 637(g)s 1(alle)k 3(y)k
1280(\210ushing)s 2115(algorithm,)s 3160(and)s 3573(its)s 3859(already)s
4625(considerable)s 5898(comple)s 3(xity)k 15(,)k 7073(mak)s 2(e)k
7654(this)s 8059(a)s 8235(daunting)s 0 8759(problem)m 890(in)s
1167(practice,)s 2062(although)s 2991(a)s 3190(f)s 2(ascinating)k
4323(one.)s 4866(T)s 5008 8711(E)m 5151 8759(X)m 5414([9],)s
5832(with)s 6348(its)s 6657(unnested)s 7600(set)s 7958(of)s
8263(`\210oating)s 0 8471(insertions')m 1041(clearly)s 1744(identi\207able)s 2875(as)s
3125(each)s 3620(page)s 4128(is)s 4338(be)s 3(gun,)k
5028(has)s 5398(the)s 5746(adv)s 6(antage)k 6766(in)s
7009(this)s 7405(respect.)s 240 fnt2 0 7822(5.3.)m 471(Size)s
938(constraints)s 2120(and)s 2561(size)s 2988(adjustments)s 
[ /Dest /LOUTconstraints /DEST pdfmark
240 fnt1
480 7346(The)m 893(g)s 1(alle)k 3(y)k 1512(\210ushing)s
2321(algorithm)s 3295(needs)s 3876(to)s 4099(kno)s 6(w)k
4665(the)s 4998(a)s 4(v)k 6(ailable)k 5890(width)s
6477(and)s 6866(height)s 7508(at)s 7725(each)s 8204(recepti)s 6(v)k 3(e)k
0 7058(symbol.)m 869(These)s 1496(symbols)s 2346(may)s 2812(lie)s
3106(within)s 3775(arbitrarily)s 4782(comple)s 3(x)k 5659(objects,)s
6443(and)s 6847(the)s 3(y)k 7311(may)s 7777(compete)s
8644(with)s 0 6770(each)m 492(other)s 1040(for)s 1375(a)s 4(v)k 6(ailable)k
2280(space)s 2864(\(as)s 3189(body)s 3720(te)s 3(xt)k
4132(and)s 4533(footnote)s 5383(tar)s 4(gets)k 6062(do\),)s
6485(so)s 6748(this)s 7141(information)s 8323(must)s 8844(be)s
0 6482(e)m 3(xtracted)k 930(from)s 1454(the)s 1802(tree)s
2215(structure)s 3106(when)s 3682(required.)s 480 6108(F)m 3(or)k
869(e)s 3(xample,)k 1783(consider)s 2653(the)s 3001(object)s
220 fnt5 480 5607(5i  @Wide  {  a  /  b  })m 240 fnt1 0 5113(and)m 406(suppose)s
1236(that)s 1656(the)s 2006(width)s 2610(of)s 220 fnt5
2883 5110(a)m 240 fnt1 3062 5113(is)m 240 fnt4 3274 5107(1)m
240 fnt3 3382 5115(i)m 240 fnt4 3459 5107(,)m 3572(2)s
240 fnt3 3700 5115(i)m 240 fnt1 3825 5113(\()m 240 fnt4
3898 5107(1)m 240 fnt3 4006 5115(i)m 240 fnt1 4131 5113(to)m
4372(the)s 4722(left)s 5101(of)s 5374(the)s 5724(mark,)s
240 fnt4 6324 5107(2)m 240 fnt3 6452 5115(i)m 240 fnt1
6577 5113(to)m 6818(the)s 7168(right\).)s 7864(What)s 8444(then)s
8916(is)s 0 4825(the)m 348(a)s 4(v)k 6(ailable)k
1256(width)s 1858(at)s 220 fnt5 2090 4822(b)m 240 fnt1
2204 4825(?)m 2423(If)s 2653(we)s 2988(let)s 3286(the)s
3634(width)s 4236(of)s 220 fnt5 4507 4822(b)m 240 fnt1
4681 4825(be)m 240 fnt3 4963 4827(l)m 240 fnt4 5041 4819(,)m
240 fnt3 5148 4827(r)m 240 fnt1 5246 4825(,)m 5353(we)s
5688(must)s 6213(ha)s 4(v)k 3(e)k 240 fnt4
480 4277(\()m 564(1)s 240 fnt3 670 4285(i)m 240 fnt4
817 4277(\255)m 240 fnt3 1038 4285(l)m 240 fnt4 1116 4277(\))m
1254(+)s 1455(\()s 1539(2)s 240 fnt3 1665 4285(i)m
240 fnt4 1812 4277(\255)m 240 fnt3 2033 4285(r)m 240 fnt4
2143 4277(\))m 2293(\243)s 2503(5)s 240 fnt3 2622 4285(i)m
240 fnt1 0 3732(with)m 482(the)s 240 fnt4 842 3726(\255)m
240 fnt1 1051 3732(\(i.e.)m 1466(max\))s 2006(operations)s 3053(arising)s
3756(from)s 4280(mark)s 4832(alignment.)s 5952(Eliminating)s 7133(them)s
7671(gi)s 6(v)k 3(es)k 240 fnt4 480 3180(1)m
240 fnt3 586 3188(i)m 240 fnt4 721 3180(+)m 922(2)s
240 fnt3 1048 3188(i)m 240 fnt4 1207 3180(\243)m 1417(5)s
240 fnt3 1536 3188(i)m 583 2893(l)m 240 fnt4 721 2885(+)m
922(2)s 240 fnt3 1048 2893(i)m 240 fnt4 1207 2885(\243)m
1417(5)s 240 fnt3 1536 2893(i)m 240 fnt4 571 2597(1)m
240 fnt3 677 2605(i)m 240 fnt4 812 2597(+)m 240 fnt3
1013 2605(r)m 240 fnt4 1207 2597(\243)m 1417(5)s 240 fnt3
1536 2605(i)m 674 2310(l)m 240 fnt4 812 2302(+)m 240 fnt3
1013 2310(r)m 240 fnt4 1207 2302(\243)m 1417(5)s 240 fnt3
1536 2310(i)m 240 fnt1 0 1799(and)m 428(since)s 1000(we)s
1359(assume)s 2144(that)s 220 fnt5 2587 1796(a)m 240 fnt1
2788 1799(\207ts)m 3156(into)s 3606(the)s 3978(a)s 4(v)k 6(ailable)k
4911(space,)s 5573(the)s 5946(\207rst)s 6402(inequality)s 7436(may)s
7927(be)s 8234(dropped,)s 0 1511(lea)m 4(ving)k 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 30 31
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Symbol
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5704 -1579(-)m 5832(30)s
6127(-)s 9066 13416 0 12991 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
240 fnt3 851 13205(l)m 240 fnt4 1013 13197(\243)m
1223(3)s 240 fnt3 1340 13205(i)m 480 12910(l)m 240 fnt4
618 12902(+)m 240 fnt3 819 12910(r)m 240 fnt4 1013 12902(\243)m
1223(5)s 240 fnt3 1342 12910(i)m 819 12622(r)m 240 fnt4
1013 12614(\243)m 1223(4)s 240 fnt3 1348 12622(i)m 240 fnt1
0 12113(Object)m 220 fnt5 697 12110(b)m 240 fnt1 871 12113(may)m
1337(ha)s 4(v)k 3(e)k 1838(width)s 240 fnt3
2440 12115(l)m 240 fnt4 2518 12107(,)m 240 fnt3 2625 12115(r)m
240 fnt1 2783 12113(for)m 3121(an)s 3(y)k 240 fnt3
3518 12115(l)m 240 fnt1 3644 12113(and)m 240 fnt3 4048 12115(r)m
240 fnt1 4206 12113(satisfying)m 5188(these)s 5735(inequalities,)s 6943(and)s
7347(no)s 7640(others.)s 480 11739(Here)m 1000(is)s 1210(another)s
1987(e)s 3(xample:)k 220 fnt5 480 11238(5i  @High  {  a  /2ix  b  })m 240 fnt1
0 10737(Assuming)m 1024(that)s 220 fnt5 1442 10734(a)m 240 fnt1
1619 10737(has)m 1989(height)s 240 fnt4 2647 10731(1)m 240 fnt3
2753 10739(i)m 240 fnt4 2828 10731(,)m 2935(1)s 240 fnt3
3041 10739(i)m 240 fnt1 3104 10737(,)m 3211(the)s 3559(height)s
240 fnt3 4217 10739(l)m 240 fnt4 4295 10731(,)m 240 fnt3
4402 10739(r)m 240 fnt1 4560 10737(of)m 220 fnt5 4831 10734(b)m
240 fnt1 5005 10737(must)m 5530(satisfy)s 240 fnt4 480 10179(1)m
240 fnt3 586 10187(i)m 240 fnt4 721 10179(+)m 922(\()s
1006(\()s 1090(1)s 240 fnt3 1196 10187(i)m 240 fnt4
1331 10179(+)m 240 fnt3 1532 10187(l)m 240 fnt4 1610 10179(\))m
1760(\255)s 1981(2)s 240 fnt3 2107 10187(i)m 240 fnt4
2182 10179(\))m 2320(+)s 240 fnt3 2521 10187(r)m 240 fnt4
2703 10179(\243)m 2913(5)s 240 fnt3 3032 10187(i)m 240 fnt1
0 9634(This)m 478(time)s 960(the)s 240 fnt4 1325 9628(\255)m
240 fnt1 1539 9634(operation)m 2501(arises)s 3098(from)s 3624(the)s
3975(mark-to-mark)s 5364(g)s 1(ap)k 5765(mode,)s 6406(which)s
7050(will)s 7479(widen)s 8123(the)s 240 fnt4 8474 9628(2)m
240 fnt3 8602 9636(i)m 240 fnt1 8728 9634(g)m 1(ap)k
0 9346(if)m 217(necessary)s 1200(to)s 1439(pre)s 6(v)k 3(ent)k
220 fnt5 2207 9343(a)m 240 fnt1 2384 9346(and)m 220 fnt5
2788 9343(b)m 240 fnt1 2962 9346(from)m 3486(o)s 3(v)k 3(erlapping.)k
4787(This)s 5263(inequality)s 6273(can)s 6662(be)s 6944(re)s 6(written)k
7856(as)s 240 fnt3 851 8795(l)m 240 fnt4 1013 8787(\243)m
288 fnt4 1223 8775(\245)m 240 fnt3 480 8504(l)m 240 fnt4
618 8496(+)m 240 fnt3 819 8504(r)m 240 fnt4 1013 8496(\243)m
1223(3)s 240 fnt3 1340 8504(i)m 819 8216(r)m 240 fnt4
1013 8208(\243)m 1223(2)s 240 fnt3 1349 8216(i)m 240 fnt1
0 7709(In)m 263(general,)s 1080(Lout)s 1599(is)s 1816(designed)s
2732(so)s 3005(that)s 3430(the)s 3785(a)s 4(v)k 6(ailable)k
4700(width)s 5309(or)s 5575(height)s 6240(at)s 6479(an)s 3(y)k
6883(point)s 7442(can)s 7838(be)s 8128(e)s 3(xpressed)k
0 7421(by)m 294(three)s 827(inequalities)s 1979(of)s 2250(the)s
2598(form)s 240 fnt3 851 6870(l)m 240 fnt4 1013 6862(\243)m
240 fnt3 1223 6870(x)m 480 6579(l)m 240 fnt4 618 6571(+)m
240 fnt3 819 6579(r)m 240 fnt4 1013 6571(\243)m 240 fnt3
1223 6579(y)m 819 6264(r)m 240 fnt4 1013 6256(\243)m 240 fnt3
1223 6264(z)m 240 fnt1 0 5743(where)m 240 fnt3 641 5745(x)m
240 fnt1 747 5743(,)m 240 fnt3 855 5745(y)m 240 fnt1
1018 5743(and)m 240 fnt3 1423 5745(z)m 240 fnt1 1575 5743(may)m
2042(be)s 288 fnt4 2325 5725(\245)m 240 fnt1 2523 5743(.)m
2688(W)s 19(e)k 3058(abbre)s 6(viate)k 4104(these)s
4652(three)s 5186(inequalities)s 6339(to)s 240 fnt3 6579 5745(l)m
240 fnt4 6658 5737(,)m 240 fnt3 6768 5745(r)m 240 fnt4
6953 5737(\243)m 240 fnt3 7166 5745(x)m 240 fnt4 7285 5737(,)m
240 fnt3 7395 5745(y)m 240 fnt4 7510 5737(,)m 240 fnt3
7620 5745(z)m 240 fnt1 7711 5743(,)m 7819(and)s 8224(we)s
8560(call)s 240 fnt3 8960 5745(x)m 240 fnt4 0 5449(,)m
240 fnt3 107 5457(y)m 240 fnt4 221 5449(,)m 240 fnt3
328 5457(z)m 240 fnt1 479 5455(a)m 240 fnt3 645 5457(size)m
1056(constr)s 3(aint)k 240 fnt1 2027 5455(.)m 480 5081(The)m
920(tw)s 2(o)k 1343(e)s 3(xamples)k 2307(abo)s 3(v)k 3(e)k
2942(sho)s 6(wed)k 3739(ho)s 6(w)k 4213(to)s
4465(propag)s 1(ate)k 5475(the)s 5836(size)s 6276(constraint)s
288 fnt4 7291 5063(\245)m 240 fnt4 7514 5075(,)m 7659(5)s
240 fnt3 7791 5083(i)m 240 fnt4 7879 5075(,)m 288 fnt4
8025 5063(\245)m 240 fnt1 8296 5081(for)m 220 fnt5 8647 5078(a / b)m
240 fnt1 0 4793(do)m 6(wn)k 586(one)s 991(le)s 6(v)k 3(el)k
1504(to)s 1746(the)s 2097(child)s 220 fnt5 2636 4790(b)m
240 fnt1 2750 4793(.)m 2917(Basser)s 3617(Lout)s 4132(contains)s
4982(a)s 5151(complete)s 6086(set)s 6414(of)s 6688(general)s
7449(rules)s 7967(for)s 8308(all)s 8604(node)s 0 4505(types,)m
627(too)s 1002(complicated)s 2244(to)s 2499(gi)s 6(v)k 3(e)k
2974(here.)s 3565(Instead,)s 4378(we)s 4729(gi)s 6(v)k 3(e)k
5203(just)s 5624(one)s 6042(e)s 3(xample)k 6921(of)s
7208(ho)s 6(w)k 7685(these)s 8248(rules)s 8779(are)s
0 4217(deri)m 6(v)k 3(ed,)k 815(using)s 1387(the)s
1735(object)s 240 fnt3 480 3721(x)m 167 fnt4 586 3629(1)m
220 fnt5 771 3716(/)m 240 fnt3 955 3721(x)m 167 fnt4
1061 3629(2)m 220 fnt5 1260 3716(/)m 240 fnt3 1444 3721(.)m
1550(.)s 1656(.)s 220 fnt5 1810 3716(/)m 240 fnt3
1994 3721(x)m 167 fnt3 2100 3634(n)m 240 fnt1 0 3176(where)m
240 fnt3 640 3178(x)m 167 fnt3 746 3091(j)m 240 fnt1
852 3176(has)m 1222(width)s 240 fnt3 1824 3178(l)m 167 fnt3
1890 3091(j)m 240 fnt4 1948 3170(,)m 240 fnt3 2055 3178(r)m
167 fnt3 2127 3091(j)m 240 fnt1 2233 3176(for)m 2571(all)s
240 fnt3 2864 3178(j)m 240 fnt1 2930 3176(.)m 480 2802(Suppose)m
1345(the)s 1689(whole)s 2326(object)s 2966(has)s 3333(width)s
