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
|
<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/css" href="../webstyle/mxh.css"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1 plus MathML 2.0//EN" "http://www.w3.org/Math/DTD/mathml2/xhtml-math11-f.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<link rel="stylesheet" type="text/css" href="../webstyle/mxh.css" />
<meta name="surtitle" content="The GELLMU Manual" />
<meta name="title" content="The GELLMU Manual" />
<meta name="subtitle" content="Version 0.8.4 Release, July 2007" />
<meta name="author" content="William F. Hammond" />
<title>The GELLMU Manual</title>
</head>
<body>
<h1 class="display">The GELLMU Manual</h1>
<h4 class="display">Version 0.8.4 Release, July 2007</h4>
<h2 class="display">William F. Hammond</h2>
<h4 class="display">
Dept. of Mathematics & Statistics<br
/> University at Albany<br
/> Albany, New York 12222 (USA)</h4>
<p class="display">Email: <kbd>hammond@math.albany.edu</kbd></p>
<h4 class="display">Revision of July 5, 2007</h4>
<h5 class="display">Copyright © 2001–2007 William F. Hammond</h5>
<h3 class="display">ABSTRACT</h3>
<blockquote>
<p>This is the manual for Generalized Extensible <em>LaTeX</em>-Like
Markup (GELLMU). The central focus in the GELLMU project is to tie
<em>LaTeX</em> to the worlds of SGML and XML by providing <em>LaTeX</em>-like markup
for writing documents under SGML and XML vocabularies (formally
known as document types). </p>
<p>The Manual explains the distinction between <em>basic</em> and
<em>advanced</em> use, provides a description of <em>regular</em>
GELLMU as an instance of advanced GELLMU, and discusses
the use of the didactic production system, which is the project's suite of
processors for working with regular GELLMU. </p>
<p>The Manual also deals with the metacommands available when
writing GELLMU markup. One of these metacommands is the project's
emulation of <em>LaTeX</em>'s <em>newcommand</em>, which makes it possible to
have macros taking multiple arguments while writing for an SGML or
XML vocabulary.
</p>
</blockquote>
<div class="tableofcontents">
<h3>Table of Contents</h3>
<dl class="tableofcontents">
<dd>1  Introduction... <a href="#SU-1">*</a>
</dd><dd>
2  Basic GELLMU... <a href="#SU-2">*</a>
</dd><dd>
3  Metacommands... <a href="#SU-3">*</a>
<dl><dd>
3.1  \documenttype... <a href="#SU-3.1">*</a>
</dd><dd>
3.2  \newcommand... <a href="#SU-3.2">*</a>
</dd><dd>
3.3  \begin{} … \end{}... <a href="#SU-3.3">*</a>
</dd><dd>
3.4  \macro and \Macro... <a href="#SU-3.4">*</a>
</dd><dd>
3.5  Macro-Level Fronting of SGML Element Names... <a href="#SU-3.5">*</a>
</dd></dl></dd><dd>
4  Advanced GELLMU... <a href="#SU-4">*</a>
<dl><dd>
4.1  Illustrations.... <a href="#SU-4.1">*</a>
</dd><dd>
4.2  Multiple Argument/Option Syntax... <a href="#SU-4.2">*</a>
</dd><dd>
4.3  Limitation in Regard to XML... <a href="#SU-4.3">*</a>
</dd></dl></dd><dd>
5  The Didactic Document Type... <a href="#SU-5">*</a>
<dl><dd>
5.1  Suggestions and Caveats... <a href="#SU-5.1">*</a>
</dd><dd>
5.2  Markup Fundamentals... <a href="#SU-5.2">*</a>
<dl><dd>
5.2.1  Explicitly named commands.... <a href="#SU-5.2.1">*</a>
</dd><dd>
5.2.2  Certain single characters.... <a href="#SU-5.2.2">*</a>
</dd><dd>
5.2.3  Certain strings... <a href="#SU-5.2.3">*</a>
</dd></dl></dd><dd>
5.3  Large Structure... <a href="#SU-5.3">*</a>
</dd><dd>
5.4  Sectioning... <a href="#SU-5.4">*</a>
</dd><dd>
5.5  Labels, References, and Anchors... <a href="#SU-5.5">*</a>
<dl><dd>
5.5.1  Labels and Sequencing... <a href="#SU-5.5.1">*</a>
</dd><dd>
5.5.2  Anchors... <a href="#SU-5.5.2">*</a>
</dd><dd>
5.5.3  Example Emulating a <em>LaTeX</em> Counter... <a href="#SU-5.5.3">*</a>
</dd></dl></dd><dd>
5.6  General Usage for Sectional Units... <a href="#SU-5.6">*</a>
<dl><dd>
5.6.1  The Content Model... <a href="#SU-5.6.1">*</a>
</dd><dd>
5.6.2  The <em>LaTeX</em>-Like Form of General Usage... <a href="#SU-5.6.2">*</a>
</dd></dl></dd><dd>
5.7  <em>verbatim</em>, <em>verblist</em>, and
<em>manmac</em>... <a href="#SU-5.7">*</a>
</dd><dd>
5.8  Accents... <a href="#SU-5.8">*</a>
</dd><dd>
5.9  Tabular Environment Emulation... <a href="#SU-5.9">*</a>
</dd><dd>
5.10  Graphic Inclusions... <a href="#SU-5.10">*</a>
</dd></dl></dd><dd>
6  Mathematics in <em>article</em>... <a href="#SU-6">*</a>
<dl><dd>
6.1  General... <a href="#SU-6.1">*</a>
</dd><dd>
6.2  Assertions... <a href="#SU-6.2">*</a>
<dl><dd>
6.2.1  Examples... <a href="#SU-6.2.1">*</a>
</dd><dd>
6.2.2  Usage for <em>assertion</em>... <a href="#SU-6.2.2">*</a>
</dd></dl></dd><dd>
6.3  Equations and Equation Arrays... <a href="#SU-6.3">*</a>
</dd><dd>
6.4  The \mathsym Metacommand... <a href="#SU-6.4">*</a>
</dd></dl></dd><dd>
7  The Didactic Production System... <a href="#SU-7">*</a>
<dl><dd>
7.1  Permission... <a href="#SU-7.1">*</a>
</dd><dd>
7.2  Materials... <a href="#SU-7.2">*</a>
</dd><dd>
7.3  Other Required Software... <a href="#SU-7.3">*</a>
</dd><dd>
7.4  Using the syntactic translator... <a href="#SU-7.4">*</a>
<dl><dd>
7.4.1  Operation in Batch Mode... <a href="#SU-7.4.1">*</a>
</dd><dd>
7.4.2  Interactive Operation... <a href="#SU-7.4.2">*</a>
</dd><dd>
7.4.3  Interrupting the Syntactic
Translator... <a href="#SU-7.4.3">*</a>
</dd></dl></dd><dd>
7.5  Using the didactic production system... <a href="#SU-7.5">*</a>
<dl><dd>
7.5.1  Staged Design... <a href="#SU-7.5.1">*</a>
</dd><dd>
7.5.2  Default Staging... <a href="#SU-7.5.2">*</a>
</dd><dd>
7.5.3  Parsing with <em>nsgmls</em>... <a href="#SU-7.5.3">*</a>
</dd><dd>
7.5.4  Processing with <em>sgmlspl</em>... <a href="#SU-7.5.4">*</a>
</dd><dd>
7.5.5  Environmental Variables... <a href="#SU-7.5.5">*</a>
</dd></dl></dd></dl></dd><dd>
Appendix A  The GELLMU Archive... <a href="#SU-8">*</a>
</dd><dd>
Appendix B  Release Notes... <a href="#SU-9">*</a>
<dl><dd>
B.1  Comments on the Syntactic Translator... <a href="#SU-9.1">*</a>
</dd><dd>
B.2  Comments on the Didactic Production System... <a href="#SU-9.2">*</a>
<dl><dd>
B.2.1  Internationalization... <a href="#SU-9.2.1">*</a>
</dd><dd>
B.2.2  Document Type Definitions... <a href="#SU-9.2.2">*</a>
</dd><dd>
B.2.3  Translation to XML... <a href="#SU-9.2.3">*</a>
</dd><dd>
B.2.4  Translation to HTML... <a href="#SU-9.2.4">*</a>
</dd><dd>
B.2.5  Translation to <em>LaTeX</em>... <a href="#SU-9.2.5">*</a>
</dd><dd>
B.2.6  Future Plans... <a href="#SU-9.2.6">*</a>
</dd></dl></dd></dl></dd></dl>
</div>
<div class="section">
<h3>1.  <a id="SU-1"></a><a id="intro"></a>Introduction</h3>
<p>GELLMU is an acronym for “Generalized Extensible
<em>LaTeX</em>-Like MarkUp”, which is the author's concept for using <em>LaTeX</em>-like
markup to write consciously for SGML document types such as HTML,
DocBook, TEI, or GELLMU's own didactic <em>LaTeX</em>-like document
type called <em>article</em>. </p>
<p>It evolved from earlier thought about delineation of a coherent subset
of <em>LaTeX</em> commands with the property that if a <em>LaTeX</em> document used
only those commands then it could be translated with full reliability
to other formats including HTML so that documents could be prepared
both for print and for the web from a single source. </p>
<p>Problems with this early thought during the years 1996–1997 included
the fact that there did not seem to be a community of <em>LaTeX</em> users
willing to focus on a narrow vocabulary and the fact then of a legacy
practice that mixed <em>LaTeX</em> commands freely with non-<em>LaTeX</em> <em>TeX</em>
commands. </p>
<p>The present idea was crystalized in the summer of 1998 while the author
was looking at Ulrich Vieth's <em>LaTeX</em> markup for the <em>TeX</em> Directory
System (TDS) specification from the <em>TeX</em> User Group
(TUG), which now is physically realized in TUG's
<em>TeX</em>Live series of <em>TeX</em>-related software distributions on
CDrom. The HTML version of that specification was derived
through an intermediate ad hoc translation from <em>LaTeX</em> to
<em>Texinfo</em>, the language of the GNU Documentation System,
which is a robust hypertex system pre-dating HTML driven by <em>TeX</em>
the Program. </p>
<p>In thinking about generalizing Vieth's ad hoc translation, which used
GNU <em>Emacs</em> Lisp (<em>Elisp</em>), one of the most widely available
<a href="http://www.gnu.org/">free</a> cross-platform programming languages
for which there is a free robust engine, the same engine that
underlies the interactive editing interface of <em>Emacs</em>, the author
realized that the structure of <em>Texinfo</em> is very much like that of an
authoring level SGML document type. From that idea it was a small
step to decide that one might profitably write <em>Elisp</em> code to use <em>LaTeX</em>-like
markup for the conscious writing of a new <em>LaTeX</em>-like <em>article</em> document
type. </p>
<p>The idea, which by itself saves keystrokes, gains significant power
with the emulation of <em>LaTeX</em>'s <em>newcommand</em>. Although SGML
markup offers both subdocument inclusions and macro substitutions
using the notion of <em>entity</em>, there is no SGML-standard macro
facility that takes arguments. Moreover, GELLMU's <em>newcommand</em>,
which is, unlike <em>LaTeX</em>'s, a simple macro substitution facility,
also provides a base for experimenting with document type extensions
in a way that the SGML notion of <em>entity</em> does not since SGML
entities are invoked with a notation that is apart from that used to
markup with SGML <em>elements</em>, which are the objects corresponding
in the GELLMU scheme with <em>LaTeX</em>-like <em>commands</em>. </p>
<p>Software associated with the GELLMU project falls into two parts:
</p>
<ol class="decimal">
<li><p> <b>The syntactic translator.</b> This is a purely syntactic layer for converting
<em>LaTeX</em>-like markup in configurable ways to SGML markup. Its output may
be handled in standard SGML or XML systems. </p>
</li>
<li><p> <b>The didactic production system.</b> This component is a sketch, which might usefully
serve as a base for further development, of an SGML production
system for an authoring environment that consists of
</p>
<ol class="lower-alpha">
<li><p> An SGML document type called <em>article</em> that is
accompanied by a corresponding XML document type.
</p>
</li>
<li><p> A package of extensible translating utilities written
in the language <em>Perl</em>.
</p>
</li>
</ol>
As its name suggests, these materials are didactic and
should be regarded as unfinished for production work. </li>
</ol>
<p></p>
<p>There are two overall concepts: <em>basic</em> mode and <em>advanced</em>
mode. The basic mode may be used to write consciously for any
standard document type such as HTML, DocBook, or TEI,
and the syntactic translator is for that mode the only software under this project that
might be relevant. The advanced mode incorporates a configurable
broader array of <em>LaTeX</em>-like markup features, mostly for brevity, in the syntactic translator.
This mode is fully developed only for use with a <em>LaTeX</em>-like document type
such as the didactic <em>article</em> document type that is part of the
didactic production system. </p>
<p>One may use any SGML or XML processing framework in working
with the <em>article</em> document type. The didactic production system includes what is
needed to produce both HTML and regular <em>LaTeX</em> forms of an
<em>article</em> instance. Consequently, one is able to produce both
DVI using the <em>LaTeX</em> format for <em>TeX</em>, the program, and PDF
using the <em>LaTeX</em> format for PDF<em>TeX</em>, the program. Moreover, one
may tune the PDF in various ways using small alterations of the
<em>Perl</em> code for translating the XML version of <em>article</em>
to regular <em>LaTeX</em>.
</p>
</div>
<div class="section">
<h3>2.  <a id="SU-2"></a><a id="basic"></a>Basic GELLMU</h3>
<p>Neither the basic nor the advanced mode involves in any way adoption
of the language of <em>LaTeX</em>. (But many command names under the didactic
<em>article</em> document type, mimic <em>LaTeX</em> command names.) There are
two fundamental ideas:
</p>
<ol class="decimal">
<li><p> A <em>LaTeX</em>-like command “<kbd>\foo</kbd>” corresponds
to an SGML element “<kbd><foo></kbd>”. </p>
</li>
<li><p> The syntactic translator is almost entirely ignorant of vocabulary
and a name like <em>foo</em> need not have meaning in it although
it must have meaning in the document type for which one is
consciously writing.<sup><a id="revfnote1" href="#fnote1">1</a></sup></p>
</li>
</ol>
<p>
To use the basic mode one must be familiar with the SGML document
type for which one is writing. Ordinary HTML is an example. Very
few of the features in the advanced markup not also part of the basic
markup<sup><a id="revfnote2" href="#fnote2">2</a></sup>
make any sense for use in the direct preparation of HTML with <em>LaTeX</em>-like
input. </p>
<p>GELLMU uses <em>LaTeX</em> special characters such as ‘<kbd>\</kbd>’,
‘<kbd>{</kbd>’, and ‘<kbd>}</kbd>’ along with <em>LaTeX</em>-like argument/option syntax,
where braces immediately following a command name indicate command
arguments and square brackets, i.e., ‘<kbd>[</kbd>’ and
‘<kbd>]</kbd>’, indicate command options. A command corresponds to
an SGML element, and in basic mode a command may have at most one
argument, the content of which corresponds to SGML element content,
and at most one option, the content of which corresponds to a list of
SGML attribute specifications. Thus for example, in basic mode for
HTML one may use the markup
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\a[href="http://www.w3.org/"]{The World Wide Web Consortium}</kbd></td></tr></tbody></table></div>
<p>
to form the HTML anchor:
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd><a href="http://www.w3.org/">The World Wide Web Consortium</a></kbd>
. </td></tr></tbody></table></div>
<p>
(The formation of anchors with the didactic <em>article</em> document
type in advanced mode is slightly more complicated because the
characters ‘<kbd>=</kbd>’ and ‘<kbd>/</kbd>’, which may acquire special (and
“overloaded”) semantic significance in mathematical
contexts, are held for delayed evaluation as empty elements and
because the syntactic translator, which does not recognize command names, regards this
usage in advanced mode as <em>multiple</em>
<a href="#argopt">argument/option syntax</a> (section 4.2), which is not part of basic
mode.)</p>
<p>An example of the distinction between basic and advanced GELLMU is that
in advanced mode it is possible and easy to arrange to have a blank line,
as in <em>LaTeX</em>, represent the beginning of a paragraph. In basic mode
for HTML one
must<sup><a id="revfnote3" href="#fnote3">3</a></sup>
use “<kbd>\p</kbd>” to begin a paragraph, and for the XML version of
HTML one must also provide markup for the end of every paragraph, which
may be done in several ways. </p>
<p>For some of the details on using the basic markup with HTML see
<a href="ghtml.html"><em>Using the GELLMU Syntactic Translator to Write HTML</em></a>.
It will be instructive to have the parallel <a href="ghtml.glm">source
markup</a> available at the same time.
</p>
</div>
<div class="section">
<h3>3.  <a id="SU-3"></a><a id="meta"></a>Metacommands</h3>
<p>A metacommand is a <em>LaTeX</em>-like command that does not correspond to an
SGML element. Each metacommand is handled internally by the
syntactic translator.