3931(constraint)s 240 fnt3 4929 2804(X)m 240 fnt4 5097 2796(,)m
240 fnt3 5204 2804(Y)m 240 fnt4 5367 2796(,)m 240 fnt3
5474 2804(Z)m 240 fnt1 5619 2802(,)m 5722(and)s 6123(we)s
6454(require)s 7182(the)s 7526(width)s 8124(constraint)s 0 2514(of)m
240 fnt3 271 2516(x)m 167 fnt3 377 2429(i)m 240 fnt1
421 2514(.)m 586(Let)s 240 fnt3 965 2516(L)m 240 fnt4
1185 2508(=)m 240 fnt1 1401 2514(max)m 167 fnt3 1808 2429(j)m
240 fnt3 1917 2516(l)m 167 fnt3 1983 2429(j)m 240 fnt1
2090 2514(and)m 240 fnt3 2495 2516(R)m 240 fnt4 2723 2508(=)m
240 fnt1 2939 2514(max)m 167 fnt3 3346 2429(j)m 240 fnt3
3455 2516(r)m 167 fnt3 3527 2429(j)m 240 fnt1 3573 2514(,)m
3681(so)s 3948(that)s 240 fnt3 4367 2516(L)m 240 fnt4
4512 2508(,)m 240 fnt3 4619 2516(R)m 240 fnt1 4821 2514(is)m
5032(the)s 5381(width)s 5984(of)s 6256(the)s 6605(whole)s
7247(object.)s 7996(W)s 19(e)k 8366(assume)s 240 fnt3
0 2203(L)m 240 fnt4 145 2195(,)m 240 fnt3 252 2203(R)m
240 fnt4 477 2195(\243)m 240 fnt3 687 2203(X)m 240 fnt4
855 2195(,)m 240 fnt3 962 2203(Y)m 240 fnt4 1125 2195(,)m
240 fnt3 1232 2203(Z)m 240 fnt1 1377 2201(.)m 1541(Then)s
240 fnt3 2090 2203(x)m 167 fnt3 2196 2116(i)m 240 fnt1
2300 2201(can)m 2689(be)s 2971(enlar)s 4(ged)k 3848(to)s
4087(an)s 3(y)k 4484(size)s 240 fnt3 4911 2203(l)m
167 fnt3 4977 2116(i)m 240 fnt4 5081 2195(,)m 240 fnt3
5188 2203(r)m 167 fnt3 5260 2116(i)m 240 fnt1 5364 2201(satisfying)m
240 fnt4 480 1608(\()m 240 fnt3 564 1616(l)m 167 fnt3
630 1529(i)m 240 fnt4 758 1608(\255)m 240 fnt3 979 1616(L)m
240 fnt4 1124 1608(\))m 1202(,)s 1309(\()s 240 fnt3
1393 1616(r)m 167 fnt3 1465 1529(i)m 240 fnt4 1593 1608(\255)m
240 fnt3 1814 1616(R)m 240 fnt4 1967 1608(\))m 2117(\243)s
240 fnt3 2327 1616(X)m 240 fnt4 2495 1608(,)m 240 fnt3
2602 1616(Y)m 240 fnt4 2765 1608(,)m 240 fnt3 2872 1616(Z)m

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 31 32
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Symbol
%%+ font Times-Bold
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Symbol
/fnt4 { /Symbol LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5714 -1579(-)m 5842(31)s
6117(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13253(which)m 642(e)s 3(xpands)k 1475(to)s
1714(eight)s 2252(inequalities:)s 240 fnt3 917 12702(l)m 167 fnt3
983 12615(i)m 240 fnt4 1123 12694(\243)m 240 fnt3 1333 12702(X)m
894 12338(L)m 240 fnt4 1123 12330(\243)m 240 fnt3 1333 12338(X)m
528 12047(l)m 167 fnt3 594 11960(i)m 240 fnt4 710 12039(+)m
240 fnt3 911 12047(r)m 167 fnt3 983 11960(i)m 240 fnt4
1123 12039(\243)m 240 fnt3 1333 12047(Y)m 503 11675(l)m 167 fnt3
569 11588(i)m 240 fnt4 685 11667(+)m 240 fnt3 886 11675(R)m
240 fnt4 1123 11667(\243)m 240 fnt3 1333 11675(Y)m 505 11311(L)m
240 fnt4 710 11303(+)m 240 fnt3 911 11311(r)m 167 fnt3
983 11224(i)m 240 fnt4 1123 11303(\243)m 240 fnt3 1333 11311(Y)m
480 10947(L)m 240 fnt4 685 10939(+)m 240 fnt3 886 10947(R)m
240 fnt4 1123 10939(\243)m 240 fnt3 1333 10947(Y)m 911 10664(r)m
167 fnt3 983 10577(i)m 240 fnt4 1123 10656(\243)m 240 fnt3
1333 10664(Z)m 886 10300(R)m 240 fnt4 1123 10292(\243)m 240 fnt3
1333 10300(Z)m 240 fnt1 0 9793(Three)m 613(are)s 960(already)s
1717(kno)s 6(wn,)k 2471(and)s 2875(slightly)s 3646(rearranging)s
4800(the)s 5148(others)s 5783(gi)s 6(v)k 3(es)k
240 fnt3 869 9242(l)m 167 fnt3 935 9155(i)m 240 fnt4
1075 9234(\243)m 240 fnt3 1285 9242(X)m 869 8870(l)m 167 fnt3
935 8783(i)m 240 fnt4 1075 8862(\243)m 240 fnt3 1285 8870(Y)m
240 fnt4 1508 8862(-)m 240 fnt3 1708 8870(R)m 480 8498(l)m
167 fnt3 546 8411(i)m 240 fnt4 662 8490(+)m 240 fnt3
863 8498(r)m 167 fnt3 935 8411(i)m 240 fnt4 1075 8490(\243)m
240 fnt3 1285 8498(Y)m 863 8134(r)m 167 fnt3 935 8047(i)m
240 fnt4 1075 8126(\243)m 240 fnt3 1285 8134(Z)m 863 7770(r)m
167 fnt3 935 7683(i)m 240 fnt4 1075 7762(\243)m 240 fnt3
1285 7770(Y)m 240 fnt4 1508 7762(-)m 240 fnt3 1708 7770(L)m
240 fnt1 0 7182(Therefore)m 997(the)s 1345(width)s 1947(constraint)s
2949(of)s 240 fnt3 3220 7184(x)m 167 fnt3 3326 7097(i)m
240 fnt1 3430 7182(is)m 480 6644(min)m 240 fnt4 861 6638(\()m
240 fnt3 945 6646(X)m 240 fnt4 1113 6638(,)m 240 fnt3
1220 6646(Y)m 240 fnt4 1443 6638(-)m 240 fnt3 1643 6646(R)m
240 fnt4 1796 6638(\))m 1874(,)s 240 fnt3 1981 6646(Y)m
240 fnt4 2144 6638(,)m 240 fnt1 2251 6644(min)m 240 fnt4
2632 6638(\()m 240 fnt3 2716 6646(Z)m 240 fnt4 2873 6638(,)m
240 fnt3 2980 6646(Y)m 240 fnt4 3203 6638(-)m 240 fnt3
3403 6646(L)m 240 fnt4 3548 6638(\))m 240 fnt1 0 6142(The)m
445(size)s 890(constraint)s 1909(of)s 2198(an)s 3(y)k
2613(node)s 3152(can)s 3559(be)s 3858(found)s 4493(by)s
4805(climbing)s 5725(the)s 6091(tree)s 6521(to)s 6778(a)s
240 fnt3 6962 6144(WIDE)m 240 fnt1 7641 6142(or)m 240 fnt3
7918 6144(HIGH)m 240 fnt1 8604 6142(node)m 0 5854(where)m 636(the)s
980(constraint)s 1978(is)s 2184(tri)s 6(vial,)k 2850(then)s
3315(propag)s 1(ating)k 4506(it)s 4694(back)s 5203(do)s 6(wn)k
5783(to)s 6018(the)s 6362(node,)s 6931(and)s 7331(this)s
7723(is)s 7929(the)s 8272(function)s 0 5566(of)m 271(procedure)s
240 fnt3 1283 5568(Constr)m 3(ained)k 240 fnt1 2530 5566(in)m
2773(Basser)s 3470(Lout.)s 480 5192(After)m 1043(some)s 1604(components)s
2813(ha)s 4(v)k 3(e)k 3314(been)s 3824(promoted)s
4799(into)s 5225(a)s 5391(tar)s 4(get,)k 6038(the)s
6386(sizes)s 6902(stored)s 7544(in)s 7788(its)s 8064(parent)s
8722(and)s 0 4904(higher)m 665(ancestors)s 1598(must)s 2117(be)s
2392(adjusted)s 3241(to)s 3473(re\210ect)s 4122(the)s 4464(increased)s
5417(size.)s 5946(This)s 6415(is)s 6618(done)s 7134(by)s
7421(yet)s 7767(another)s 8537(set)s 8855(of)s 0 4616(recursi)m 6(v)k 3(e)k
925(rules,)s 1500(upw)s 2(ard-mo)k 3(ving)k 3081(this)s
3481(time,)s 4016(which)s 4662(cease)s 5239(as)s 5492(soon)s
6006(as)s 6260(some)s 6825(ancestor')s 13(s)k 7835(size)s
8266(does)s 8760(not)s 0 4328(change.)m 830(These)s 1445(rules)s
1948(are)s 2283(embodied)s 3273(in)s 3504(procedure)s 240 fnt3
4504 4330(AdjustSize)m 240 fnt1 5541 4328(of)m 5800(Basser)s 6485(Lout.)s
7089(The)s 7505(adjustment)s 8601(must)s 0 4040(be)m 282(done)s
804(before)s 1470(relinquishing)s 2785(control)s 3517(to)s 3756(an)s 3(y)k
4153(other)s 4704(g)s 1(alle)k 3(y)k 15(,)k
5376(b)s 4(ut)k 5738(not)s 6104(after)s 6600(e)s 6(v)k 3(ery)k
7176(component.)s 240 fnt2 0 3391(5.4.)m 471(The)s 926(limited)s
1696(lookahead)s 2802(pr)s 4(oblem)k 
[ /Dest /LOUTlookahead /DEST pdfmark
240 fnt1 480 2914(Basser)m
1189(Lout)s 1714(assumes)s 2575(that)s 3006(there)s 3552(will)s
3991(be)s 4286(enough)s 5062(internal)s 5859(memory)s 6723(to)s
6975(hold)s 7472(the)s 7833(symbol)s 8606(table)s 0 2626(plus)m
461(a)s 638(fe)s 6(w)k 1055(pages,)s 1719(b)s 4(ut)k
2092(not)s 2469(an)s 2764(entire)s 3374(document.)s 4493(This)s
4980(section)s 5726(describes)s 6677(the)s 7036(consequent)s 8185(problems)s
0 2338(and)m 441(ho)s 6(w)k 940(the)s 3(y)k
1441(were)s 1999(solv)s 3(ed.)k 2763(Other)s 3405(interpreters,)s
4636(notably)s 5446(interacti)s 6(v)k 3(e)k 6538(editors)s
7277(running)s 8113(on)s 8448(virtual)s 0 2050(memory)m 851(systems,)s
1715(w)s 2(ould)k 2370(not)s 2736(necessarily)s 3851(need)s
4361(this)s 4757(assumption.)s 480 1676(Although)m 1434(Basser)s 2122(Lout)s
2625(can)s 3005(read)s 3466(and)s 3861(format)s 4548(an)s 3(y)k
4936(le)s 3(g)k 1(al)k 5442(input,)s 6033(its)s
6300(memory)s 7142(consumption)s 8427(will)s 8844(be)s 0 1388(optimized)m
1004(when)s 1570(the)s 1908(b)s 4(ulk)k 2381(of)s
2642(the)s 2980(document)s 3974(resides)s 4677(in)s 4910(g)s 1(alle)k 3(ys)k
5624(whose)s 6282(tar)s 4(gets)k 6955(can)s 7334(be)s
7606(identi\207ed)s 8557(at)s 8778(the)s 0 1100(moment)m 843(the)s 3(y)k
1304(are)s 1650(encountered.)s 2981(Let)s 3358(us)s 3620(tak)s 2(e)k
4071(the)s 4417(typical)s 5121(e)s 3(xample)k 5982(of)s
6252(a)s 6416(root)s 6860(g)s 1(alle)k 3(y)k
7492(which)s 8133(is)s 8341(a)s 8506(list)s 8855(of)s
0 812(pages,)m 652(a)s 220 fnt5 818 809(@BodyT)m 26(e)k 6(xt)k
240 fnt1 1991 812(g)m 1(alle)k 3(y)k 2625(tar)s 4(geted)k
3448(into)s 3872(the)s 4220(pages,)s 220 fnt5 4872 809(@Chapter)m
240 fnt1 5934 812(g)m 1(alle)k 3(ys)k 6658(tar)s 4(geted)k
7481(into)s 220 fnt5 7905 809(@BodyT)m 26(e)k 6(xt)k
240 fnt1 9019 812(,)m 0 524(and)m 220 fnt5 404 521(@Section)m
240 fnt1 1404 524(g)m 1(alle)k 3(ys)k 2128(tar)s 4(geted)k
2951(into)s 3376(the)s 220 fnt5 3724 521(@Chapter)m 240 fnt1
4787 524(g)m 1(alle)k 3(ys:)k 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 32 33
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1579(-)m 5833(32)s
6127(-)s 9066 13416 0 13312 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
220 fnt5 480 13255(@P)m 8(ageList)k 480 12967(//)m
480 12679(@BodyT)m 26(e)k 6(xt)k 480 12391(//)m 480 12103(@Chapter {)m
480 11815(    @Section { ...)m 13( })k 480 11527(    @Section { ...)m 13( })k 480 11239(    ...)m
480 10951(    @Section { ...)m 13( })k 480 10663(})m 480 10375(@Chapter {)m 480 10087(    ...)m
480 9799(})m 240 fnt1 0 9305(Basser)m 702(Lout)s 1220(is)s
1436(able)s 1896(to)s 2141(read)s 2616(and)s 3026(process)s
3800(such)s 4302(g)s 1(alle)k 3(ys)k 5032(one)s
5440(paragraph)s 6459(at)s 6697(a)s 6869(time)s 7355(\(strictly)s 15(,)k
8194(from)s 8724(one)s 220 fnt5 0 9014(//)m 240 fnt1
185 9017(at)m 417(the)s 765(outer)s 1316(le)s 6(v)k 3(el)k
1826(of)s 2097(a)s 2263(g)s 1(alle)k 3(y)k
2897(to)s 3136(the)s 3484(ne)s 3(xt\),)k 4079(as)s
4329(we)s 4664(no)s 6(w)k 5125(describe.)s 480 8643(When)m
1147(the)s 1534(parser)s 2215(encounters)s 3341(the)s 3727(be)s 3(ginning)k
4774(of)s 5083(a)s 5288(g)s 1(alle)k 3(y)k 15(,)k
5998(lik)s 2(e)k 220 fnt5 6449 8640(@Chapter)m 240 fnt1
7550 8643(or)m 220 fnt5 7848 8640(@Section)m 240 fnt1 8788 8643(,)m