</p>
<div class="subsection">
<h4>3.1.  <a id="SU-3.1"></a><a id="doctype"></a>\documenttype</h4>
<p>A document prepared in GELLMU source usually begins with a
<em>documenttype</em> command. For example,
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\documenttype{html}</kbd></td></tr></tbody></table></div>
<p>
is used to begin a document prepared for the most common form
of classical HTML. </p>
<p>The syntactic translator has two public variables
<em>gellmu-doctype-keylist</em> and <em>gellmu-doctype-info</em>,
which are <em>Elisp</em> associative lists, that enable one to match XML
or SGML “<kbd><!DOCTYPE ... ></kbd>” declarations with
<em>LaTeX</em>-like
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\documenttype[</kbd><em>my-optional-key</em><kbd>]{</kbd><em>my-doctype</em><kbd>}</kbd></td></tr></tbody></table></div>
<p>
commands, where <em>my-optional-key</em> is available to override a
default key for <em>my-doctype</em>. Thus, for example,
“<kbd>\documenttype{html}</kbd>” points to the default key for
“<kbd>html</kbd>”, which is “<kbd>html-4.01</kbd>” and which points to
the <em>W3C HTML 4.01 Transitional</em> document type, while
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\documenttype[xhtml-1.0s]{html}</kbd></td></tr></tbody></table></div>
<p>
indicates <em>W3C XHTML 1.0 Strict</em>. </p>
<p>A user may configure these variables without modifying the source
code for the GELLMU syntactic translator, but minimal knowledge of <em>Elisp</em> will
be required. A future release might provide a configuration file
for this purpose. </p>
<p>A second option for the <em>documenttype</em> metacommand, which must
follow the single required argument, is provided for writing an
internal declaration subset. The contents of an internal declaration
subset constructed this way may be any internal declaration subset
material. However, some care is required for entering characters
that are special. To ease the handling of special characters four
metacommands have been provided for use inside the internal declaration
subset:
</p>
<dl>
<dd> <kbd>\attlist{...}</kbd></dd>
<dd> <kbd>\element{...}</kbd></dd>
<dd> <kbd>\entity{...}</kbd></dd>
<dd> <kbd>\notation{...}</kbd></dd>
</dl>
<p>
For example, a user who wishes to be able in source to use
“<kbd>&quo;</kbd>” to reference the ASCII quotation mark
when writing consciously in basic mode for TEI.2 would begin
the source file with:
</p>
<dl class="verblist">
<dd><kbd>
\documenttype{TEI.2}[</kbd></dd>
<dd><kbd>
\entity{quo "&#x22;"}</kbd></dd>
<dd><kbd>
]</kbd></dd>
</dl>
<p>
</p>
</div>
<div class="subsection">
<h4>3.2.  <a id="SU-3.2"></a><a id="newcommand"></a>\newcommand</h4>
<p>From a user's viewpoint this provides emulation of <em>LaTeX</em>'s
<em>newcommand</em>. But it is a simple facility providing macro
substitution with arguments forward in a source file from the
point of its occurrence. It differs from the <em>newcommand</em>
facility in <em>LaTeX</em> in that it does not add the name
of a newcommand to any namespace. Instead, as the syntactic translator encounters
each newcommand definition, it performs the corresponding expansions
and then forgets the name.<sup><a id="revfnote4" href="#fnote4">4</a></sup></p>
<p>The general construction of a newcommand definition is
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\newcommand{</kbd><em>name</em><kbd>}[</kbd><em>nargs</em><kbd>][</kbd><em>first</em><kbd>]{</kbd><em>value</em><kbd>}</kbd></td></tr></tbody></table></div>
<p>
where <em>name</em> is the name of the newcommand,
<em>nargs</em> optionally specifies the number of its arguments,
<em>first</em> is an optionally-provided default value for the first
argument, and <em>value</em> denotes the value string. </p>
<p>In the value string the character ‘<kbd>#</kbd>’ is used to reference an
argument by the numeric value of its position. Thus, “<kbd>#1</kbd>”
refers to the first argument that is provided at an invocation of
the newcommand, “<kbd>#2</kbd>” the second, etc., and there is no limit
on the number of arguments. It is not required that <em>nargs</em> be
supplied in order to define and use a newcommand taking
arguments. However, for the sake of automatic error checking the
use of <em>nargs</em> is strongly recommended when the definition of
a newcommand taking arguments is entered. </p>
<p><b>Example.</b> In writing HTML one might use
</p>
<dl class="verblist">
<dd><kbd>
\newcommand{\href}[2][http://www.w3.org/]{\a[href="#1"]{#2}}</kbd></dd>
</dl>
<p>
for brevity in writing many HTML anchors. With this definition the
invocation
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\href{http://www.myweb.mydomain/me.html}{my web page}</kbd></td></tr></tbody></table></div>
<p> gives
rise to the HTML markup
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd><a href="http://www.myweb.mydomain/me.html">my web page</a></kbd></td></tr></tbody></table></div>
<p>
while the invocation
“<kbd>\href{Web Central}</kbd>” gives rise to
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd><a href="http://www.w3.org/">Web Central</a></kbd> . </td></tr></tbody></table></div>
<p></p>
<p><b>Rules.</b>
</p>
<ol class="decimal">
<li><p> The name of a newcommand may not be referenced in its
value string.<sup><a id="revfnote5" href="#fnote5">5</a></sup>
</p>
</li>
<li><p> A newcommand may not be invoked before it is defined unless
the invocation occurs in the value string of another newcommand
definition in which case the definition of the latter may be first and
<b>must</b> be first if the invocation of the former in the definition
of the latter involves argument substitutions. </p>
</li>
</ol>
<p></p>
<p>Failure to observe these rules may cause the syntactic translator to enter an infinite
recursive loop. If a user suspects this may have happened, then the
invocation of the syntactic translator should be <a href="#interrupt">interrupted</a> (section 7.4.3).
</p>
</div>
<div class="subsection">
<h4>3.3.  <a id="SU-3.3"></a><a id="beginend"></a>\begin{} … \end{}</h4>
<p>These provide emulation of <em>LaTeX</em> environment notation without
actually providing anything that is not otherwise available. Markup
which resembles that for a <em>LaTeX</em> environment simply resolves to an
SGML element. This usage may be convenient for SGML elements of
large scope such as, for example, the <em>body</em> of an HTML
document. </p>
<p>With advanced mode the special form
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\begin{document} . . . \end{document}</kbd></td></tr></tbody></table></div>
<p>
may be used to emulate the corresponding feature of <em>LaTeX</em> for a
document type, such as the didactic <em>article</em> document type,
that in the large consists of a preamble and a body.
</p>
</div>
<div class="subsection">
<h4>3.4.  <a id="SU-3.4"></a><a id="macmac"></a>\macro and \Macro</h4>
<p>Use of these is discouraged in the absence of a need. One situation
that presents a need is name “fronting”: see the
discussion below in <a href="#fronting">section 3.5</a>.
Please note that in most situations one may use <em>newcommand</em>
without an argument for simple macro substitutions. </p>
<p><em>macro</em> and <em>Macro</em> do very much the same thing except
for the order of expansions. Every <em>macro</em> is expanded forward
as encountered before any newcommand definition is expanded. Every
<em>Macro</em> is expanded forward after every newcommand
has been expanded. </p>
<p>There are four primary differences between <em>macro</em> and <em>Macro</em>,
on the one hand, and <em>newcommand</em>, on the other hand.
</p>
<ol class="decimal">
<li><p> Neither <em>macro</em> nor <em>Macro</em> can be used to define a
macro that takes arguments. </p>
</li>
<li><p> The name of a newcommand must consist of word characters,
but there is no restriction on the characters, apart from unbalanced
brace characters (‘<kbd>{</kbd>’ and ‘<kbd>}</kbd>’), that may appear in
the name field of a <em>macro</em> or <em>Macro</em> metacommand. </p>
</li>
<li><p> If the name of a <em>macro</em> or <em>Macro</em> does not begin
with the command sequence introducer, i.e., the character ‘<kbd>\</kbd>’,
then an invocation of that metacommand is given by every forward match
of its name. The use of such names is strongly discouraged because
document segments can then become opaque much too easily. </p>
</li>
<li><p> A newcommand invocation, absent the use of a semi-colon
for termination, is only effective at the whole word level — with
<em>word</em> here denoting a maximal string of successive word
characters — whereas <em>macro</em> and <em>Macro</em> invocations are
effective regardless of word boundaries. </p>
</li>
</ol>
<p></p>
<p>Elaboration on the last point: If <kbd>x</kbd> is the name of a
newcommand, then invocations are
only considered by the syntactic translator on the string “<kbd>\x</kbd>” when it is followed
by a non-word character. For example, if the locale is us-ascii,
then the word characters are the 52 upper and lower case letters
and the ten numerals. Therefore with <em>newcommand</em>, as with its
namesake in regular <em>LaTeX</em>, the use of “x” as a name will
not intercept the occasions of “<kbd>\x</kbd>” as an initial
substring of “<kbd>\xy</kbd>”. With either <em>macro</em> or
<em>Macro</em> such interception does take place. One may block it at
the point of an invocation with the markup “<kbd>\x;</kbd>”, and when
this is done, the terminating semi-colon is removed. </p>
<p>Human authors using either <em>macro</em> or <em>Macro</em> may find
unanticipated interactions between the three forms of macro
substitution. </p>
<p>Unbalanced brace characters, i.e., the characters ‘<kbd>{</kbd>’ and
‘<kbd>}</kbd>’, may not be used in the name field or the value field of
any form of macro metacommand.