8934(it)s 0 8355(initiates)m 831(a)s 1023(ne)s 6(w)k
1495(g)s 1(alle)k 3(y)k 2155(process.)s 3061(The)s
3515(special)s 4258(recepti)s 6(v)k 3(e)k 5206(symbol)s
220 fnt5 5991 8352(@Input)m 240 fnt1 6784 8355(is)m 7019(substituted)s
8139(for)s 8502(the)s 8876(as)s 0 8067(yet)m 357(unread)s
1071(right)s 1588(parameter)s 2607(of)s 2884(the)s 3237(g)s 1(alle)k 3(y)k 15(.)k
3972(As)s 4294(each)s 4795(paragraph)s 5813(of)s 6090(the)s
6443(right)s 6960(parameter)s 7979(is)s 8195(read,)s 8718(it)s
8916(is)s 0 7779(deleted)m 763(from)s 1302(the)s 1665(parse)s
2240(tree)s 2668(and)s 3087(injected)s 3916(into)s 4356(the)s
4719(g)s 1(alle)k 3(y')k 13(s)k 220 fnt5
5524 7776(@Input)m 240 fnt1 6231 7779(.)m 6410(The)s 6853(g)s 1(alle)k 3(y)k
7502(is)s 7727(then)s 8212(resumed.)s 0 7491(The)m 429(parser)s
1074(thus)s 1526(acts)s 1950(as)s 2202(an)s 2487(e)s 3(xtra)k
3022(concurrent)s 4106(process;)s 4937(it)s 5131(has)s 5503(lo)s 6(w)k
5912(priority)s 15(,)k 6721(so)s 6989(that)s 7409(input)s
7963(is)s 8175(read)s 8646(only)s 0 7203(when)m 597(there)s
1151(is)s 1382(nothing)s 2188(else)s 2636(to)s 2897(do.)s
3322(Since)s 3930(g)s 1(alle)k 3(ys)k 4675(may)s
5162(be)s 5465(nested,)s 6205(a)s 6392(stack)s 6965(of)s
220 fnt5 7257 7200(@Input)m 240 fnt1 8045 7203(symbols)m 8916(is)s
0 6915(needed,)m 781(each)s 1271(with)s 1749(its)s 2020(o)s 6(wn)k
2480(en)s 9(vironment)k 3735(and)s 4135(style.)s 4745(If)s
4971(a)s 5132(g)s 1(alle)k 3(y)k 5762(is)s
5967(encountered)s 7190(for)s 7523(which)s 8161(a)s 8322(tar)s 4(get)k
8916(is)s 0 6627(not)m 370(immediately)s 1622(identi\207able)s 2757(\(a)s
3006(footnote,)s 3914(for)s 4257(e)s 3(xample\),)k 5254(it)s
5450(is)s 5664(read)s 6137(in)s 6385(its)s 6665(entirety)s
7452(and)s 7860(hung)s 8397(in)s 8645(pure)s 0 6339(parse)m
551(tree)s 954(form)s 1468(from)s 1983(an)s 240 fnt3
2256 6341(UN)m 6(A)k 8(TT)k 12(A)k 7(CHED)k
240 fnt1 3811 6339(inde)m 3(x)k 4386(in)s 4619(the)s
4957(usual)s 5508(w)s 2(ay)k 15(,)k 5987(with)s
6459(an)s 6733(en)s 9(vironment)k 7983(b)s 4(ut)k
8335(without)s 0 6051(a)m 166(style.)s 781(It)s 986(will)s
1412(be)s 1694(\210ushed)s 2444(later)s 2927(when)s 3503(its)s
3779(component)s 4903(is)s 5113(promoted.)s 480 5677(In)m 735(addition)s
1575(to)s 1813(producing)s 2836(a)s 3001(steady)s 3665(\210o)s 6(w)k
4138(of)s 4407(components)s 5614(from)s 6137(input,)s 6735(we)s
7069(must)s 7593(also)s 8030(ensure)s 8708(that)s 0 5389(recepti)m 6(v)k 3(e)k
928(symbols)s 1783(do)s 2083(not)s 2455(unduly)s 3182(block)s
3781(their)s 4285(promotion.)s 5452(The)s 220 fnt5 5886 5386(@F)m 6(ootSect)k
240 fnt1 7044 5389(symbol)m 7810(at)s 8049(the)s 8403(foot)s
8855(of)s 0 5101(each)m 495(page)s 1003(is)s 1213(a)s
1379(typical)s 2084(e)s 3(xample:)k 3057(until)s 3550(it)s
3742(is)s 3952(deleted)s 4700(the)s 5048(page)s 5556(cannot)s
6254(be)s 6536(printed.)s 480 4727(Recepti)m 6(v)k 3(e)k
1501(symbols)s 2368(are)s 2733(e)s 3(xpanded)k 3724(only)s
4222(on)s 4537(demand,)s 5421(so)s 220 fnt5 5705 4724(@F)m 6(ootSect)k
240 fnt1 6874 4727(can)m 7281(be)s 7581(deleted)s 8347(as)s
8616(soon)s 0 4439(as)m 250(we)s 585(can)s 974(pro)s 3(v)k 3(e)k
1570(that)s 1988(it)s 2180(is)s 2390(not)s 2757(w)s 2(anted.)k
3610(The)s 4038(symbol)s 4799(table)s 5319(can)s 5708(tell)s
6067(us)s 6332(that)s 6750(only)s 220 fnt5 7230 4436(@F)m 6(ootNote)k
240 fnt1 8402 4439(g)m 1(alle)k 3(ys)k 0 4151(\(with)m
220 fnt5 555 4148(@F)m 6(ootPlace&&f)k 6(ollo)k 3(wing)k
240 fnt1 2935 4151(tar)m 4(gets\))k 3688(w)s 2(ant)k
4205(it,)s 4438(so)s 4697(it)s 4883(might)s 5494(be)s
5770(possible)s 6604(to)s 6836(deduce)s 7564(that)s 220 fnt5
7975 4148(@F)m 6(ootSect)k 240 fnt1 0 3863(may)m 466(be)s
748(deleted)s 1496(as)s 1746(soon)s 2256(as)s 2506(body)s
3040(te)s 3(xt)k 3455(enters)s 4076(the)s 4424(follo)s 6(wing)k
5401(page.)s 480 3489(The)m 904(author)s 1571(w)s 2(as)k
1987(unable)s 2677(to)s 2912(mak)s 2(e)k 3479(this)s
3871(w)s 2(ork,)k 4463(so)s 4725(Basser)s 5418(Lout)s
5925(requires)s 6741(the)s 7085(user)s 7538(to)s 7773(identify)s
8565(those)s 0 3201(g)m 1(alle)k 3(ys)k 715(which)s
1348(will)s 1764(carry)s 2299(the)s 2637(b)s 4(ulk)k
3111(of)s 3372(the)s 3711(document)s 4705(\()s 220 fnt5
4778 3198(@Chapter)m 240 fnt1 5781 3201(,)m 220 fnt5 5879 3198(@Section)m
240 fnt1 6819 3201(,)m 220 fnt5 6916 3198(@BodyT)m 26(e)k 6(xt)k
240 fnt1 8030 3201(\))m 8149(as)s 240 fnt3 8389 3203(for)m 8(cing)k
0 2915(galle)m 7(ys)k 240 fnt1 665 2913(,)m 792(by)s
1107(writing)s 220 fnt5 1871 2910(f)m 6(orce into)k 240 fnt1
2841 2913(instead)m 3596(of)s 220 fnt5 3888 2910(into)m 240 fnt1
4315 2913(in)m 4579(their)s 5097(de\207nitions.)s 6291(As)s 6629(described)s
7624(in)s 7888(the)s 8257(pre)s 6(vious)k 0 2625(section,)m
790(when)s 1373(a)s 1546(forcing)s 2296(g)s 1(alle)k 3(y)k
2937(attaches)s 3763(to)s 4009(a)s 4182(tar)s 4(get,)k
4835(all)s 5135(recepti)s 6(v)k 3(e)k 6063(symbols)s
6919(preceding)s 7922(the)s 8277(tar)s 4(get)k 8883(in)s
0 2337(its)m 278(g)s 1(alle)k 3(y)k 914(are)s
1263(deleted,)s 2062(remo)s 3(ving)k 3031(all)s 3326(impediments)s
4614(to)s 4855(\210ushing.)s 5793(F)s 3(or)k 6184(e)s 3(xample,)k
7100(when)s 7678(a)s 7846(forcing)s 8592(body)s 0 2049(te)m 3(xt)k
421(g)s 1(alle)k 3(y)k 1062(enters)s 1690(a)s
1863(ne)s 6(w)k 2317(page,)s 2882(the)s 220 fnt5
3237 2046(@F)m 6(ootSect)k 240 fnt1 4395 2049(symbol)m 5162(on)s
5466(the)s 5820(preceding)s 6823(page)s 7338(will)s 7771(be)s
8060(deleted.)s 8921(It)s 0 1761(seems)m 629(lik)s 2(ely)k
1219(that)s 1631(a)s 1791(system)s 2509(which)s 3145(could)s
3729(af)s 6(ford)k 4358(to)s 4591(w)s 2(ait)k
5054(until)s 5541(all)s 5828(input)s 6374(w)s 2(as)k
6789(read)s 7252(before)s 7912(deleting)s 8729(an)s 3(y)k
0 1473(recepti)m 6(v)k 3(e)k 922(symbols)s 1771(w)s 2(ould)k
2426(not)s 2792(need)s 3302(forcing)s 4045(g)s 1(alle)k 3(ys.)k
480 1099(Galle)m 3(ys)k 1258(whose)s 1925(tar)s 4(gets)k
2607(are)s 2953(a)s 3118(long)s 3597(w)s 2(ay)k
4047(from)s 4570(their)s 5066(in)s 9(v)k 4(ocation)k
6119(points)s 6755(can)s 7143(be)s 7424(a)s 7589(problem.)s
8549(If)s 8778(the)s 0 811(direction)m 917(is)s 220 fnt5
1139 808(f)m 6(ollo)k 3(wing)k 240 fnt1 1969 811(,)m
2087(such)s 2595(g)s 1(alle)k 3(ys)k 3330(are)s
3689(held)s 4170(in)s 4425(internal)s 5221(memory)s 6083(for)s
6433(a)s 6610(long)s 7101(time,)s 7643(unless)s 8304(the)s 3(y)k
8779(are)s 0 523(to)m 248(be)s 539(sorted.)s 1296(If)s
1535(the)s 1892(direction)s 2807(is)s 220 fnt5 3026 520(preceding)m
240 fnt1 3977 523(,)m 4093(then)s 4571(either)s 5183(the)s
5540(entire)s 6148(interv)s 3(ening)k 7296(document)s 8309(must)s
8844(be)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 33 34
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Times-Italic
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5710 -1579(-)m 5838(33)s
6122(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13253(held)m 466(in)s 704(memory)s 1551(\(pre)s 6(v)k 3(ented)k
2617(by)s 2907(the)s 3250(tar)s 4(get)k 3844(from)s
4364(\210ushing\),)s 5317(or)s 5572(else)s 5994(some)s 6551(forcing)s
7289(g)s 1(alle)k 3(y)k 7918(prematurely)s 0 12965(deletes)m
714(the)s 1062(tar)s 4(get,)k 1708(lea)s 4(ving)k
2461(the)s 2809(g)s 1(alle)k 3(y)k 3443(bereft.)s
480 12591(The)m 929(typical)s 1655(e)s 3(xample)k 2539(of)s
2832(the)s 3201(latter)s 3771(case)s 4260(occurs)s 4956(when)s
5553(the)s 5922(g)s 1(alle)k 3(y)k 6578(is)s
6809(an)s 7113(entry)s 7680(in)s 7944(the)s 8313(table)s
8855(of)s 0 12303(contents,)m 907(launched)s 1832(backw)s 2(ards)k
2907(from)s 3435(the)s 3786(be)s 3(ginning)k 4797(of)s
5071(a)s 5241(chapter)s 6007(or)s 6269(section.)s 7113(Its)s
7406(tar)s 4(get)k 8008(in)s 8254(the)s 8606(table)s
0 12015(of)m 286(contents)s 1150(will)s 1592(ha)s 4(v)k 3(e)k
2108(been)s 2633(deleted)s 3397(long)s 3891(before,)s 4624(to)s
4879(permit)s 5578(the)s 5941(rest)s 6361(of)s 6648(the)s
7011(document)s 8031(to)s 8286(print,)s 8860(so)s 0 11727(the)m
349(g)s 1(alle)k 3(y)k 985(ultimately)s 2009(emer)s 4(ges)k
2854(as)s 3106(an)s 3391(unattached)s 4487(g)s 1(alle)k 3(y)k
5122(promoted)s 6099(out)s 6467(of)s 6740(the)s 7090(root)s
7537(g)s 1(alle)k 3(y)k 15(.)k 8268(All)s
8630(such)s 0 11439(g)m 1(alle)k 3(ys)k 717(are)s
1056(written)s 1781(to)s 2013(an)s 2288(auxiliary)s 3183(\207le,)s
3588(inde)s 3(x)k 3(ed)k 4390(by)s 4676(the)s
5016(missing)s 5806(tar)s 4(get.)k 6501(On)s 6843(the)s
7184(ne)s 3(xt)k 7645(run,)s 8063(just)s 8460(before)s
0 11151(that)m 418(tar)s 4(get)k 1017(is)s 1227(deleted,)s
2024(the)s 2372(auxiliary)s 3275(\207le)s 3636(is)s 3846(check)s 2(ed)k
4686(and)s 5090(an)s 3(y)k 5487(g)s 1(alle)k 3(ys)k
6211(for)s 6549(it)s 6741(are)s 7088(read)s 7557(in)s
7800(and)s 8204(\210ushed.)s 240 fnt2 0 10502(5.5.)m 471(Horizontal)s
1628(galleys)s 
[ /Dest /LOUThorizontal /DEST pdfmark
240 fnt1 480 10025(There)m 1108(is)s 1333(a)s
1514(strong)s 2180(analogy)s 3007(between)s 3876(breaking)s 4781(a)s
4962(column)s 5752(of)s 6038(te)s 3(xt)k 6468(into)s
6908(page-sized)s 8003(pieces,)s 8722(and)s 0 9737(breaking)m 912(a)s
1101(paragraph)s 2137(into)s 2585(line-sized)s 3594(pieces.)s 4378(In)s
4657(f)s 2(act,)k 5142(the)s 5513(tw)s 2(o)k
5946(dif)s 6(fer)k 6552(only)s 7055(in)s 7321(direction:)s
8359(v)s 3(ertical)k 0 9449(for)m 343(body)s 883(te)s 3(xt,)k
1351(horizontal)s 2381(for)s 2724(paragraphs.)s 3943(In)s 4205(this)s
4607(section)s 5347(we)s 5687(de\207ne)s 240 fnt3 6334 9451(horizontal)m
7384(galle)s 7(ys)k 240 fnt1 8049 9449(,)m 8162(and)s
8572(sho)s 6(w)k 0 9161(ho)m 6(w)k 493(the)s 3(y)k
989(pro)s 3(vide)k 1806(an)s 2122(unlimited)s 3129(number)s