</p>
</div>
<div class="subsection">
<h4>3.5.  <a id="SU-3.5"></a><a id="fronting"></a>Macro-Level Fronting of SGML Element Names</h4>
<p>The word <em>fronting</em> as used here describes the practice of
modifying the meaning of an SGML element name by using one or
more of the macro facilities to generate usage of the same name as
an element combined with other markup using the syntax that would
otherwise correspond to basic use of the element. </p>
<p>Suppose, for example, one wants all paragraphs in HTML (marked
with <kbd>\p</kbd> in GELLMU source) to be placed in a (style) class called
<em>custom</em>. </p>
<p><b>Recommended procedure:</b> Create a new unique name and then use
<em>macro</em> to front it.
</p>
<dl class="verblist">
<dd><kbd>
\newcommand{\cp}[1][]{\p[class="custom"]{#1}}</kbd></dd>
<dd><kbd>
\macro{\p}{\cp}</kbd></dd>
</dl>
<p>
Each invocation of “<kbd>\p{...}</kbd>” will first be replaced by “<kbd>\cp{...}</kbd>”
because all <em>macro</em> definitions are expanded before any
newcommand definition is expanded. Subsequent expansion
of the newcommand will yield
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\p[class="custom"]{...}</kbd> . </td></tr></tbody></table></div>
<p></p>
<p>This will not intercept the alternate, otherwise nearly equivalent,
markup given with <kbd>\begin{p}</kbd> … <kbd>\end{p}</kbd> since <em>newcommand</em>
is based on simple macro substitution and does not operate at the
level of namespaces.
</p>
</div>
</div>
<div class="section">
<h3>4.  <a id="SU-4"></a><a id="advanced"></a>Advanced GELLMU</h3>
<p>The idea with advanced GELLMU is that for SGML document
types sharing structural characteristics with <em>LaTeX</em> one might
wish to have the syntactic translator provide <em>LaTeX</em>-like markup syntax beyond the level
used with basic GELLMU and that these additional layers of syntax
should be configurable. The only substantial realization of this
program so far is the case of the GELLMU didactic document type called <em>article</em>.
The specifics of that realization are discussed in the following
section.
</p>
<div class="subsection">
<h4>4.1.  <a id="SU-4.1"></a><a id="illustrations"></a>Illustrations.</h4>
<p>One might want to be able to use blank lines, as in
<em>LaTeX</em>, for introducing new paragraphs in a document type that
provides paragraphs. </p>
<p>In some article-level document types each sectional unit has a unit
header providing markup for various, often optional, unit descriptors.
It is convenient to be able to use <em>LaTeX</em>-like multiple
<a href="#argopt">argument/option syntax</a> (section 4.2) for these. </p>
<p>If the document type provides authoring-level mathematical markup
beyond inclusions of the World Wide Web Consortium's
<a href="http://www.w3.org/Math/">Mathematical Markup Language</a> (MathML)
under its <a href="http://www.w3.org/TR/REC-xml-names">XML namespace</a>
regime, then one might want to be able to use the ‘<kbd>$</kbd>’ character
to toggle in and out of inline math, and if the document provides
for math displays, then one might want to use, as in <em>LaTeX</em>, the
strings “<kbd>\[</kbd>” and “<kbd>\]</kbd>” as delimiters for
unstructured mathematical displays, and markup such as
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\begin{equation} . . . \end{equation}</kbd></td></tr></tbody></table></div>
<p>
for a single equation, and markup such as
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\begin{eqnarray} . . . \end{eqnarray}</kbd></td></tr></tbody></table></div>
<p>
for a list of equations. </p>
<p>It is important to emphasize, however, that by overall system design
the syntactic translator operates without substantial knowledge of vocabulary. While
it is true that if ‘<kbd>$</kbd>’ is to provide a toggle for an inline
element containing math, say, <em>tmath</em>, then the syntactic translator needs to have
that association made, but the association is provided as the
value of a configuration variable in the syntactic translator that can be changed
between documents so that the syntactic translator may be used with many document
types. </p>
<p>One way to make such configuration convenient is to use an array of
<em>Elisp</em> functions that are fronts with various variable configuration
packages for the basic function <em>gellmu-trans</em> in the syntactic translator.
</p>
<p>The general outline for advanced GELLMU with arbitrary document types
is not fully developed in the present release. Instead the project
has concentrated on the realization of these ideas for the project's
didactic <em>article</em> document type, which is the subject of the
next section. </p>
<p>As the syntactic translator stands now, basic mode is characterized in the syntactic translator by the
true setting for its Boolean variable <em>gellmu-straight-sgml</em>,
while the configuration used by default for the didactic document type (which
<em>could</em> be handled in basic mode with more verbose source markup)
has that variable set false and also the variable
<em>gellmu-regular-sgml</em> set false. </p>
<p>The term <a id="regular"></a><em>regular</em> GELLMU refers to use of the
syntactic translator with the default configuration for the didactic document type. It involves nearly
maximal emulation of <em>LaTeX</em>-like markup; it implies both <em>advanced</em> mode
and the <a href="#ddt">didactic document type</a> (section 5) <em>article</em>.
</p>
</div>
<div class="subsection">
<h4>4.2.  <a id="SU-4.2"></a><a id="argopt"></a>Multiple Argument/Option Syntax</h4>
<p>An essential point in the present design is that the whole system
is built from components, each of which has its own
function<sup><a id="revfnote6" href="#fnote6">6</a></sup>.
Consistent with this design the syntactic translator operates with knowledge of syntax
but little or no knowledge of language. </p>
<p>Multiple argument/option syntax has been built into advanced mode as
part of the overall idea of providing, where sensible, <em>LaTeX</em>-like
features in a precise user markup interface for writing in document
types under SGML and XML. </p>
<p>What are the rules for converting the multiple argument/option syntax
in source markup into SGML? Direct conversion by the syntactic translator of this
type of usage into XML is not available because such conversion
requires some language knowledge and the program does not operate with
knowledge of language at that level<sup><a id="revfnote7" href="#fnote7">7</a></sup>.
One obtains an XML version of a
document in the didactic production system by using a translator with
minimal knowledge of the command vocabulary to create the XML version
from an SGML version that is the immediate output of the syntactic translator. </p>
<p>In multiple argument/option syntax, which is much like that of
<em>LaTeX</em>, arguments and options follow command names. Arguments are
delimited by braces, i.e., ‘<kbd>{</kbd>’ and ‘<kbd>}</kbd>’ and options
by square brackets, i.e., ‘<kbd>[</kbd>’ and ‘<kbd>]</kbd>’. There
must be no white space between the arguments and options nor between
the command name and the first member of an argument/option sequence. </p>
<p>Each command with a multiple argument/option sequence is translated to
an open tag whose name is the name of the command. Each argument is
translated to an <em>ag0</em> element and each option to an <em>op0</em>
element. (Both <em>ag0</em> and <em>op0</em> lie in GELLMU's reserved
name space.) There are two exceptional cases.
</p>
<ol class="decimal">
<li><p> The first argument or option is an option inside which the very
first character is a colon, i.e., ‘<kbd>:</kbd>’. This is the method
provided in advanced mode for the direct entry of an SGML attribute
sequence.<sup><a id="revfnote8" href="#fnote8">8</a></sup>
The entire contents of the option string, apart from the
leading ‘<kbd>:</kbd>’, which is discarded, are understood to be a
sequence of SGML attributes for the SGML element whose name is the
name of the command. There is no syntax check of the attribute
contents by the syntactic translator. Such an <em>attribute option</em> is not treated
as an <em>op0</em> element. In particular, an attribute option is
correctly followed immediately by a semi-colon, i.e., the character
‘<kbd>;</kbd>’, if and only if the corresponding SGML element is a
defined-empty element under the SGML document type. Since SGML
attributes correspond to very little of classical <em>LaTeX</em><sup><a id="revfnote9" href="#fnote9">9</a></sup>,
attribute options are seldom used<sup><a id="revfnote10" href="#fnote10">10</a></sup>
in the didactic production system. One such use is for the GELLMU equivalent of latex's
<em>equation*</em> and <em>eqnarray*</em> environments, which is marked up
this way:
</p>
<dl class="verblist">
<dd><kbd>
\begin{equation}[:nonum="true"]</kbd></dd>
<dd><kbd>
e = mc^2</kbd></dd>
<dd><kbd>
\end{equation}</kbd></dd>
</dl>
to produce:
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" mode="display"
><mtable><mtr class="labeled"><mtd></mtd><mtd><mrow><mi>e</mi><mo>=</mo><mi>m</mi><msup><mi>c</mi><mn>2</mn></msup
></mrow></mtd></mtr></mtable></math
>
</li>
<li><p> The first argument is the only argument and there are no options
apart from a possible attribute option. This case, which is extremely
common, is exceptional relative to argument/option handling
since the sole argument simply becomes element content without an
<em>ag0</em> wrapper.
</p>
</li>
</ol>
<p></p>
<p>When a command has a multiple argument/option sequence, the question
arises whether the <em>ag0</em> and <em>op0</em> elements that arise from
the arguments and options are the only content of the element
corresponding to the command. The syntax does not provide a way to
determine this. On the other hand, the SGML document type definition
does provide information that indicates whether other content is
possible. It is beyond the scope of the design of the syntactic translator for the
syntactic translator to read a document type definition. The syntactic translator does, however,
have a configurable list variable <em>gellmu-autoclose-list</em>
that contains the names of elements
for which no content beyond the elements arising from arguments and
options is possible. While it is not necessary that every such
command be entered in this list, when such a command not in the list
is not explicitly followed by an element closing command, it is
possible in some instances for an SGML parser to infer incorrectly
the location of end of the element. Thus, the didactic production system provides a
command <em>anch</em> for making anchors. The document type definition
provides for one option, a reference, and one argument, the anchored
text.<sup><a id="revfnote11" href="#fnote11">11</a></sup>
Because the syntactic translator does not consider the document type definition,
if one enters the markup
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\anch[href="http://www.w3.org/"]{W3C} HQ</kbd> ,</td></tr></tbody></table></div>
<p>
unless the name <em>anch</em> is in the list<sup><a id="revfnote12" href="#fnote12">12</a></sup>
<em>gellmu-autoclose-list</em>,
an SGML parser will not have reason to close the <em>anch</em> until
it sees the space following the anchored text “W3C”, and so
that space will be considered insignificant white space with the result
that there will be no space between the anchored text and the following
“HQ”.
</p>
</div>
<div class="subsection">
<h4>4.3.  <a id="SU-4.3"></a><a id="xmllimit"></a>Limitation in Regard to XML</h4>
<p>A final general comment about advanced mode is that the features it
can provide beyond basic mode when one is writing consciously for an
XML document type are somewhat limited. For example, blank lines
cannot easily be made adequate for paragraph markup with the XML form
of the didactic <em>article</em> document type. Although it is not a
specific limitation for future editions of the syntactic translator, the vision is that
use of advanced mode will be specifically for a somewhat rich SGML
version of a document type.
</p>
</div>
</div>
<div class="section">
<h3>5.  <a id="SU-5"></a><a id="ddt"></a>The Didactic Document Type</h3>
<p>The didactic document type is the document type underlying what is called regular
GELLMU. It is the heart of the idea of GELLMU as a bridge for authors
from <em>LaTeX</em> to the world of XML. More specifically, the bridge is
from the world of a <em>LaTeX</em> <em>article</em> to a document type in the
world of XML, also called <em>article</em>, that has a structure and a
vocabulary similar to those of the <em>LaTeX</em> document class.<sup><a id="revfnote13" href="#fnote13">13</a></sup>
The techniques used in the didactic production system are extensible and can be carried over
to other types of documents than articles. It is important to note
that there are many features in regular <em>LaTeX</em> which have no analogue
so far in the development of this project. One might hope to get an
idea of the extent of coverage by reviewing the examples in the
<a href="#archive">project archive</a> (appendix A). </p>
<p>When an author prepares a document as a <em>LaTeX</em> <em>article</em>, the
document is being marked up as data for a specific typesetting
program: Donald Knuth's program <em>TeX</em> running with the main <em>LaTeX</em>
facilities loaded. </p>
<p>When an author prepares a document as GELLMU source, the syntactic translator provides
a <em>LaTeX</em>-like markup interface, but its output is not data for a
specific typesetting program. Rather it is data for a broad class of
processors. This means that multiple output formats can be obtained
from a single source without the need for human intervention because
XML provides a framework that makes it relatively easy to create
reliable programs for translation from an XML document type to other
formats. It offers, moreover, the possibility of translation to
future formats free of any need for human intervention once
translators from the original document type to such formats are
written. The small price one pays for this advantage in moving from
<em>LaTeX</em> markup to GELLMU markup is that the author must learn a few
new things.<sup><a id="revfnote14" href="#fnote14">14</a></sup></p>
<p>There are two formal constructions of the didactic document type. The name of the
document type is <em>article</em>. The first construction is an SGML
version of <em>article</em> that provides features convenient for
authors that are not available under XML. The second is an XML
version. For most non-technical purposes the two constructions should
be regarded as equivalent. </p>
<p>The SGML construction of an <em>article</em> is derived from GELLMU
source markup for a document by using the syntactic translator. The didactic document
type is accompanied by a translator implemented under the Perl
language framework <em>sgmlspl</em> by David Megginson (see
the release notes in <a href="#release">appendix B</a>
for more information) for converting the SGML version of an
<em>article</em> to the XML version. </p>
<p>The description in this section of the manual deals primarily with
source level markup for the didactic document type and with how it is handled <sup><a id="revfnote15" href="#fnote15">15</a></sup>
by the time the XML version of an article is generated. Secondarily
there is comment on how it is rendered in the chief output formats
of the didactic production system, which are PDF, classic HTML, and XHTML+MathML. </p>
<p>A quick glance at the <a href="#flow">flowchart</a> (section 7.5.2) shows that the first
XML stage — author-level XML — may be viewed as a second entry
point to didactic production system processing. Some day this could become a reasonable
formatting route for translations from things like <em>Texinfo</em>,
<em>DocBook</em>, and, even perhaps, classical <em>LaTeX</em> itself via a
processor such as <em>tex4ht</em>.
</p>
<div class="subsection">
<h4>5.1.  <a id="SU-5.1"></a><a id="caveat"></a>Suggestions and Caveats</h4>
<p>Although this is the manual for a software release, it is not a book.
A document of book size would be required for a full description of
the didactic production system. </p>
<p>Much of the markup vocabulary is copied from <em>LaTeX</em>. There are some
instances where there is some deviation from <em>LaTeX</em> usage, and many
of those instances are mentioned here. </p>
<p>Definitive information about the didactic document type may be derived by consulting the
document type definition. Because the didactic production system is conceived as a base for
future development there are sketches in the document type definition
that are not covered by the didactic processors. For example,
although there is sketched code for the analogues of <em>LaTeX</em>'s
<em>paragraph</em> and <em>subparagraph</em> commands, which are sectional
in nature, that is found in the translation from SGML to XML, there is
no sketched code for these elements in the two formatters. </p>
<p>Another way to obtain information about the didactic production system is by studying
examples including this manual and the examples in the
<a href="#archive">project archive</a> (appendix A).
</p>
</div>
<div class="subsection">
<h4>5.2.  <a id="SU-5.2"></a><a id="mufund"></a>Markup Fundamentals</h4>
<p>There are several kinds of commands:
</p>
<div class="subsubsection">
<h5>5.2.1.  <a id="SU-5.2.1"></a><a id="explicitnames"></a>Explicitly named commands.</h5>
<p>Apart from macro level
metacommands an explicitly named command begins with <b>a maximal
string introduced by the character</b> ‘<kbd>\</kbd>’ <b>followed by
word characters, including the numerals</b> ‘<kbd>0</kbd>’, ‘<kbd>1</kbd>’,
…, ‘<kbd>9</kbd>’. The notion of <em>word character</em> depends on
one's locale, a concept that is formalized in GNU <em>Emacs</em>. In the
ASCII character set the word characters are the 52 upper and
lower case letters and the 10 numerals. <b>The first numeral, if
any, must not be ‘<kbd>0</kbd>’</b> since such names are reserved for use by
the syntactic translator. Command names are case sensitive. </p>
<p>An explicitly named command is a <em>container</em>, corresponding to an
SGML <em>element</em>, if its name is immediately followed, without
intervening white space, by the character ‘<kbd>{</kbd>’. In that case
the delimited zone of containment normally ends with the subsequent
balancing character ‘<kbd>}</kbd>’. (<em>LaTeX</em>-like
<a href="#argopt">multiple argument/option</a> (section 4.2) chains deserve more
discussion; for now it will suffice to point out that the use of the
<kbd>\anch</kbd> command in this document for making “anchors” is an
example, and, of course, <em>LaTeX</em>'s <kbd>\frac</kbd> command is another example.