3953(of)s 4257(paragraph)s 5302(breaking)s 6225(styles,)s 6909(as)s
7192(well)s 7691(as)s 7974(solv)s 3(e)k 8565(some)s
0 8873(other)m 587(problems.)s 1677(Re)s 3(grettably)k 15(,)k
2917(lack)s 3412(of)s 3719(time)s 4235(has)s 4641(pre)s 6(v)k 3(ented)k
5669(their)s 6202(incorporation)s 7583(into)s 8044(the)s 8429(Basser)s
0 8585(Lout)m 512(interpreter)s 13(.)k 480 8211(Imagine)m 1337(a)s
1521(g)s 1(alle)k 3(y)k 2173(whose)s 2859(components)s
4085(are)s 4450(separated)s 5428(by)s 5740(horizontal)s 6782(concatenation)s
8186(operators)s 0 7923(instead)m 725(of)s 986(v)s 3(ertical)k
1742(ones,)s 2278(perhaps)s 3062(indicated)s 3986(by)s 4269(a)s
220 fnt5 4425 7920(hor)m -3(iz)k 3(ontally)k 5582(into)s
240 fnt1 5977 7923(clause.)m 6728(Then)s 7266(all)s 7549(object)s
8182(breaking,)s 0 7635(including)m 957(paragraph)s 1970(breaking,)s 2914(could)s
3504(be)s 3786(replaced)s 4653(by)s 4947(g)s 1(alle)k 3(y)k
5581(component)s 6705(promotion)s 7759(lik)s 2(e)k 8171(this:)s
220 fnt5 480 7134(def @P)m 8(ar)k 2(ag)k 2(r)k 2(aph r)k -3(ight x)k
480 6846({)m 480 6558(    def @LinePlace { @Galle)m 4(y })k 480 5982(    def @LineList)m 480 5694(    {)m
480 5406(        @HExpand @LinePlace)m 480 5118(        //1vx  @LineList)m 480 4830(    })m 480 4254(    def @P)m 8(ar hor)k -3(iz)k 3(ontally into { @LinePlace&&preceding })k
480 3966(        r)m -3(ight x)k 480 3678(    { x })m 480 3102(    @LineList  //  @P)m 8(ar { 0.2i @Wide {}  &0i  x  &1r)k -8(t })k
480 2814(})m 240 fnt1 0 2320(The)m 220 fnt5 431 2317(@HExpand)m
240 fnt1 1607 2320(operator)m 9(,)k 2504(which)s 3149(is)s
3362(a)s 3531(primiti)s 6(v)k 3(e)k 4456(of)s
4730(Basser)s 5430(Lout,)s 5992(horizontally)s 7204(e)s 3(xpands)k
8040(the)s 8391(g)s 1(aps)k 8883(in)s 0 2032(its)m
290(right)s 816(parameter)s 1844(until)s 2352(the)s 2715(result)s
3319(\207lls)s 3743(the)s 4105(a)s 4(v)k 6(ailable)k
5028(space,)s 5681(thus)s 6145(implementing)s 7541(line)s 7970(adjustment,)s
0 1744(e)m 3(xcept)k 689(when)s 1274(the)s 1631(parameter)s
2654(contains)s 3511(tab)s 4(ulation)k 4529(g)s 1(aps)k
5027(lik)s 2(e)k 220 fnt5 5447 1741(&1r)m -8(t)k
240 fnt1 5853 1744(,)m 5969(which)s 6620(cause)s 7216(the)s
7573(parameter)s 8596(to)s 8844(be)s 0 1456(already)m 757(e)s 3(xpanded.)k
1836(The)s 2264(result)s 2854(of)s 220 fnt5 480 955(@P)m 8(ar)k 2(ag)k 2(r)k 2(aph { A shor)k -8(t par)k 2(ag)k 2(r)k 2(aph of te)k 6(xt.)k 13( })k
240 fnt1 0 456(w)m 2(ould)k 655(then)s 1124(be)s
1406(something)s 2456(lik)s 2(e)k 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 34 35
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1579(-)m 5833(34)s
6127(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
768 13253(A)m 1073(short)s 1687(paragraph)s 480 12965(of)m
751(te)s 3(xt.)k 0 12512(depending)m 1061(on)s 1368(the)s
1726(a)s 4(v)k 6(ailable)k 2645(horizontal)s 3679(space.)s
4384(An)s 4744(unlimited)s 5729(range)s 6326(of)s 6607(paragraph)s
7630(breaking)s 8531(styles)s 0 12224(could)m 590(be)s 872(de\207ned,)s
1684(including)s 2641(ragged)s 3350(right,)s 3908(ragged)s 4617(left,)s
5041(break-and-center)s 9(,)k 6757(and)s 7161(so)s 7427(on.)s
480 11850(In)m 765(Basser)s 1492(Lout,)s 2081(indented)s 2992(paragraphs)s
4122(are)s 4499(produced)s 5477(by)s 5801(preceding)s 6827(them)s
7394(with)s 7906(a)s 8102(horizontal)s 0 11562(concatenation)m 1380(operator)s 9(,)k
2269(for)s 2602(e)s 3(xample)k 220 fnt5 3459 11559(|0.5i)m
240 fnt1 3855 11562(.)m 4014(This)s 4485(has)s 4849(the)s
5192(unfortunate)s 6345(ef)s 6(fect)k 6935(of)s 7201(making)s
7967(an)s 8244(indented)s 0 11274(paragraph)m 1007(into)s 1426(a)s
1586(single)s 2207(component)s 3325(of)s 3590(the)s 3932(enclosing)s
4895(g)s 1(alle)k 3(y)k 15(,)k 5561(so)s
5821(that)s 6233(it)s 6419(will)s 6839(al)s 2(w)k 2(ays)k
7544(be)s 7820(k)s 2(ept)k 8283(together)s 0 10986(on)m
297(one)s 699(page.)s 1315(Horizontal)s 2392(g)s 1(alle)k 3(ys)k
3116(solv)s 3(e)k 3674(this)s 4070(problem)s 4927(with)s
5409(a)s 5575(simple)s 6268(change)s 7002(to)s 220 fnt5
7241 10983(@LineList)m 240 fnt1 8215 10986(:)m 220 fnt5 480 10485(def @LineList)m
480 10197({)m 480 9909(    |0.5i  @HExpand @LinePlace)m 480 9621(    //1vx  @LineList)m 480 9333(})m 240 fnt1
0 8839(sho)m 6(wing)k 860(the)s 1210(\210e)s 3(xibility)k
2192(that)s 2611(comes)s 3275(from)s 3801(bringing)s 4666(the)s
5016(full)s 5404(po)s 6(wer)k 6057(of)s 6330(the)s
6680(Lout)s 7193(language)s 8115(to)s 8356(bear)s 8829(on)s
0 8551(paragraph)m 1013(layout.)s 1775(It)s 1980(is)s 2190(easy)s
2669(to)s 2908(mak)s 2(e)k 3480(pro)s 3(vision)k
4438(for)s 4776(a)s 4942(tag)s 5287(on)s 5584(the)s
5932(\207rst)s 6363(line.)s 480 8177(Although)m 1451(Basser)s 2158(Lout)s
2679(permits)s 3456(recepti)s 6(v)k 3(e)k 4387(symbols)s
5246(within)s 5923(paragraphs,)s 7089(the)s 3(y)k 7561(are)s
7918(of)s 8198(little)s 8700(use,)s 0 7889(because)m 835(their)s
1355(a)s 4(v)k 6(ailable)k 2286(width)s 2911(is)s
3144(calculated)s 4193(after)s 4711(paragraph)s 5747(breaking,)s 6714(and)s
7141(the)s 7512(incoming)s 8492(g)s 1(alle)k 3(y)k
0 7601(cannot)m 736(spread)s 1456(o)s 3(v)k 3(er)k
1973(more)s 2558(than)s 3065(one)s 3505(line.)s 4066(W)s 9(ith)k
4630(horizontal)s 5692(g)s 1(alle)k 3(ys,)k 6510(such)s
7044(symbols)s 7931(w)s 2(ould)k 8625(ha)s 4(v)k 3(e)k
0 7313(in\207nite)m 733(a)s 4(v)k 6(ailable)k 1641(width,)s
2293(and)s 2697(we)s 3032(could)s 3622(easily)s 4233(produce)s
5060(a)s 5226(\207lled)s 5775(paragraph)s 6788(of)s 7059(footnotes)s
8000(lik)s 2(e)k 8412(this:)s 200 fnt1 480 6838(1)m
240 fnt1 559 6743(See)m 987(Jones)s 1597(and)s 2028(Saunders)s
2983(\(1982\).)s 200 fnt1 3932 6838(2)m 240 fnt1 4027 6743(Or)m
4366(so)s 4659(Jacobsen)s 480 6443(\(1973\))m 1167(asserts.)s 200 fnt1
2087 6538(3)m 240 fnt3 2174 6445(ibid)m 240 fnt1 2552 6443(,)m
2659(p.)s 2883(327.)s 0 5940(based)m 603(on)s 900(an)s
1183(in\207nite)s 1916(horizontal)s 2940(sequence)s 3873(of)s 220 fnt5
4144 5937(@F)m 6(ootPlace)k 240 fnt1 5400 5940(symbols)m 6249(inside)s
6876(a)s 7042(horizontal)s 8066(g)s 1(alle)k 3(y)k 15(.)k
480 5566(When)m 1133(body)s 1692(te)s 3(xt)k 2132(is)s
2367(placed)s 3074(on)s 3395(pages,)s 4072(the)s 4445(length)s
5125(of)s 5421(each)s 5940(column)s 6740(v)s 6(aries)k
7380(depending)s 8456(on)s 8778(the)s 0 5278(a)m 4(v)k 6(ailable)k
914(v)s 3(ertical)k 1687(space.)s 2389(Horizontal)s 3472(g)s 1(alle)k 3(ys)k
4203(could)s 4799(analogously)s 6017(produce)s 6850(lines)s 7359(of)s
7636(v)s 6(arying)k 8421(length,)s 0 4990(and)m 404(so)s
670(could)s 1260(\207ll)s 1580(non-rectangular)s 3153(shapes.)s 480 4616(An)m
835(important)s 1829(theoretical)s 2896(bene\207t)s 3612(of)s 3888(horizontal)s
4918(g)s 1(alle)k 3(ys)k 5647(is)s 5862(that)s
6285(the)s 3(y)k 6753(w)s 2(ould)k 7413(permit)s
8102(horizontal)s 0 4328(and)m 403(v)s 3(ertical)k 1168(to)s
1405(be)s 1685(treated)s 2390(in)s 2631(a)s 2795(perfectly)s
3695(symmetrical)s 4928(w)s 2(ay)k 15(,)k 5415(whereas)s
6247(at)s 6477(present)s 7225(paragraph)s 8236(breaking)s 0 4040(is)m
243(horizontal)s 1300(only)s 15(,)k 1851(and)s 2288(g)s 1(alle)k 3(y)k
2955(breaking)s 3878(is)s 4121(v)s 3(ertical)k 4921(only)s 15(.)k
5529(This)s 6038(must)s 6596(simplify)s 7479(the)s 7860(treatment)s
8855(of)s 0 3752(non-European)m 1432(languages)s 2459(which)s 3121(\207ll)s
3460(in)s 3722(unusual)s 4542(directions,)s 5610(although)s 6525(it)s
6736(is)s 6965(not)s 7351(itself)s 7918(suf\207cient)s 8887(to)s
0 3464(implement)m 1082(them.)s 480 3090(There)m 1132(are)s 1519(a)s
1725(fe)s 6(w)k 2170(minor)s 2841(problems)s 3822(with)s
4343(horizontal)s 5407(g)s 1(alle)k 3(ys.)k 6284(First,)s
6867(the)s 7255(syntactic)s 8197(o)s 3(v)k 3(erhead)k
0 2802(of)m 319(enclosing)s 1337(each)s 1880(paragraph)s 2941(in)s
220 fnt5 3233 2799(@P)m 8(ar)k 2(ag)k 2(r)k 2(aph { ...)k 13( })k
240 fnt1 5064 2802(or)m 5371(whate)s 6(v)k 3(er)k
6346(is)s 6604(unacceptable.)s 8065(Permitting)s 0 2514(user)m 4(-de\207ned)k
1234(operators)s 2172(to)s 2409(ha)s 4(v)k 3(e)k
2908(lo)s 6(wer)k 3504(precedence)s 4633(than)s 5100(the)s
5446(white)s 6031(space)s 6616(between)s 7468(tw)s 2(o)k
7876(w)s 2(ords)k 8508(might)s 0 2226(help)m 450(here.)s
1009(Second,)s 1805(the)s 2137(b)s 4(uilt-in)k 2877(paragraph)s
3874(break)s 2(er)k 4632(includes)s 5464(h)s 1(yphenation,)k
6738(and)s 7126(it)s 7302(permits)s 8053(line)s 8451(breaks)s
0 1938(in)m 246(the)s 598(input)s 1153(to)s 1396(determine)s
2410(line)s 2828(breaks)s 3506(in)s 3753(the)s 4105(output,)s
4827(if)s 5048(desired.)s 5905(These)s 6536(features)s 7345(must)s
7874(someho)s 6(w)k 8844(be)s 0 1650(preserv)m 3(ed.)k
1081(Finally)s 15(,)k 1841(we)s 2167(ha)s 4(v)k 3(e)k
2659(e)s 3(xplained)k 3634(ho)s 6(w)k 4086(the)s
4425(Basser)s 5113(Lout)s 5616(interpreter)s 6659(assigns)s 7392(equal)s
7956(width)s 8549(to)s 8778(the)s 0 1362(wider)m 607(columns)s
1473(of)s 1748(tables)s 2359(\(Section)s 3216(2.5\).)s 3763(The)s
4194(equi)s 6(v)k 6(alent)k 5242(situation)s 6126(in)s
6372(v)s 3(ertical)k 7143(g)s 1(alle)k 3(ys)k
7871(occurs)s 8550(when)s 0 1074(tw)m 2(o)k 416(recepti)s 6(v)k 3(e)k
1345(symbols)s 2201(compete)s 3074(for)s 3419(v)s 3(ertical)k
4193(space)s 4786(\(e.g.)s 220 fnt5 5262 1071(@T)m 26(e)k 6(xtPlace)k
240 fnt1 6487 1074(and)m 220 fnt5 6898 1071(@F)m 6(ootSect)k
240 fnt1 7989 1074(\),)m 8182(and)s 8593(there)s 0 786(it)m
187(is)s 392(con)s 9(v)k 3(entional)k 1666(to)s
1900(grant)s 2446(as)s 2691(much)s 3274(as)s 3519(required)s
4368(to)s 4602(the)s 4945(\207rst)s 5371(arri)s 6(v)k 6(al.)k
6140(It)s 6339(is)s 6544(not)s 6905(clear)s 7423(to)s
7657(the)s 8000(author)s 8665(ho)s 6(w)k 0 498(these)m
547(dif)s 6(ferent)k 1422(approaches)s 2549(can)s 2938(be)s