For the present discussion these commands are considered to be
containers.)</p>
<p>An explicitly named command corresponds to an SGML
<em>defined-empty element</em> if its name is immediately followed,
without intervening white space, by the character ‘<kbd>;</kbd>’. </p>
<p>An explicitly named command corresponds to an SGML element closing
tag if its name is immediately followed, without intervening
white space, by the character ‘<kbd>:</kbd>’. </p>
<p>The name of an explicitly named command is terminated by a non-word
character. There is a small, possibly acceptable, level of syntactic
ambiguity unless the name terminator is one of ‘<kbd>{</kbd>’,
‘<kbd>;</kbd>’, ‘<kbd>:</kbd>’, or ‘<kbd>[</kbd>’. </p>
<p>In basic mode if the name terminator is ‘<kbd>[</kbd>’, then that
character introduces a list of SGML attribute specifications, each of
the form <em>name</em>="<em>value</em>", and the list must be
terminated by the character ‘<kbd>]</kbd>’. Then if the following
character is ‘<kbd>{</kbd>’, the named command is a container that ends
with the balancing ‘<kbd>}</kbd>’. Otherwise the following character
may be ‘<kbd>;</kbd>’ if the named command is a defined-empty element and
must be so in that case for direct editing of an XML document type. </p>
<p>In advanced mode if the name terminator is ‘<kbd>[</kbd>’, then that
character introduces a <em>LaTeX</em>-like command option — part of the
emulation of <em>LaTeX</em>'s multiple <a href="#argopt">argument/option syntax</a> (section 4.2)
— unless it is immediately followed, without intervening white space,
by the character ‘<kbd>:</kbd>’, in which case the bracketed content is
a list of SGML attribute specifications. (The initial ‘<kbd>:</kbd>’,
which may be used optionally in basic mode, is discarded.)</p>
<p>In any other case there is some syntactical ambiguity. The syntactic translator will
produce a corresponding SGML open tag unless the logical variable
<em>gellmu-xml-strict</em> has been set.<sup><a id="revfnote16" href="#fnote16">16</a></sup> If
the usage is consistent with the structure of the document type, an
SGML parser will in many cases be able to handle the result
correctly. The result of this type of syntactic ambiguity in source
markup is not tolerated if one is editing directly for an XML document
type. The terminator can be a blank space, but, if so, the
blank space is likely to become invisible after SGML parsing much
in the way that in <em>LaTeX</em> the markup
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\LaTeX document</kbd></td></tr></tbody></table></div>
<p>
will be collapsed into the single word form “<em>LaTeX</em>document”
when typeset.<sup><a id="revfnote17" href="#fnote17">17</a></sup>
</p>
</div>
<div class="subsubsection">
<h5>5.2.2.  <a id="SU-5.2.2"></a><a id="single"></a>Certain single characters.</h5>
<p>The characters
‘<kbd>\</kbd>’, ‘<kbd>{</kbd>’, ‘<kbd>}</kbd>’, ‘<kbd>^</kbd>’,
‘<kbd>_</kbd>’, ‘<kbd>$</kbd>’, ‘<kbd>%</kbd>’, and ‘<kbd>~</kbd>’
have command meanings that are similar to their meanings in <em>LaTeX</em>.
The characters ‘<kbd>;</kbd>’ and ‘<kbd>:</kbd>’ are ordinary characters that
have special meaning at the end of a command name. The character
‘<kbd>#</kbd>’ is also a special character used, as with <em>LaTeX</em>, in
<em>newcommand</em> templates. In source for the didactic
<em>article</em> document type any non-alphanumeric ASCII
character may be escaped (referenced for itself) with a named command,
e.g. ‘<kbd>~</kbd>’ may be referenced for itself as <kbd>\tld;</kbd>. This
is <b>necessary</b> in order to provide delayed evaluation for
ultimate translation to one of many possible ultimate formats. </p>
<p>The following language meanings apply to both basic and advanced
markup:
</p>
<ol class="decimal">
<li><p> “<kbd>\</kbd>”: <b>Command introducer.</b><br
/> Escape in basic mode: <kbd>\\</kbd> . This escape is
incorrect in advanced mode since this notation has a different
meaning — forced linebreak — in <em>LaTeX</em> itself. For the
didactic <em>article</em>
document type the escape is <kbd>\bsl;</kbd> . For other document
types one may resort to an entity reference
if adverse to providing a corresponding
defined-empty element or if one lacks control of the document type.
</p>
</li>
<li><p> “<kbd>{</kbd>”: <b>Command argument opener.</b><br
/> Escape: <kbd>\{</kbd> or <kbd>\lbr;</kbd> .
</p>
</li>
<li><p> “<kbd>}</kbd>”: <b>Command argument closer.</b><br
/> Escape: <kbd>\}</kbd> or <kbd>\rbr;</kbd> .
</p>
</li>
<li><p> “<kbd>[</kbd>”: <b>Command option opener.</b><br
/> Escape: <kbd>\lsb;</kbd> (usually not necessary<sup><a id="revfnote18" href="#fnote18">18</a></sup>).
</p>
</li>
<li><p> “<kbd>]</kbd>”: <b>Command option closer.</b><br
/> Escape: <kbd>\rsb;</kbd> .
</p>
</li>
<li><p> “<kbd>;</kbd>”: <b>Command terminator for defined-empty tags.</b><br
/> Escape: <kbd>\scl;</kbd> .
Usually an ordinary character.
Its use as a command terminator is invisible and may be
omitted optionally in some contexts. This syntax is analogous to
the use of ‘<kbd>;</kbd>’ as an entity reference terminator in SGML.
</p>
</li>
<li><p> “<kbd>:</kbd>”: <b>Command terminator for close tags.</b><br
/> Escape: <kbd>\cln;</kbd> .
Otherwise an ordinary character.
Its use as a command terminator is invisible.
</p>
</li>
<li><p> “<kbd>%</kbd>”: <b>Comment introducer, in force to end of line.</b><br
/> Escape: <kbd>\%</kbd> or <kbd>\pct;</kbd> .
</p>
</li>
<li><p> “<kbd>#</kbd>”: <b>Argument marker in <em>newcommand</em> definitions.</b><br
/> Escape: <kbd>\#</kbd> or <kbd>\hsh;</kbd> .
In the definition of a newcommand “<kbd>#1</kbd>” indicates the first
invocation argument, “<kbd>#2</kbd>” the second invocation argument, etc.
(There is no limit on the number of arguments.)
</p>
</li>
</ol>
<p></p>
<p>The following language meanings apply to advanced markup with
allusion to the didactic <em>article</em> document type.
</p>
<ol class="decimal">
<li><p> “<kbd>~</kbd>”: <b>Non-breaking interword space.</b><br
/> Escape: <kbd>\tld;</kbd>.<sup><a id="revfnote19" href="#fnote19">19</a></sup><br
/> Equivalent: <kbd>\nbs;</kbd>, cf. <kbd>&nbsp;</kbd> in HTML.
</p>
</li>
<li><p> “<kbd>^</kbd>”: <b>Superscript command.</b><br
/> Escape: <kbd>\crt;</kbd> .<br
/> Equivalent: <kbd>\sup</kbd> or, in math, <kbd>\msup</kbd> .
</p>
</li>
<li><p> “<kbd>_</kbd>”: <b>Subscript command.</b><br
/> Escape: <kbd>\_</kbd> or <kbd>\und;</kbd> .<br
/> Equivalent: <kbd>\sub</kbd> or, in math, <kbd>\msub</kbd> .
</p>
</li>
<li><p> “<kbd>&</kbd>”: <b>Dual use: tabular cells and entity introducer.</b><br
/> Escape: <kbd>\&</kbd> or <kbd>\amp;</kbd> .<br
/> ‘<kbd>&</kbd>’ introduces an entity reference if it is followed
by anything other than white space. It is used, as in <em>LaTeX</em>, as
a <em>tabular</em> cell delineator when it is followed by white space.
</p>
</li>
<li><p> “<kbd>$</kbd>”: <b>Toggle inline math mode.</b><br
/> Escape: <kbd>\$</kbd> or <kbd>\dol;</kbd> .<br
/> Equivalent: “<kbd>\tmath{ . . . }</kbd>”. <br
/> Nearly equivalent: “<kbd>\( . . . \)</kbd>”
or “<kbd>\math{ . . . }</kbd>”.<sup><a id="revfnote20" href="#fnote20">20</a></sup>
</p>
</li>
</ol>
<p>
</p>
</div>
<div class="subsubsection">
<h5>5.2.3.  <a id="SU-5.2.3"></a><a id="certainstrings"></a>Certain strings</h5>
<p>These are strings of plain text with markup significance in the didactic document type that
are part of markup in <em>LaTeX</em>.
</p>
<ol class="decimal">
<li><p> “<kbd>--</kbd>” <br
/> <b>Short dash</b> as used with a range
of numbers, e.g., 1–2.<br
/> Equivalent: <kbd>\rdash;</kbd> .
</p>
</li>
<li><p> “<kbd>---</kbd>” <br
/> <b>Long dash</b> as used for
punctuation, e.g., a dash — like this.<br
/> Equivalent: <kbd>\pdash;</kbd> .
</p>
</li>
<li><p> “<kbd>\ </kbd>” <br
/> <b>Blank interword space.</b><br
/> Equivalent: <kbd>\spc;</kbd> .
</p>
</li>
<li><p> “<kbd>\,</kbd>” <br
/> <b>Small horizontal space.</b><br
/> Equivalent: <kbd>\hsp;</kbd> .
</p>
</li>
<li><p> “<kbd>\\</kbd>” <br
/> <b>Forced line break.</b><br
/> “<kbd>\\</kbd>” may be used at the end of a line of
input for a forced line break. In a <em>tabular</em> environment
(with the didactic <em>article</em> document type, as in
<em>LaTeX</em>) it begins a new <em>tabular</em> row. Any other use is
deprecated, and will result in translation to the defined-empty
element <em>bsl</em> corresponding to the ASCII character
‘<kbd>\</kbd>’ with a warning from the syntactic translator.<br
/> Equivalents: <kbd>\brk;</kbd> for a
line break outside of a <em>tabular</em> environment.<sup><a id="revfnote21" href="#fnote21">21</a></sup>
</p>
</li>
<li><p> Blank line.<br
/> <b>Begin new paragraph command.</b><br
/> Equivalent: <kbd>\parb</kbd> . Nearly equivalent: <kbd>\par</kbd> .