3220(reconciled.)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 35 36
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Helvetica
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5709 -1582(-)m 5837(35)s
6123(-)s 9066 13413 0 13413 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
240 fnt2 0 12672(6.)m 291(Cr)s 4(oss)k
926(r)s 4(efer)k 4(ences)k 
[ /Dest /LOUT18_651_s6_0_1 /DEST pdfmark
240 fnt1 480 12240(Cross)m
1064(references,)s 2138(such)s 2622(as)s 2859(`see)s 3286(page)s
3782(57')s 4121(and)s 4512(`see)s 4940(Figure)s 5607(5,)s 16(')k
5871(are)s 6205(a)s 6358(useful)s 6985(b)s 4(ut)k
7334(highly)s 7987(error)s 4(-prone)k 0 11952(feature)m 716(of)s
985(documents.)s 2184(Scribe)s 2848([7])s 3163(introduced)s 4242(a)s
4406(method)s 5180(of)s 5449(k)s 2(eeping)k 6256(them)s
6792(up)s 7083(to)s 7320(date)s 7772(automatically)s 0 11664(as)m
245(the)s 587(document)s 1585(changes:)s 2517(the)s 2859(user)s
3311(gi)s 6(v)k 3(es)k 3852(each)s 4342(referenced)s
5401(entity)s 5993(a)s 6153(tag,)s 6547(and)s 6945(operators)s
7879(are)s 8220(pro)s 3(vided)k 0 11376(that)m 418(return)s
1045(the)s 1393(page)s 1901(or)s 2160(sequence)s 3093(number)s
3884(of)s 4155(the)s 4503(entity)s 5101(with)s 5583(a)s
5749(gi)s 6(v)k 3(en)k 6329(tag.)s 480 11002(A)m
712(cross)s 1256(reference)s 2201(tak)s 2(es)k 2743(an)s
3028(object)s 3674(\(such)s 4251(as)s 4503(a)s 4671(page)s
5181(number\))s 6042(from)s 6568(one)s 6972(point)s 7526(in)s
7771(the)s 8122(document)s 0 10714(and)m 435(copies)s 1128(it)s
1351(to)s 1621(another)s 9(,)k 2467(and)s 2902(this)s
3329(generalization)s 4770(suggests)s 5663(other)s 6245(applications.)s 7595(F)s 3(or)k
8015(e)s 3(xample,)k 8960(a)s 0 10426(running)m 831(header)s
1562(is)s 1806(copied)s 2536(from)s 3094(the)s 3475(title)s
3935(of)s 4240(a)s 4440(nearby)s 5179(chapter)s 9(,)k
6013(and)s 6451(a)s 6651(reference)s 7628(is)s 7872(copied)s
8602(from)s 0 10138(a)m 207(bibliographic)s 1576(database.)s 2604(Making)s
3443(the)s 3832(unity)s 4419(of)s 4731(these)s 5319(applications)s
6566(manifest)s 7489(is)s 7740(an)s 8065(interesting)s 0 9850(language)m
920(design)s 1602(problem.)s 240 fnt2 0 9201(6.1.)m 471(The)s
926(cr)s 4(oss)k 1494(r)s 4(efer)k 4(ence)k
2496(abstraction)s 
[ /Dest /LOUTcross /DEST pdfmark
240 fnt1 480 8770(In)m 736(de)s 6(v)k 3(eloping)k
1844(the)s 2192(cross)s 2734(reference)s 3677(abstraction,)s 4832(it)s
5024(seemed)s 5799(best)s 6244(to)s 6483(be)s 3(gin)k
7069(with)s 7551(the)s 7899(database)s 8779(ap)s 8998(-)s
0 8482(plication,)m 943(since)s 1490(it)s 1682(is)s 1892(the)s
2240(simplest.)s 3200(Database)s 4132(relations)s 5005(are)s 5352(naturally)s
6255(mapped)s 7071(into)s 7496(Lout)s 8008(de\207nitions:)s 220 fnt5
480 7981(def @Ref)m 6(erence)k 480 7693(    named @T)m 26(ag {})k 480 7405(    named @A)m 6(uthor {})k
480 7117(    named @Title {})m 480 6829(    named @Jour)m -5(nal {})k 480 6541({})m 240 fnt1
0 6047(The)m 434(set)s 766(of)s 1043(all)s 1343(in)s 9(v)k 4(ocations)k
2490(of)s 220 fnt5 2768 6044(@Ref)m 6(erence)k 240 fnt1
4055 6047(is)m 4272(a)s 4444(relation)s 5237(whose)s 5911(attrib)s 4(utes)k
6853(are)s 7206(the)s 7561(parameters,)s 8722(and)s 0 5759(whose)m
659(tuples)s 1271(are)s 1608(the)s 1946(in)s 9(v)k 4(ocations.)k
3191(T)s 19(o)k 3481(complete)s 4403(the)s 4741(correspondence,)s
6339(we)s 6665(need)s 7165(only)s 7635(declare)s 8370(that)s
8778(the)s 220 fnt5 0 5468(@T)m 26(ag)k 240 fnt1
623 5471(parameter)m 1637(is)s 1847(special,)s 2617(serving)s 3374(as)s
3624(the)s 3972(k)s 2(e)k 3(y)k 4367(attrib)s 4(ute.)k
480 5097(F)m 3(ollo)k 6(wing)k 1508(the)s 1856(database)s
2735(model,)s 3440(we)s 3775(ne)s 3(xt)k 4244(need)s
4755(a)s 4921(notation)s 5762(for)s 6100(retrie)s 6(ving)k
7075(the)s 7423(in)s 9(v)k 4(ocation)k 8477(with)s
8960(a)s 0 4809(gi)m 6(v)k 3(en)k 580(tag:)s
220 fnt5 480 4308(@Ref)m 6(erence&&kingston91)k 240 fnt1 0 3809(This)m
240 fnt3 534 3811(cr)m 10(oss)k 1143(r)s 8(efer)k 8(ence)k
240 fnt1 2141 3809(is)m 2410(lik)s 2(e)k 2881(an)s
3223(arro)s 6(w)k 3887(pointing)s 4796(to)s 5094(the)s
5501(in)s 9(v)k 4(ocation.)k 6721(T)s 19(o)k
7080(access)s 7800(its)s 8135(attrib)s 4(utes,)k 0 3521(we)m
335(write)s 220 fnt5 480 3069(@Ref)m 6(erence&&kingston91 @Open { @A)k 6(uthor)k 11(, @Title })k
240 fnt1 0 2570(The)m 220 fnt5 484 2567(@Open)m 240 fnt1
1347 2570(operator)m 2260(e)s 6(v)k 6(aluates)k 3245(its)s
3578(right)s 4146(parameter)s 5217(in)s 5517(an)s 5857(en)s 9(vironment)k
7174(which)s 7873(includes)s 8778(the)s 0 2282(e)m 3(xported)k
892(parameters)s 1990(of)s 2261(its)s 2537(left.)s 480 1908(An)m
829(in)s 9(v)k 4(ocation)k 1882(is)s 2091(chosen)s
2812(to)s 3050(be)s 3331(a)s 3496(running)s 4293(header)s
4989(because)s 5801(of)s 6071(its)s 6346(proximity)s 7342(to)s
7580(the)s 7927(place)s 8486(where)s 0 1620(it)m 223(is)s
465(used,)s 1043(rather)s 1691(than)s 2192(by)s 2517(its)s
2825(tag.)s 3313(Such)s 3881(proximity)s 4910(is)s 5151(naturally)s
6086(e)s 3(xpressed)k 7116(by)s 7442(tw)s 2(o)k
7884(special)s 8634(tags,)s 220 fnt5 0 1329(preceding)m 240 fnt1
1049 1332(and)m 220 fnt5 1491 1329(f)m 6(ollo)k 3(wing)k
240 fnt1 2321 1332(;)m 2471(for)s 2848(e)s 3(xample,)k
220 fnt5 3800 1329(@Sym&&f)m 6(ollo)k 3(wing)k 240 fnt1
5682 1332(will)m 6146(point)s 6737(to)s 7014(the)s 7400(closest)s
8149(follo)s 6(wing)k 0 1044(in)m 9(v)k 4(ocation)k
1083(of)s 220 fnt5 1383 1041(@Sym)m 240 fnt1 2121 1044(in)m
2393(the)s 2771(\207nal)s 3280(printed)s 4045(document.)s 5182(This)s
5688(is)s 5927(much)s 6546(simpler)s 7351(conceptually)s 8657(than)s
0 756(reference)m 937(to)s 1169(the)s 1511(internal)s 2288(state)s
2775(of)s 3039(the)s 3381(document)s 4378(formatter)s 5319(at)s
5544(a)s 5704(critical)s 6413(moment,)s 7298(the)s 7639(usual)s
8192(approach)s 0 468(to)m 239(running)s 1037(headers.)s 480 94(It)m
691(turns)s 1227(out)s 1600(that)s 2025(the)s 2380(abo)s 3(v)k 3(e)k
3009(design)s 3698(solv)s 3(es)k 4350(all)s 4650(the)s
5005(cross)s 5554(referencing)s 6701(problems)s 7649(encountered)s 8883(in)s

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 36 37
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Helvetica
%%+ font Times-Bold
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5705 -1581(-)m 5833(36)s
6126(-)s 9066 13414 0 13305 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13251(practice)m 825(e)s 3(xcept)k 1521(one,)s
1988(which)s 2645(may)s 3126(be)s 3422(typi\207ed)s 4226(by)s
4535(the)s 4897(problem)s 5769(of)s 6054(\207nding)s 6801(the)s
7164(number)s 7969(of)s 8255(the)s 8618(page)s 0 12963(on)m
303(which)s 952(the)s 1306(chapter)s 2076(whose)s 2750(tag)s
3102(is)s 220 fnt5 3318 12960(intro)m 240 fnt1 3804 12963(be)m 3(gins.)k
4596(T)s 19(w)k 2(o)k 5074(cross)s 5622(referencing)s
6769(steps)s 7304(are)s 7658(needed,)s 8449(\207rst)s 8887(to)s
220 fnt5 0 12672(@Chapter&&intro)m 240 fnt1 1714 12675(,)m 1821(then)s
2290(from)s 2814(there)s 3347(to)s 220 fnt5 3586 12672(@P)m 8(age&&preceding)k
240 fnt1 5556 12675(,)m 5663(where)s 6303(the)s 6651(page)s
7159(number)s 7950(is)s 8160(kno)s 6(wn.)k 480 12301(Gi)m 6(v)k 3(en)k
1113(our)s 1492(success)s 2260(so)s 2526(f)s 2(ar)k 9(,)k
2886(this)s 3282(last)s 3673(problem)s 4530(pro)s 3(v)k 3(es)k
5213(to)s 5452(be)s 5734(surprisingly)s 6930(dif\207cult.)s 7850(W)s 19(e)k
8219(\207rst)s 8650(try)s 220 fnt5 480 11800(@Chapter&&intro @Open {)m 480 11512(    @P)m 8(age&&preceding @Open { @P)k 8(ageNum })k
480 11224(})m 240 fnt1 0 10730(b)m 4(ut)k 363(this)s
761(f)s 2(ails)k 1222(because)s 220 fnt5 2037 10727(@P)m 8(age&&preceding)k
240 fnt1 4069 10730(is)m 4281(e)s 6(v)k 6(aluated)k
5245(in)s 5490(the)s 5840(present)s 6592(conte)s 3(xt,)k
7402(not)s 7770(in)s 8015(the)s 8365(conte)s 3(xt)k
0 10442(of)m 220 fnt5 271 10439(@Chapter&&intro)m 240 fnt1 2045 10442(as)m
2295(required.)s 3255(So)s 3561(our)s 3940(ne)s 3(xt)k
4409(attempt)s 5185(is)s 220 fnt5 480 9941(def @Chapter)m 480 9653(    named @P)m 8(ageNum { @P)k 8(age&&preceding @Open { @P)k 8(ageNum } })k
480 9365(    ...)m 240 fnt1 0 8914(with)m 482(the)s 220 fnt5
830 8911(@P)m 8(age&&preceding)k 240 fnt1 2860 8914(cross)m 3402(reference)s
4345(attached)s 5199(to)s 5438(the)s 5786(chapter;)s 6601(we)s
6936(write)s 220 fnt5 480 8413(@Chapter&&intro @Open { @P)m 8(ageNum })k 240 fnt1
0 7914(This)m 604(also)s 1170(f)s 2(ails,)k 1813(because)s
2754(parameters)s 3980(are)s 4456(e)s 6(v)k 6(aluated)k
5546(after)s 6170(substitution,)s 7521(so)s 7915(once)s 8552(ag)s 1(ain)k
220 fnt5 0 7623(@P)m 8(age&&preceding)k 240 fnt1 2015 7626(is)m
2209(e)s 6(v)k 6(aluated)k 3156(in)s 3383(the)s
3716(wrong)s 4365(conte)s 3(xt.)k 5215(W)s 19(e)k
5568(could)s 6143(of)s 6398(course)s 7063(de\207ne)s 7688(a)s
7839(ne)s 6(w)k 8270(operator)s 0 7338(speci\207cally)m 1142(for)s
1480(this)s 1876(case:)s 220 fnt5 480 6837(@P)m 8(age&&{ @Preceding @Chapter&&intro })k
240 fnt1 0 6338(or)m 267(some)s 836(such.)s 1448(This)s
1932(is)s 2151(free)s 2585(of)s 2864(the)s 3221(anno)s 2(ying)k
4172(conte)s 3(xt-sensiti)k 6(vity)k 15(,)k 6029(b)s 4(ut)k
6399(it)s 6599(seems)s 7243(quite)s 7785(comple)s 3(x,)k
8722(and)s 0 6050(the)m 348(e)s 3(xpected)k 1253(cross)s
1795(reference)s 220 fnt5 2738 6047(@P)m 8(age&&preceding)k 240 fnt1
4768 6050(does)m 5258(not)s 5624(appear)s 13(.)k 480 5676(The)m
939(author)s 1642(w)s 2(as)k 2095(lost)s 2532(in)s
2806(these)s 3385(obscurities)s 4503(for)s 4873(some)s 5465(time,)s
6028(and)s 6464(ultimately)s 7518(rescued)s 8338(himself)s 0 5388(by)m
306(looking)s 1103(ahead)s 1731(to)s 1982(the)s 2342(implementation)s
3912(of)s 4195(the)s 220 fnt5 4555 5385(preceding)m 240 fnt1
5578 5388(and)m 220 fnt5 5994 5385(f)m 6(ollo)k 3(wing)k
240 fnt1 6897 5388(tags,)m 7401(to)s 7652(see)s 8025(if)s
8254(a)s 8433(simple)s 0 5100(e)m 3(xtension)k 971(of)s
1242(it)s 1434(w)s 2(ould)k 2089(solv)s 3(e)k
2647(the)s 2995(problem.)s 3956(This)s 4432(led)s 4782(to)s
5021(the)s 220 fnt5 5369 5097(@T)m 26(agged)k 240 fnt1
6358 5100(operator:)m 220 fnt5 480 4599(@P)m 8(age&&preceding @T)k 26(agged intro)k
240 fnt1 0 4100(placed)m 686(at)s 922(the)s 1274(be)s 3(ginning)k
2286(of)s 2562(the)s 2914(body)s 3452(of)s 3727(the)s
4079(chapter)s 4847(will)s 5277(attach)s 220 fnt5 5908 4097(intro)m
240 fnt1 6391 4100(as)m 6645(an)s 6933(e)s 3(xtra)k
7471(tag)s 7820(to)s 8063(the)s 8416(closest)s 0 3812(preceding)m
996(in)s 9(v)k 4(ocation)k 2050(of)s 220 fnt5
2321 3809(@P)m 8(age)k 240 fnt1 3040 3812(,)m 3147(so)s
3413(that)s 220 fnt5 480 3311(@P)m 8(age&&intro @Open { @P)k 8(ageNum })k
240 fnt1 0 2812(yields)m 635(the)s 996(desired)s 1758(page)s
2279(number)s 13(.)k 3174(There)s 3801(is)s 4024(something)s
5087(lo)s 6(w-le)k 6(v)k 3(el)k 6043(and)s
6460(ad)s 6757(hoc)s 7170(about)s 7775(the)s 220 fnt5
8137 2809(@T)m 26(agged)k 240 fnt1 0 2524(operator)m 9(,)k
894(b)s 4(ut)k 1256(the)s 1604(tw)s 2(o)k
2014(cross)s 2556(references)s 3587(do)s 3880(appear)s 4577(naturally)s 15(,)k
5518(and)s 5922(it)s 6114(w)s 2(orks.)k 240 fnt2
0 1875(6.2.)m 471(Implementation)s 2159(of)s 2431(cr)s 4(oss)k
2999(r)s 4(efer)k 4(ences)k 
[ /Dest /LOUTcross_impl /DEST pdfmark
240 fnt1 480 1398(Before)m
1185(an)s 1466(object)s 2109(can)s 2496(be)s 2777(sized)s
3324(and)s 3727(printed,)s 4509(the)s 4855(v)s 6(alues)k
5510(of)s 5779(an)s 3(y)k 6175(cross)s 6715(references)s
7745(within)s 8411(it)s 8601(must)s 0 1110(be)m 279(kno)s 6(wn.)k
1086(If)s 1312(the)s 3(y)k 1772(refer)s 2277(to)s
2512(in)s 9(v)k 4(ocations)k 3650(that)s 4064(ha)s 4(v)k 3(e)k
4561(not)s 4924(yet)s 5272(been)s 5777(read,)s 6292(there)s
6821(is)s 7027(a)s 7190(problem.)s 8147(Scribe)s 8809([7])s
0 822(solv)m 3(es)k 649(it)s 844(by)s 1141(capitalizing)s
2311(on)s 2611(the)s 2962(f)s 2(act)k 3381(that)s
3802(documents)s 4893(are)s 5243(formatted)s 6232(repeatedly)s 7284(during)s
7965(the)s 8317(drafting)s 0 534(process.)m 868(All)s 1214(tagged)s
1897(in)s 9(v)k 4(ocations)k 3024(are)s 3358(copied)s
4040(to)s 4266(an)s 4535(auxiliary)s 5425(\207le)s 5772(during)s
6437(the)s 6771(\207rst)s 7189(run,)s 7601(and)s 7992(inde)s 3(x)k 3(ed)k
8788(for)s 0 246(quick)m 593(retrie)s 6(v)k 6(al)k
1429(on)s 1725(the)s 2072(second.)s 2901(A)s 3130(ne)s 6(w)k
3576(auxiliary)s 4478(\207le)s 4839(is)s 5048(written)s 5780(during)s
6457(the)s 6805(second)s 7527(run,)s 7952(for)s 8289(retrie)s 6(v)k 6(al)k

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 37 38
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Italic
%%+ font Helvetica
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
%%IncludeResource: font Helvetica
/Helveticafnt5 vec2 /Helvetica LoutRecode
/fnt5 { /Helveticafnt5 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5708 -1579(-)m 5836(37)s
6124(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
0 13253(on)m 301(the)s 654(third,)s 1217(and)s
1625(so)s 1896(on.)s 2305(Cross)s 2906(references)s 3941(al)s 2(w)k 2(ays)k
4657(lag)s 5007(one)s 5413(run)s 5794(behind)s 6509(the)s
6862(rest)s 7270(of)s 7546(the)s 7899(document;)s 8960(a)s
0 12965(perfect)m 711(cop)s 2(y)k 1217(may)s 1671(be)s
1942(produced)s 2879(by)s 3161(formatting)s 4210(the)s 4547(same)s
5082(v)s 3(ersion)k 5828(twice,)s 6440(e)s 3(xcept)k
7110(in)s 7341(a)s 7495(fe)s 6(w)k 7889(pathological)s
0 12677(cases)m 555(that)s 973(f)s 2(ail)k 1343(to)s
1582(con)s 9(v)k 3(er)k 4(ge.)k 480 12303(Cross)m
1123(referencing)s 2310(in)s 2600(Lout)s 3159(is)s 3416(implemented)s
4769(on)s 5113(top)s 5519(of)s 5837(a)s 6050(simple)s
6790(database)s 7716(system.)s 8591(Each)s 0 12015(database)m 879(is)s
1089(either)s 1692(writable)s 2530(or)s 2790(readable)s 3655(b)s 4(ut)k
4017(not)s 4383(both)s 4867(at)s 5099(once,)s 5658(and)s
6062(holds)s 6633(a)s 6799(set)s 7124(of)s 7395(k)s 2(e)k 3(y-v)k 6(alue)k
8384(entries:)s 0 11727(the)m 348(k)s 2(e)k 3(ys)k
833(are)s 1180(ASCII)s 1861(strings,)s 2605(and)s 3009(the)s
3358(v)s 6(alues)k 4014(are)s 4361(Lout)s 4873(objects,)s
5658(possibly)s 6510(with)s 6992(en)s 9(vironments,)k 8393(written)s
0 11439(in)m 290(Lout)s 850(source.)s 1685(Operations)s 2833(are)s
3227(pro)s 3(vided)k 4181(for)s 4566(writing)s 5357(an)s
5687(entry)s 15(,)k 6318(con)s 9(v)k 3(erting)k
7429(from)s 8001(writable)s 8887(to)s 0 11151(readable,)m 916(retrie)s 6(v)k 6(al)k
1753(by)s 2047(k)s 2(e)k 3(y)k 15(,)k
2480(and)s 2884(sequential)s 3908(retrie)s 6(v)k 6(al)k
4745(in)s 4988(k)s 2(e)k 3(y)k 5383(order)s 13(.)k
480 10777(The)m 905(implementation,)s 2509(which)s 3148(is)s 3354(quite)s
3885(unsophisticated,)s 5477(emplo)s 2(ys)k 6334(one)s 6732(or)s
6988(more)s 7532(ASCII)s 240 fnt3 8208 10779(database)m 0 10491(\207les)m
240 fnt1 380 10489(,)m 485(containing)s 1545(the)s 1891(v)s 6(alues,)k
2600(and)s 3001(one)s 3401(ASCII)s 240 fnt3 4078 10491(inde)m 4(x)k
4650(\207le)s 240 fnt1 4992 10489(per)m 5354(database,)s 6282(containing)s
7342(the)s 7688(k)s 2(e)k 3(ys.)k 8283(T)s 19(o)k
8580(write)s 0 10201(an)m 283(entry)s 15(,)k 866(the)s
1214(v)s 6(alue)k 1782(is)s 1992(\207rst)s 2423(appended)s
3399(to)s 3638(a)s 3804(database)s 4683(\207le,)s 5095(then)s
5564(a)s 5730(line)s 6144(lik)s 2(e)k 220 fnt5
480 9700(@Chapter&&intro  ch1.ld  57)m 240 fnt1 0 9204(is)m 204(appended)s 1174(to)s
1406(the)s 1748(inde)s 3(x)k 2326(\207le,)s 2731(gi)s 6(ving)k
3384(the)s 3725(\207le)s 4080(and)s 4478(of)s 6(fset)k
5068(where)s 5702(the)s 6043(v)s 6(alue)k 6605(is)s
6809(stored.)s 7550(T)s 19(o)k 7844(con)s 9(v)k 3(ert)k
8602(from)s 0 8916(writable)m 831(to)s 1062(readable,)s 1971(the)s
2311(inde)s 3(x)k 2887(\207le)s 3241(is)s 3443(sorted.)s
4183(Then)s 4725(retrie)s 6(v)k 6(al)k 5554(by)s
5840(k)s 2(e)k 3(y)k 6228(requires)s 7040(a)s
7198(binary)s 7856(search)s 8515(of)s 8778(the)s 0 8628(inde)m 3(x)k
584(\207le)s 945(and)s 1349(one)s 1751(seek)s 2237(into)s
2662(a)s 2828(database)s 3707(\207le,)s 4119(and)s 4523(sequential)s
5547(retrie)s 6(v)k 6(al)k 6384(by)s 6678(k)s 2(e)k 3(y)k
7073(is)s 7283(tri)s 6(vial.)k 480 8254(This)m 945(database)s
1813(system)s 2526(is)s 2725(used)s 3211(in)s 3443(se)s 6(v)k 3(eral)k
4154(w)s 2(ays.)k 4797(F)s 3(or)k 5175(an)s
5447(e)s 3(xternal)k 6257(database,)s 7176(say)s 7538(of)s
7798(bibliographic)s 0 7966(references,)m 1093(the)s 1447(user)s 1912(creates)s
2631(the)s 2985(database)s 3871(\207le)s 4238(of)s 4516(v)s 6(alues)k
5178(\(without)s 6054(en)s 9(vironments\),)k 7540(Lout)s 8058(creates)s
8778(the)s 0 7678(inde)m 3(x)k 587(\207le)s 951(whene)s 6(v)k 3(er)k
1935(it)s 2130(cannot)s 2831(\207nd)s 3265(one,)s 3721(and)s
4128(retrie)s 6(v)k 6(als)k 5057(by)s 5354(k)s 2(e)k 3(y)k
5752(proceed)s 6570(as)s 6823(usual.)s 7495(Cross)s 8095(references)s
0 7390(with)m 476(tags)s 906(other)s 1451(than)s 220 fnt5
1913 7387(preceding)m 240 fnt1 2918 7390(and)m 220 fnt5 3316 7387(f)m 6(ollo)k 3(wing)k
240 fnt1 4200 7390(are)m 4540(treated)s 5241(as)s 5485(described)s
6453(abo)s 3(v)k 3(e,)k 7119(by)s 7407(writing)s
8144(all)s 8430(tagged)s 0 7102(in)m 9(v)k 4(ocations)k
1131(\(with)s 1681(en)s 9(vironments\))k 3092(to)s 3320(a)s
3475(single)s 4092(database,)s 5011(which)s 5643(is)s 5842(con)s 9(v)k 3(erted)k
6820(to)s 7049(readable)s 7903(at)s 8125(the)s 8462(end)s
8855(of)s 0 6814(the)m 334(run)s 695(for)s 1018(retrie)s 6(v)k 6(als)k
1930(on)s 2212(the)s 2545(ne)s 3(xt)k 3000(run.)s
3468(Sorted)s 4135(g)s 1(alle)k 3(ys,)k 4900(such)s
5382(as)s 5617(inde)s 3(x)k 6186(entries,)s 6915(are)s
7247(written)s 7965(out)s 8316(inde)s 3(x)k 3(ed)k
0 6526(by)m 307(tar)s 4(get)k 920(and)s 1337(k)s 2(e)k 3(y)k
1746(and)s 2163(retrie)s 6(v)k 3(ed)k 3074(sequentially)s
4297(on)s 4607(the)s 4969(ne)s 3(xt)k 5451(run.)s
5948(Unsorted)s 6896(g)s 1(alle)k 3(ys)k 7634(with)s
8130(preceding)s 0 6238(tar)m 4(gets)k 684(which)s 1327(pop)s
1741(of)s 6(f)k 2086(the)s 2435(top)s 2795(of)s
3067(the)s 3416(root)s 3863(g)s 1(alle)k 3(y)k
4498(without)s 5290(\207nding)s 6023(a)s 6190(tar)s 4(get,)k
6837(such)s 7334(as)s 7585(entries)s 8273(in)s 8518(tables)s
0 5950(of)m 274(contents,)s 1181(are)s 1532(treated)s 2242(similarly)s 15(,)k
3186(e)s 3(xcept)k 3870(that)s 4291(the)s 3(y)k
4758(are)s 5108(inde)s 3(x)k 3(ed)k 5922(by)s
6219(tar)s 4(get)k 6821(and)s 7229(a)s 7398(sequence)s
8335(number)s 0 5662(that)m 418(preserv)s 3(es)k 1368(their)s
1865(relati)s 6(v)k 3(e)k 2627(order)s 3191(during)s
3869(the)s 4217(sort.)s 480 5288(When)m 1107(Lout)s 1617(processes)s
2581(a)s 2745(multi-\207le)s 3687(document,)s 4735(one)s 5135(cross)s
5674(reference)s 6615(database)s 7492(\207le)s 7850(is)s 8058(written)s
8788(for)s 0 5000(each)m 504(input)s 1065(\207le,)s 1486(b)s 4(ut)k
1858(the)s 3(y)k 2330(share)s 2899(a)s 3074(common)s
3979(inde)s 3(x)k 4572(\207le.)s 5050(At)s 5358(end)s
5772(of)s 6052(run,)s 6487(the)s 6844(ne)s 6(w)k
7301(inde)s 3(x)k 7894(\207le)s 8264(is)s 8484(sorted)s
0 4712(and)m 404(mer)s 4(ged)k 1176(with)s 1658(the)s
2007(old)s 2371(one)s 2774(in)s 3017(such)s 3514(a)s
3680(w)s 2(ay)k 4132(as)s 4383(to)s 4622(preserv)s 3(e)k
5485(entries)s 6172(relating)s 6955(to)s 7194(\207les)s 7644(not)s
8010(read)s 8480(on)s 8778(the)s 0 4424(current)m 737(run.)s
1221(This)s 1699(pro)s 3(vides)k 2572(some)s 3135(support)s
3914(for)s 4254(piecemeal)s 5278(formatting,)s 6395(b)s 4(ut)k
6758(e)s 6(v)k 3(entually)k 7801(the)s 8150(\207les)s