</p>
</li>
<li><p> “<kbd>``</kbd>” <br
/> <b>Left (double) quotation mark.</b><br
/> Equivalent: <kbd>\ldq;</kbd> .
</p>
</li>
<li><p> “<kbd>''</kbd>” <br
/> <b>Right (double) quotation mark.</b><br
/> Equivalent: <kbd>\rdq;</kbd> .
</p>
</li>
<li><p> “<kbd>\(</kbd>” <br
/> <b>Begin <em>math mode</em> command.</b><br
/> Equivalent: <kbd>\begin{math}</kbd> .
</p>
</li>
<li><p> “<kbd>\)</kbd>” <br
/> <b>End <em>math mode</em> command.</b><br
/> Equivalent: <kbd>\end{math}</kbd> .
</p>
</li>
<li><p> “<kbd>\[</kbd>” <br
/> <b>Begin <em>displaymath mode</em> command.</b><br
/> Equivalent: <kbd>\begin{displaymath}</kbd> .
</p>
</li>
<li><p> “<kbd>\]</kbd>” <br
/> <b>End <em>displaymath mode</em> command.</b><br
/> Equivalent: <kbd>\end{displaymath}</kbd> .
</p>
</li>
<li><p> “<kbd>.  </kbd>”, “<kbd>?  </kbd>”, “<kbd>!  </kbd>” <br
/> <b>End-of-sentence marks.</b><br
/> Equivalent: <kbd>\eos;</kbd>, <kbd>\eoq;</kbd>, <kbd>\eoe;</kbd> .<br
/> A period followed either by two blank spaces or by a newline
is recorded as an end of sentence. There is similar provision
for the question mark and the exclamation point. These tagged
forms may be used explicitly for the corresponding punctuation
inside math displays to distinguish punctuation from
mathematical use of the punctuation symbols. Explicit markup
for a comma is “<kbd>\cma;</kbd>”.<sup><a id="revfnote22" href="#fnote22">22</a></sup>
</p>
</li>
</ol>
<p>
</p>
</div>
</div>
<div class="subsection">
<h4>5.3.  <a id="SU-5.3"></a><a id="large"></a>Large Structure</h4>
<p>Overall an <em>article</em> consists of a <em>preamble</em> followed by
a <em>body</em>. As <a href="#beginend">noted previously</a> (section 3.3) advanced mode
provides a special form of usage
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\begin{document} . . . \end{document}</kbd></td></tr></tbody></table></div>
<p>
with the paired metacommands <em>begin</em> and <em>end</em> that with an
<em>article</em> delimit its <em>body</em>. This is enabled with the
<em>gellmu-trans</em> call for the syntactic translator, and, consistent with regular
<em>LaTeX</em> usage the <em>preamble</em> is present without explicit tagging. </p>
<p>The only required markup in a <em>preamble</em> is a <em>title</em>, and it
is formally correct for its content to be empty. The SGML content
model for a <em>body</em> is somewhat loose, but is usually understood
to consist of <em>section</em>s and may contain ordinary paragraphs
(<em>par</em>, which must be marked up explicitly, or <em>parb</em>,
which is begun with a blank line). Although a <em>body</em> may be entirely
empty (likely not useful) or may consist only of <em>par</em> and
<em>parb</em> elements, all inline text must be within one of these
basic paragraph containers. </p>
<p>For example this formally correct textless document is handled without
noise by the didactic production system:
</p>
<dl class="verblist">
<dd><kbd>
\documenttype{article}</kbd></dd>
<dd><kbd>
\title{}</kbd></dd>
<dd><kbd>
\begin{document}\end{document}</kbd></dd>
</dl>
<p>
while the following document with text outside of a paragraph fails
initial validation in the didactic production system:
</p>
<dl class="verblist">
<dd><kbd>
\documenttype{article}</kbd></dd>
<dd><kbd>
\title{}</kbd></dd>
<dd><kbd>
\begin{document}</kbd></dd>
<dd><kbd>
x</kbd></dd>
<dd><kbd>
\end{document}</kbd></dd>
</dl>
<p>
The error may be corrected by placing a blank line before the
character ‘<kbd>x</kbd>’. </p>
<p>The content model for <em>preamble</em> is tighter than that for
<em>body</em>. This makes it possible to have a greater level of
error-checking than would otherwise be possible. For example, a
preamble must have exactly one <em>title</em> although it is not
specified where in the preamble a title might be. There may be at
most one of each of the elements <em>surtitle</em>, <em>subtitle</em>, and
<em>date</em>. Although <em>newcommand</em>, which is a metacommand, does
not affect the document type definition and may be used at different
locations in the preamble, the small number of actual elements that
may be multiply used in the preamble, such as <em>mathsym</em> (which is
partly a metacommand) must be located together.
</p>
</div>
<div class="subsection">
<h4>5.4.  <a id="SU-5.4"></a><a id="sectioning"></a>Sectioning</h4>
<p>In classical <em>LaTeX</em> one writes simply
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\section{Some title for a section}</kbd></td></tr></tbody></table></div>
<p>
to begin a new section. While this markup specifically delineates
the section title, <em>LaTeX</em> understands that a section has begun.
The <em>section</em> command has an option whose content is an alternate
title for the table of contents, and the starred form of the command
suppresses an otherwise automatic section number. </p>
<p>With SGML the classical approach is something along the following
lines:
</p>
<dl class="verblist">
<dd><kbd>
<section><sectiontitle>Some title for a section</sectiontitle></kbd></dd>
<dd><kbd>
<para> A paragraph.</kbd></dd>
<dd><kbd>
<para> Another paragraph.</kbd></dd>
<dd><kbd>
     . . .</kbd></dd>
<dd><kbd>
</section></kbd></dd>
</dl>
<p>
<em>Basic</em> GELLMU markup corresponding to this would
be:<sup><a id="revfnote23" href="#fnote23">23</a></sup>
</p>
<dl class="verblist">
<dd><kbd>
\begin{section}\sectiontitle{Some title for a section}</kbd></dd>
<dd><kbd>
\para A paragraph.</kbd></dd>
<dd><kbd>
\para Another paragraph.</kbd></dd>
<dd><kbd>
    . . .</kbd></dd>
<dd><kbd>
\end{section}</kbd></dd>
</dl>
<p>
If, moreover, the markup is to be well-formed XML markup, then each
<em>para</em> tag would need explicit closure with <kbd></para></kbd>. </p>
<p>The main point here is that the open and close tags for a section
in a classical SGML document type encompass the whole contents of
a section, and separate markup is required for the section
title.<sup><a id="revfnote24" href="#fnote24">24</a></sup></p>
<p>The didactic SGML document type under <em>advanced</em> GELLMU seeks to
model classical <em>LaTeX</em> as closely as possible in order to provide a
bridge for authors from <em>LaTeX</em> to SGML (and, indeed, XML). For
this reason a command <em>section</em> similar to the classical <em>LaTeX</em>
command that delineates a section title is provided in the didactic
SGML document type. At the same time this document type has a whole
section container <em>Section</em> (upper case <em>S</em>) that in the
simplest case consists of a <em>shead</em> container for its title (or
header) followed by any number of paragraphs. The XML form of the
didactic document type supports only this latter tag, which means that
the translation script that converts SGML to XML has an unambiguous
way of performing the conversion from <em>section</em> to <em>Section</em>
provided that the author's source leads to an SGML instance which is
valid<sup><a id="revfnote25" href="#fnote25">25</a></sup>
under the didactic document type.
</p>
</div>
<div class="subsection">
<h4>5.5.  <a id="SU-5.5"></a><a id="labelref"></a>Labels, References, and Anchors</h4>
<p>A <em>label</em> command may be placed anywhere that text may be placed
in order to mark a location and associate a symbolic “key”
with that location. A <em>ref</em> command may be placed anywhere that
text may be placed to generate a visible allusion called its
<em>reference value</em>, for example a section number, to the location
associated with a label key. An <em>anch</em> command may be placed
anywhere that text may be placed to provide a hypertext reference
either by key to an internal location or by uniform resource
identifier (URI) to an external resource. </p>
<p>At this point the discussion will become descriptive of of the entire
didactic production system rather than simply of its document type.
</p>
<div class="subsubsection">
<h5>5.5.1.  <a id="SU-5.5.1"></a><a id="seq"></a>Labels and Sequencing</h5>
<p>The basic usage for <em>label</em> is
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\label[:series="</kbd>
<em>series-name</em>
<kbd>" serseq="</kbd>
<em>number</em>
<kbd>" refkey="</kbd>
<em>ref-key</em>
"<kbd>]{</kbd>
<em>key</em>
<kbd>}</kbd></td></tr></tbody></table></div>
<p>
where use of the attributes is optional and, moreover, the required
<em>key</em> may be empty, i.e., the markup <kbd>\label{}</kbd> is permitted.