8601(must)s 0 4136(all)m 293(be)s 575(formatted)s 1561(together)s 13(.)k
480 3762(When)m 1120(a)s 220 fnt5 1297 3759(preceding)m 240 fnt1
2319 3762(or)m 220 fnt5 2590 3759(f)m 6(ollo)k 3(wing)k
240 fnt1 3491 3762(cross)m 4044(reference)s 4998(is)s 5220(found,)s
5897(it)s 6100(is)s 6321(attached)s 7187(to)s 7437(a)s
7614(g)s 1(alle)k 3(y)k 8259(inde)s 3(x)k
8855(of)s 0 3474(type)m 240 fnt3 474 3476(CR)m 9(OSS_PREC)k
240 fnt1 1973 3474(or)m 240 fnt3 2238 3476(CR)m 9(OSS_FOLL)k
240 fnt1 3653 3474(,)m 3766(together)s 4615(with)s 5103(an)s
5392(automatically)s 6752(generated)s 7745(tag)s 8097(composed)s 0 3186(of)m
258(the)s 593(current)s 1316(\207le)s 1663(name)s 2224(and)s
2615(a)s 2767(sequence)s 3687(number)s 13(.)k 4556(When)s
5172(a)s 5324(tagged)s 6007(in)s 9(v)k 4(ocation)k
7048(is)s 7244(found,)s 7897(it)s 8076(is)s 8272(attached)s
0 2898(to)m 237(a)s 240 fnt3 401 2900(CR)m 9(OSS_T)k 12(ARG)k
240 fnt1 1875 2898(inde)m 3(x.)k 2565(These)s 3190(g)s 1(alle)k 3(y)k
3822(inde)s 3(x)k 3(es)k 4595(are)s 4940(carried)s
5658(along)s 6241(through)s 7040(the)s 7386(dynamic)s 8261(tree,)s
8722(and)s 0 2610(e)m 6(v)k 3(entually)k 1049(pop)s
1470(of)s 6(f)k 1822(the)s 2178(top)s 2545(of)s
2824(the)s 3180(root)s 3633(g)s 1(alle)k 3(y)k 15(,)k
4313(at)s 4553(which)s 5203(point)s 5763(it)s 5963(is)s
6181(easy)s 6668(to)s 6915(determine)s 7934(which)s 8584(cross)s
0 2322(references)m 1029(refer)s 1536(to)s 1773(which)s 2413(in)s 9(v)k 4(ocations,)k
3608(since)s 4153(the)s 4499(inde)s 3(x)k 3(es)k
5273(are)s 5618(no)s 6(w)k 6077(in)s 6318(\207nal)s
6796(printed)s 7529(document)s 8531(order)s 13(.)k 0 2034(Each)m
541(referenced)s 1613(in)s 9(v)k 4(ocation)k 2674(is)s
2891(then)s 3367(written)s 4107(to)s 4353(the)s 4708(cross)s
5257(reference)s 6207(database,)s 7144(multiply)s 8015(inde)s 3(x)k 3(ed)k
8832(by)s 0 1746(the)m 344(generated)s 1327(tags)s 1758(of)s
2025(the)s 2369(associated)s 3404(cross)s 3942(references.)s 5082(On)s
5427(the)s 5771(ne)s 3(xt)k 6236(run,)s 6657(when)s
7229(the)s 7573(same)s 220 fnt5 8115 1743(preceding)m 240 fnt1
0 1458(and)m 220 fnt5 408 1455(f)m 6(ollo)k 3(wing)k
240 fnt1 1302 1458(cross)m 1848(references)s 2883(are)s 3234(found,)s
3904(chances)s 4716(are)s 5067(good)s 5609(that)s 6031(the)s
6383(same)s 6934(tags)s 7374(will)s 7804(be)s 8090(generated,)s
0 1170(and)m 404(the)s 752(appropriate)s 1896(v)s 6(alues)k
2552(can)s 2941(be)s 3223(retrie)s 6(v)k 3(ed)k
4120(from)s 4644(the)s 4992(database)s 5871(immediately)s 15(.)k
480 796(This)m 982(approach)s 1942(w)s 2(as)k 2389(the)s
2763(genesis)s 3544(of)s 3842(the)s 220 fnt5 4216 793(@T)m 26(agged)k
240 fnt1 5231 796(operator)m 9(,)k 6151(whose)s 6845(implementation)s
8428(is)s 8665(no)s 6(w)k 0 508(immediate:)m 1106(for)s
1436(each)s 220 fnt5 1923 505(@T)m 26(agged)k 240 fnt1
2903 508(operator)m 3751(we)s 4078(produce)s 4897(one)s 240 fnt3
5290 510(CR)m 9(OSS_PREC)k 240 fnt1 6775 508(or)m 240 fnt3
7026 510(CR)m 9(OSS_FOLL)k 240 fnt1 8492 508(g)m 1(alle)k 3(y)k
0 220(inde)m 3(x,)k 645(replacing)s 1596(the)s 1953(generated)s
2949(tag)s 3304(with)s 3795(the)s 4152(right)s 4672(parameter)s
5696(of)s 5976(the)s 220 fnt5 6333 217(@T)m 26(agged)k
240 fnt1 7331 220(operator)m 13(.)k 8288(Nothing)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 38 39
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5708 -1579(-)m 5836(38)s
6123(-)s 9066 13416 0 13307 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore
0 13253(more)m 547(is)s 757(required.)s 240 fnt2
0 12460(7.)m 291(Conclusion)s 
[ /Dest /LOUT18_651_s7_0_1 /DEST pdfmark
240 fnt1 480 12028(Since)m 1054(its)s
1316(public)s 1953(release)s 2657(in)s 2886(October)s 3702(1991,)s
4275(the)s 4609(Basser)s 5292(Lout)s 5790(interpreter)s 6829(has)s
7185(been)s 7680(ported)s 8335(without)s 0 11740(incident)m 819(to)s
1047(a)s 1202(wide)s 1712(v)s 6(ariety)k 2412(of)s
2672(Unix)s 3195(systems)s 3992(and)s 4385(hardw)s 2(are.)k
5425(It)s 5619(w)s 2(as)k 6029(tested)s 6633(e)s 3(xtensi)k 6(v)k 3(ely)k
7753(before)s 8408(release)s 0 11452(on)m 293(its)s 565(o)s 6(wn)k
1025(documentation,)s 2549(and)s 2949(the)s 3293(fe)s 6(w)k
3695(minor)s 4321(b)s 4(ugs)k 4817(which)s 5455(ha)s 4(v)k 3(e)k
5952(emer)s 4(ged)k 6824(since)s 7367(then)s 7832(ha)s 4(v)k 3(e)k
8329(all)s 8617(been)s 0 11164(\207x)m 3(ed)k 534(in)s
777(the)s 1125(second)s 1848(release,)s 2617(scheduled)s 3632(to)s
3871(appear)s 4568(in)s 4811(mid-1992.)s 480 10790(Se)m 6(v)k 3(en)k
1105(substantial)s 2173(packages)s 3093(of)s 3355(de\207nitions)s 4407(are)s
4746(distrib)s 4(uted)k 5813(with)s 6286(Basser)s 6975(Lout.)s
7582(The)s 8001(Document)s 8998(-)s 0 10502(Layout)m 748(package,)s
1649(and)s 2063(its)s 2349(v)s 6(ariants)k 3160(ReportLayout)s
4560(and)s 4974(BookLayout,)s 6289(pro)s 3(vide)k 7083(the)s
7441(standard)s 8320(features)s 0 10214(that)m 411(all)s 696(documents)s
1776(require:)s 2610(pages,)s 3254(columns,)s 4165(paragraphs,)s 5313(headings,)s
6263(footnotes,)s 7252(\210oating)s 8028(\207gures)s 8722(and)s 0 9926(tables,)m
683(chapters)s 1550(and)s 1973(sections,)s 2870(displays)s 3724(and)s
4148(lists,)s 4658(access)s 5339(to)s 5597(bibliographic)s 6945(databases,)s
7987(cross)s 8549(refer)s 8998(-)s 0 9638(ences,)m 623(and)s
1012(so)s 1263(on)s 1545([11].)s 2092(The)s 2505(BookLayout)s
3748(package)s 4572(has)s 4927(e)s 3(xtra)k 5446(features)s
6237(needed)s 6958(by)s 7237(books,)s 7902(including)s 8843(an)s
0 9350(automatically)m 1355(generated)s 2343(table)s 2864(of)s 3136(contents,)s
4041(Roman)s 4791(page)s 5300(numbers)s 6176(for)s 6515(the)s
6864(pref)s 2(atory)k 7792(material,)s 8682(run)s 8998(-)s
0 9062(ning)m 468(page)s 965(headers,)s 1790(odd)s 2197(and)s
2589(e)s 6(v)k 3(en)k 3078(page)s 3574(layouts,)s
4361(and)s 4754(a)s 4908(sorted)s 5539(inde)s 3(x.)k
6220(The)s 6637(Eq)s 6949(package)s 7778(formats)s 8546(equa)s
8998(-)s 0 8774(tions,)m 572(and)s 976(P)s 3(as)k
1356(formats)s 2136(P)s 3(ascal)k 2798(programs)s 3752([10];)s
4262(T)s 19(ab)k 4668(formats)s 5448(tables)s 6056([12];)s
6566(and)s 6970(Fig)s 7342(dra)s 3(ws)k 7961(\207gures)s
8663([6].)s 480 8400(The)m 899(non-e)s 3(xpert)k 1983(user)s
2431(who)s 2888(uses)s 3341(these)s 3879(packages)s 4797(percei)s 6(v)k 3(es)k
5732(a)s 5889(system)s 6603(of)s 6865(a)s 7021(standard)s
7880(quite)s 8404(similar)s 0 8112(to)m 246(other)s 804(fully)s
1317(de)s 6(v)k 3(eloped)k 2357(batch)s 2940(formatters,)s
4034(although)s 4936(the)s 5292(interf)s 2(ace)k 6187(is)s
6405(considerably)s 7688(more)s 8243(coherent)s 0 7824(than,)m 525(say)s 15(,)k
942(the)s 1297(trof)s 6(f)k 1792(f)s 2(amily')k 13(s)k
2630([8].)s 3078(The)s 3512(e)s 3(xpert)k 4173(user)s
4637(percei)s 6(v)k 3(es)k 5588(a)s 5760(system)s
6490(which)s 7139(is)s 7355(radically)s 8251(dif)s 6(ferent)k
0 7536(from)m 547(pre)s 6(vious)k 1440(ones,)s 2009(in)s
2276(which)s 2941(a)s 3131(great)s 3691(deal)s 4168(can)s
4580(be)s 4886(achie)s 6(v)k 3(ed)k 5808(v)s 3(ery)k
6308(quickly)s 15(.)k 7198(T)s 19(o)k 7522(tak)s 2(e)k
7997(an)s 8304(e)s 3(xtreme)k 0 7248(e)m 3(xample,)k
936(P)s 3(as)k 1338(w)s 2(as)k 1781(designed,)s
2761(implemented,)s 4138(tested,)s 4825(and)s 5251(documented)s 6501(in)s
6766(one)s 7190(afternoon.)s 8292(Eq)s 8639(took)s 0 6960(about)m
587(a)s 747(week,)s 1353(b)s 4(ut)k 1709(most)s
2229(of)s 2494(that)s 2906(time)s 3380(w)s 2(as)k
3796(spent)s 4355(in)s 4592(marshalling)s 5767(the)s 6110(v)s 6(ast)k
6543(repertoire)s 7520(of)s 7785(mathematical)s 0 6672(symbols,)m 934(and)s
1367(\207ne-tuning)s 2499(the)s 2876(spacing.)s 3800(Most)s 4381(of)s
4681(the)s 5059(ef)s 6(fort)k 5671(seems)s 6335(to)s
6603(go)s 6925(into)s 7379(designing)s 8392(a)s 8588(good)s
0 6384(interf)m 2(ace;)k 944(most)s 1469(symbols)s 2318(are)s
2665(implemented)s 3971(in)s 4214(just)s 4619(one)s 5021(or)s
5280(a)s 5446(fe)s 6(w)k 5852(lines)s 6354(of)s
6625(Lout.)s 480 6010(A)m 698(group)s 1297(of)s 1556(about)s
2135(20)s 2418(satis\207ed)s 3246(non-e)s 3(xpert)k 4327(users)s
4856(has)s 5214(gro)s 6(wn)k 5864(up)s 6145(within)s
6800(the)s 7136(author')s 13(s)k 7944(department,)s 0 5722(mainly)m
703(Honours)s 1563(students)s 2383(with)s 2849(no)s 3127(in)s 9(v)k 3(estment)k
4208(in)s 4436(older)s 4971(systems)s 5764(to)s 5987(hold)s
6456(them)s 6978(back.)s 7579(Basser)s 8260(Lout)s 8756(has)s
0 5434(been)m 511(adv)s 3(ertised)k 1550(on)s 1849(the)s
2199(Internet)s 3003(ne)s 6(ws)k 3542(as)s 3794(a)s 4(v)k 6(ailable)k
4704(via)s 5058(anon)s 3(ymous)k 240 fnt3 6213 5436(ftp)m
240 fnt1 6458 5434(,)m 6567(so)s 6835(the)s 7185(e)s 3(xtent)k
7828(of)s 8101(its)s 8379(outside)s 0 5146(user)m 469(community)s
1624(is)s 1845(hard)s 2339(to)s 2589(g)s 1(auge.)k
3335(About)s 4005(50)s 4311(people)s 5016(ha)s 4(v)k 3(e)k
5528(mailed)s 6247(comments)s 7292(or)s 7562(questions)s 8528(to)s
8778(the)s 0 4858(author;)m 733(man)s 3(y)k 1327(of)s
1608(these)s 2166(people)s 2871(ha)s 4(v)k 3(e)k
3382(ported)s 4062(the)s 4420(program,)s 5348(written)s 6092(small)s
6674(de\207nitions,)s 7802(and)s 8217(modi\207ed)s 0 4570(the)m 348(standard)s
1216(packages.)s 480 4196(Future)m 1160(w)s 2(ork)k 1711(could)s
2301(usefully)s 3125(be)s 3(gin)k 3711(with)s 4194(the)s
4542(impro)s 3(v)k 3(ements)k 5955(suggested)s 6957(in)s
7200(this)s 7596(paper:)s 8294(o)s 3(v)k 3(erlap)k
8998(-)s 0 3908(ping)m 489(spanning)s 1418(columns,)s 2346(better)s
2960(semantics)s 3964(for)s 4312(a)s 4(v)k 6(ailable)k
5231(space,)s 5880(and)s 6294(especially)s 7314(horizontal)s 8349(g)s 1(alle)k 3(ys.)k
0 3620(Support)m 814(for)s 1147(non-)s 1575(European)s 2544(languages)s
3547(is)s 3752(also)s 4185(needed.)s 5022(Ho)s 6(we)k 6(v)k 3(er)k 9(,)k
5977(the)s 6320(main)s 6850(task)s 7291(is)s 7496(the)s
7839(de)s 6(v)k 3(elopment)k 0 3332(of)m 271(an)s
553(interacti)s 6(v)k 3(e)k 1607(document)s 2610(editor)s
3227(based)s 3829(on)s 4126(Lout.)s 4741(A)s 4971(structure)s
5861(editor)s 6478(similar)s 7199(to)s 7438(Lilac)s 7980([13],)s
8484(which)s 0 3044(already)m 753(has)s 1119(objects)s 1843(and)s
2243(user)s 4(-)k 2705(de\207ned)s 3463(symbols,)s 4364(is)s
4570(en)s 9(visaged;)k 5626(since)s 6168(cross)s 6706(references)s
7733(are)s 8076(easy)s 8550(when)s 0 2756(the)m 343(whole)s
979(document)s 1978(is)s 2182(a)s 4(v)k 6(ailable,)k
3136(the)s 3479(only)s 3954(major)s 4565(ne)s 6(w)k
5007(problem)s 5859(is)s 6064(the)s 6406(treatment)s 7362(of)s
7628(g)s 1(alle)k 3(ys,)k 8402(includ)s 8998(-)s
0 2468(ing)m 359(the)s 707(e)s 3(xpansion)k 1732(and)s
2136(retraction)s 3107(of)s 3378(recepti)s 6(v)k 3(e)k
4300(symbols.)s 240 fnt2 0 1719(Note.)m 240 fnt1 657 1720(Since)m
1253(the)s 1610(abo)s 3(v)k 3(e)k 2240(w)s 2(as)k
2670(written)s 3412(the)s 3768(author)s 4448(has)s 4827(completed)s
5889(a)s 6064(re)s 6(vised)k 6815(v)s 3(ersion)k
7581(of)s 7861(Basser)s 8567(Lout,)s 0 1432(in)m 243(which)s
885(the)s 1233(problem)s 2090(concerning)s 3206(a)s 4(v)k 6(ailable)k
4114(space)s 4701(mentioned)s 5769(in)s 6012(Section)s 6786(2.5)s
7132(has)s 7502(been)s 8011(resolv)s 3(ed.)k 240 fnt2
0 683(Ackno)m 2(wledgment.)k 240 fnt1 2027 684(The)m 2534(author)s
3283(gratefully)s 4344(ackno)s 6(wledges)k 5824(man)s 3(y)k
6485(v)s 6(aluable)k 7424(discussions)s 8644(with)s 0 396(Douglas)m
862(W)s 22(.)k 1183(Jones,)s 1835(especially)s 2857(during)s
3548(the)s 3909(de)s 6(v)k 3(elopment)k 5209(of)s
5493(the)s 5854(g)s 1(alle)k 3(y)k 6501(abstraction;)s
7674(and)s 8091(also)s 8543(man)s 3(y)k 0 108(helpful)m
732(comments)s 1766(on)s 2063(presentation)s 3288(by)s 3582(the)s
3930(anon)s 3(ymous)k 5083(referee.)s 
grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
0 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Page: 39 40
%%BeginPageSetup
%%PageResources: font Times-Roman
%%+ font Times-Bold
%%+ font Times-Italic
/pgsave save def
%%IncludeResource: font Times-Roman
/Times-Romanfnt1 vec2 /Times-Roman LoutRecode
/fnt1 { /Times-Romanfnt1 LoutFont } def
%%IncludeResource: font Times-Bold
/Times-Boldfnt2 vec2 /Times-Bold LoutRecode
/fnt2 { /Times-Boldfnt2 LoutFont } def
%%IncludeResource: font Times-Italic
/Times-Italicfnt3 vec2 /Times-Italic LoutRecode
/fnt3 { /Times-Italicfnt3 LoutFont } def
0.0500 dup scale 10 setlinewidth
%%EndPageSetup
gsave
0 0 translate
240 fnt1 0.0 0.0 0.0 LoutSetRGBColor LoutTextureSolid 11900 16840 0 16840 240 288 60 LoutGraphic
gsave
LoutPageSet
grestore
gsave
0 16840 translate
0.0000 rotate
5706 -1579(-)m 5834(39)s
6125(-)s 9066 13414 0 13414 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore
240 fnt2 0 12961(Refer)m 4(ences)k 240 fnt1
0 12507(1.)m 480(Kingston,)s 1501(Jef)s 6(fre)k 3(y)k
2244(H..)s 2677(Document)s 3770(F)s 3(ormatting)k 4918(with)s
5436(Lout)s 5888(.)s 6088(T)s 16(ech.)k 6690(Rep.)s
7216(408)s 7659(\(1991\))s 8286(,)s 8429(Basser)s 480 12219(Department)m
1668(of)s 1939(Computer)s 2956(Science,)s 3806(The)s 4234(Uni)s 6(v)k 3(ersity)k
5288(of)s 5559(Sydne)s 3(y)k 15(,)k 6367(Australia)s
7242(.)s 
[ /Dest /LOUT12_1490_s7_0_1 /DEST pdfmark
0 11716(2.)m 480(Kingston,)s 1492(Jef)s 6(fre)k 3(y)k
2227(H..)s 2652(A)s 2910(ne)s 6(w)k 3385(approach)s
4347(to)s 4613(document)s 5645(formatting)s 6646(.)s 6838(T)s 16(ech.)k
7432(Rep.)s 7950(412)s 8392(\(1991\))s 9019(,)s 480 11428(Basser)m
1177(Department)s 2365(of)s 2636(Computer)s 3653(Science,)s 4503(The)s
4931(Uni)s 6(v)k 3(ersity)k 5985(of)s 6256(Sydne)s 3(y)k 15(,)k
7064(Australia)s 7939(.)s 
[ /Dest /LOUT12_1490_s7_0_2 /DEST pdfmark
0 10925(3.)m 480(Kingston,)s 1491(Jef)s 6(fre)k 3(y)k
2224(H..)s 2647(The)s 3101(Basser)s 3824(Lout)s 4362(Document)s
5445(F)s 3(ormatter)k 6383(,)s 6516(1991)s 6971(.)s
7161(Computer)s 8204(program;)s 480 10637(V)m 26(ersion)k 1287(2)s
1480(publicly)s 2337(a)s 4(v)k 6(ailable)k 3264(in)s
3526(the)s 240 fnt3 3893 10639(pub)m 240 fnt1 4326 10637(subdirectory)m
5595(of)s 5885(the)s 6252(home)s 6859(directory)s 7794(of)s
240 fnt3 8084 10639(ftp)m 240 fnt1 8408 10637(to)m 8667(host)s
240 fnt3 480 10351(ftp.cs.su.oz.au)m 240 fnt1 1924 10349(with)m 2439(login)s
3021(name)s 240 fnt3 3628 10351(anonymous)m 240 fnt1 4808 10349(and)m
5246(no)s 5572(passw)s 2(ord.)k 6671(Distrib)s 4(ution)k
7912(via)s 8297(email)s 8916(is)s 480 10061(a)m 4(v)k 6(ailable)k
1388(for)s 1726(non-)s 240 fnt3 2154 10063(ftp)m 240 fnt1
2459 10061(sites.)m 3047(All)s 3407(enquiries)s 4334(to)s 4573(jef)s 6(f@cs.su.oz.au.)k

[ /Dest /LOUT12_1490_s7_0_3 /DEST pdfmark
0 9558(4.)m 480(Furuta,)s 1211(Richard,)s 2075(Sco\207eld,)s 2965(Jef)s 6(fre)k 3(y)k 15(,)k
3710(and)s 4113(Sha)s 3(w)k 15(,)k 4734(Alan.)s
5363(Document)s 6419(formatting)s 7480(systems:)s 8402(surv)s 3(e)k 3(y)k 15(,)k
480 9270(concepts,)m 1424(and)s 1828(issues)s 2390(.)s 240 fnt3
2554 9272(Computing)m 3673(Surve)s 7(ys)k 240 fnt2 4465 9269(14)m
240 fnt1 4699 9270(,)m 4806(417\211472)s 5700(\(1982\))s 6327(.)s

[ /Dest /LOUT12_1490_s7_0_4 /DEST pdfmark
0 8765(5.)m 480(K)s 6(ernighan,)k 1645(Brian)s 2287(W)s 22(.)k
2649(and)s 3107(Cherry)s 15(,)k 3917(Lorinda)s 4789(L..)s
5213(A)s 5497(system)s 6275(for)s 6667(typesetting)s 7824(mathematics)s
9022(.)s 240 fnt3 480 8479(Communications)m 2158(of)s 2439(the)s
2784(A)s 7(CM)k 240 fnt2 3351 8476(18)m 240 fnt1
3585 8477(,)m 3692(182\211193)s 4576(\(1975\))s 5203(.)s 
[ /Dest /LOUT12_1490_s7_0_5 /DEST pdfmark
0 7977(6.)m
480(Kingston,)s 1488(Jef)s 6(fre)k 3(y)k 2218(H..)s
2638(Fig)s 3033(\211)s 3236(a)s 3425(Lout)s 3961(package)s
4824(for)s 5185(dra)s 3(wing)k 6042(\207gures)s 6684(.)s
6871(T)s 16(ech.)k 7460(Rep.)s 7973(411)s 8392(\(1991\))s
9019(,)s 480 7689(Basser)m 1177(Department)s 2365(of)s 2636(Computer)s
3653(Science,)s 4503(The)s 4931(Uni)s 6(v)k 3(ersity)k
5985(of)s 6256(Sydne)s 3(y)k 15(,)k 7064(Australia)s
7939(.)s 
[ /Dest /LOUT12_1490_s7_0_6 /DEST pdfmark
0 7184(7.)m 480(Reid,)s 1042(Brian)s 1633(K..)s
2033(A)s 2266(High-)s 2813(Le)s 6(v)k 3(el)k
3406(Approach)s 4410(to)s 4652(Computer)s 5672(Document)s 6732(Production)s
7779(.)s 7946(In)s 240 fnt3 8206 7186(Pr)m 10(oceed)k
8999(-)s 480 6898(ings)m 935(of)s 1217(the)s 1564(7th)s
1926(Symposium)s 3075(on)s 3370(the)s 3717(Principles)s 4755(of)s
5038(Pr)s 10(o)k 2(gr)k 3(amming)k 6422(Langua)s 2(g)k 2(es)k
7527(\(POPL\),)s 8377(Las)s 8780(V)s 26(e)k 8999(-)s
480 6610(gas)m 868(NV)s 240 fnt1 1192 6608(,)m 1299(pages)s
1895(24\21131)s 2470(,)s 2577(1980)s 3052(.)s 
[ /Dest /LOUT12_1490_s7_0_7 /DEST pdfmark
0 6103(8.)m
480(Joseph)s 1207(F)s 19(.)k 1443(Ossanna.)s 2436(Nrof)s 6(f/T)k 8(rof)k 6(f)k
3605(User')s 13(s)k 4284(Manual)s 5010(.)s 5193(T)s 16(ech.)k
5777(Rep.)s 6285(54)s 6597(\(1976\))s 7224(,)s 7349(Bell)s
7821(Laboratories)s 9019(,)s 480 5815(Murray)m 1251(Hill,)s 1729(NJ)s
2051(07974)s 2645(.)s 
[ /Dest /LOUT12_1490_s7_0_8 /DEST pdfmark
0 5310(9.)m 480(Knuth,)s 1186(Donald)s
1949(E..)s 240 fnt3 2319 5312(The)m 2731(T)s 2882 5264(E)m
3033 5312(XBook)m 240 fnt1 3675 5310(.)m 3839(Addison-W)s 19(esle)k 3(y)k
5419(,)s 5526(1984)s 6000(.)s 
[ /Dest /LOUT12_1490_s7_0_9 /DEST pdfmark
0 4807(10.)m 480(Kingston,)s
1485(Jef)s 6(fre)k 3(y)k 2212(H..)s 2629(Eq)s
2973(\211)s 3173(a)s 3359(Lout)s 3892(package)s 4752(for)s
5110(typesetting)s 6232(mathematics)s 7430(.)s 7614(T)s 16(ech.)k
8200(Rep.)s 8711(410)s 480 4519(\(1991\))m 1107(,)s 1248(Basser)s
1980(Department)s 3203(of)s 3509(Computer)s 4561(Science,)s 5446(The)s
5909(Uni)s 6(v)k 3(ersity)k 6998(of)s 7304(Sydne)s 3(y)k 15(,)k
8147(Australia)s 9022(.)s 480 4231(\(Contains)m 1461(an)s 1744(appendix)s
2677(describing)s 3726(the)s 4074(P)s 3(as)k 4454(P)s 3(ascal)k
5116(formatter)s 13(.\))k 
[ /Dest /LOUT12_1490_s7_0_10 /DEST pdfmark
0 3728(11.)m 480(Kingston,)s 1478(Jef)s 6(fre)k 3(y)k
2198(H..)s 2608(A)s 2851(be)s 3(ginners')k 3903(guide)s
4504(to)s 4756(Lout)s 5208(.)s 5385(T)s 16(ech.)k
5964(Rep.)s 6467(409)s 6891(\(1991\))s 7518(,)s 7638(Basser)s
8348(Depart)s 8998(-)s 480 3440(ment)m 1018(of)s 1289(Computer)s
2306(Science,)s 3156(The)s 3584(Uni)s 6(v)k 3(ersity)k
4638(of)s 4909(Sydne)s 3(y)k 15(,)k 5717(Australia)s
6592(.)s 
[ /Dest /LOUT12_1490_s7_0_11 /DEST pdfmark
0 2937(12.)m 480(Kingston,)s 1475(Jef)s 6(fre)k 3(y)k
2193(H..)s 2600(T)s 19(ab)k 3017(\211)s 3207(a)s
3384(Lout)s 3907(package)s 4757(for)s 5106(formatting)s 6177(tables)s
6725(.)s 6900(T)s 16(ech.)k 7476(Rep.)s 7977(413)s
8392(\(1991\))s 9019(,)s 480 2649(Basser)m 1177(Department)s 2365(of)s
2636(Computer)s 3653(Science,)s 4503(The)s 4931(Uni)s 6(v)k 3(ersity)k
5985(of)s 6256(Sydne)s 3(y)k 15(,)k 7064(Australia)s
7939(.)s 
[ /Dest /LOUT12_1490_s7_0_12 /DEST pdfmark
0 2146(13.)m 480(Brooks,)s 1279(K)s 6(enneth)k
2141(P)s 26(..)k 2472(Lilac:)s 3068(a)s 3234(tw)s 2(o-vie)k 6(w)k
4183(document)s 5187(editor)s 5744(.)s 240 fnt3 5908 2148(IEEE)m
6490(Computer)s 240 fnt1 7453 2146(,)m 7560(7\21119)s 8091(\(1991\))s
8718(.)s 
[ /Dest /LOUT12_1490_s7_0_13 /DEST pdfmark

grestore
0 0 0 0 240 288 60 1417 -15423 LoutGr2
1 LoutMargSet
grestore

grestore

grestore

grestore

pgsave restore
showpage

%%Trailer
%%DocumentNeededResources: font Times-Roman
%%+ font Times-Bold
%%+ font Times-Italic
%%+ font Symbol
%%+ font Helvetica
%%DocumentSuppliedResources: procset LoutStartUp
%%+  procset LoutTabPrependGraphic
%%+  procset LoutFigPrependGraphic
%%+  procset LoutBasicSetup
%%+ encoding vec2
%%Pages: 40
%%EOF