The <em>key</em> must be a case-sensitive string that is
<b>monocase</b> unique.<sup><a id="revfnote26" href="#fnote26">26</a></sup>
The didactic production system will provide a unique automatically generated string value
for <em>key</em> if none is provided by the author; this can be useful
if a <em>series</em> name is specified as an attribute for the label. </p>
<p>An author should never reference a label key not provided by the
author, but the empty element <em>popkey</em> is intended for processing
evaluation as the last label <em>key</em>, automatic or not, preceding
its location. </p>
<p>Sequencing<sup><a id="revfnote27" href="#fnote27">27</a></sup>
may be handled under the GELLMU didactic <em>article</em>
document type using labels and references. Toward this end one
makes use of three SGML attributes that are provided with the
<em>label</em> tag:
</p>
<dl>
<dt><b>
series</b></dt>
<dd>The value is the name of a sequenced family of labels.
A label may belong to at most one family, but there may be multiple
labels at the same location. There is no default value of series. </dd><dt><b>
serseq</b></dt>
<dd>The value is the sequence number of the label in its series
if a series is defined. It is meaningless if no series is specified
for the label. </dd><dt><b>
refkey</b></dt>
<dd>The name of a label key from which to spawn an automatically
generated value for the attribute <em>serseq</em> of the current label. </dd></dl>
<p></p>
<p>Every label has a reference value that is normally accessed with
the <em>ref</em> command. This results in the creation, when
the XML version is generated, of an XML entity reference with name
based on the reference's <em>key</em> argument, that matches a CDATA
entity definition at the top of the XML document. The use of indirection
provided by this entity technique means that it is immaterial whether the
reference is forward or backward. </p>
<p>The <em>evalref</em> command gives access to the literal value of a
reference without indirection, and places that value as a literal in
the XML version of an article. Thus, <em>evalref</em> is the name of a
tag only in the SGML document type and in the author-level XML document
type but not in the elaborated XML document type.
An <em>evalref</em> invocation will be successful only with a backward
reference. This is extremely useful for managing non-default
numbering of sectional units. For ordinary label references its use
is undesirable even though it is possible for backward references. </p>
<p>The reference value of a label is determined as follows:
</p>
<ol class="decimal">
<li><p> Basic reference values are positive integers. Upper and lower
case alphabetic values and upper and lower case roman numeral values
may be obtained by applying the <em>series</em> command (not to be
confused with the <em>series</em> attribute for the <em>label</em> command)
to a basic reference value with <em>type</em> attribute of <em>series</em>
set to one of ‘<kbd>A</kbd>’, ‘<kbd>a</kbd>’, ‘<kbd>I</kbd>’, or ‘<kbd>i</kbd>’.
</p>
</li>
<li><p> If the label is assigned to a label series and is given a
<em>refkey</em> attribute, then the reference value of the label is the
reference value of the label referenced by the key that is the value
of the <em>refkey</em>. (This mechanism is used to re-start the
sequencing of the sectional unit id's at the end of this document.)
</p>
</li>
<li><p> Else if the label is assigned to a label series and the author
supplies an explicit <b>literal</b> numeric value for the
<em>serseq</em> attribute, then the value of <em>serseq</em> is its
reference value. (Markup — in particular, <em>evalref</em> —
cannot be used in defining an attribute value.)
</p>
</li>
<li><p> Else if the label is assigned to a label series, the reference
value of the label is the next (positive integer) value for a label
in that series. (This mechanism is used to control the sectional
id of the last section of this document. It may also be used to
run parallel interleaved sequences of sectional units, such as, for
example, questions and answers, within a document.)
</p>
</li>
<li><p> Else the reference value of the label is the sectional unit
identifier, i.e., its <em>sunit</em> value rather than the logical
value in its attribute <em>sid</em>, of the smallest sectional
unit containing the label. These values may not be numeric. For
example the string “A.3.2” might be a sectional unit
identifier. The <em>series</em> command should not be used to express
type conversion of a reference value that might resolve as a sectional
unit identifier.
</p>
</li>
</ol>
<p>
</p>
</div>
<div class="subsubsection">
<h5>5.5.2.  <a id="SU-5.5.2"></a>Anchors</h5>
<p>The basic usage for <em>anch</em> is
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\anch[</kbd>
<em>reference specs</em>
<kbd>]{</kbd>
<em>anchored text</em>
<kbd>}</kbd></td></tr></tbody></table></div>
<p>
where the option, which is not an attribute option but rather
becomes the element <em>anchref</em> in XML (while the anchor's argument
— its “presented content” — becomes <em>anchv</em>), is
expected to contain white space separated strings of the form
<kbd>name="value"</kbd><sup><a id="revfnote28" href="#fnote28">28</a></sup>
with name restricted to one of the following:
</p>
<dl>
<dt><b>fref</b></dt>
<dd> A footnote reference. Value is a string
that becomes the content of an automatically created
footnote to the text in <em>anchv</em>. This usage is deprecated;
use \footnote instead.
</dd>
<dt><b>href</b></dt>
<dd> A web reference as with <em>href</em> in HTML.
That is, value is a URI. It <em>could be</em> of the form
“<kbd>#labelkey</kbd>” where “<kbd>labelkey</kbd>” is the name of a label
key that is preferably and more easily used with <em>iref</em>.
(The ‘<kbd>#</kbd>’ needs to be escaped, i.e., marked up as
“<kbd>\#</kbd>”.) In a non hypertext formatting the URI
may be presented as a note or footnote associated with the text in
<em>anchv</em>.
</dd>
<dt><b>Href</b></dt>
<dd> Same as <em>href</em> except that the author wishes
to suppress any note or footnote presentation of the URI. This
might be the case if, for example, the URI might be obviously
deducible from the <em>anchv</em> content.
</dd>
<dt><b>iref</b></dt>
<dd> An internal reference; value must be a label key arising
from <em>label</em> or <em>klabel</em><sup><a id="revfnote29" href="#fnote29">29</a></sup>. </dd>
</dl>
<p>
Note also that there is a command <em>urlanch</em> (probably should have
been <em>urianch</em>), taking a single argument, used for URIs,
which is intended to have the same effect as a newcommand with
one argument for creating a web anchor with the URI as presented
content.
</p>
</div>
<div class="subsubsection">
<h5>5.5.3.  <a id="SU-5.5.3"></a><a id="counters"></a>Example Emulating a <em>LaTeX</em> Counter</h5>
<p>Suppose that one wants to fashion an inline enumerated list at some
point in a document. An <em>enumerate</em> environment is a list
structure that, while it may occur in a paragraph, is not inline. The
idea is to give each item a label and fashion the inline list item
number by referencing that label. One writes a newcommand to ease
this. </p>
<p>The name of a <em>LaTeX</em> counter is emulated with the name of the
<em>series</em> attribute for one or more labels. Unless one wishes to
be able to reference the items apart from the immediate reference, one
need not provide a label key. The didactic production system will provide a default labelkey
and the command “<kbd>\popkey</kbd>”, which grabs the key of the last preceding
label, may be used to furnish the key for the immediate reference.
If one wants small Roman numerals, one wraps the “<kbd>\ref</kbd>” command
in a “<kbd>\series</kbd>” command. Since <em>series</em> requires an actual
number, one must use <em>evalref</em> instead of <em>ref</em>, which is
permitted so long as the reference follows the label.
Here's the markup:
</p>
<dl class="verblist">
<dd><kbd>
\label[:series="foo" serseq="0"]{} % zero the counter named foo</kbd></dd>
<dd><kbd>
\newcommand{\ti}{%</kbd></dd>
<dd><kbd>
\label[:series="foo"]{}(\series[:type="i"]{\evalref{\popkey}})}</kbd></dd>
<dd><kbd>
Hilbert's three most important contributions to algebraic geometry</kbd></dd>
<dd><kbd>
are \ti~the basis theorem, \ti~the nullstellensatz, and \ti~the syzygy</kbd></dd>
<dd><kbd>
theorem.</kbd></dd>
</dl>
<p>
The rendering is this:
<a id="KEY-1"></a>
Hilbert's three most important contributions to algebraic geometry
are <a id="KEY-2"></a>(i) the basis theorem, <a id="KEY-3"></a>(ii) the nullstellensatz, and <a id="KEY-4"></a>(iii) the syzygy
theorem. </p>
<p>With the current didactic production system if one had used “<kbd>\ref</kbd>” instead of
“<kbd>evalref</kbd>”, the translator from author-level XML to elaborated
XML, which resolves references, would have issued a warning in the
scroll, but the build would have run to otherwise successful completion
by ignoring the presence of the <em>series</em> command.
</p>
</div>
</div>
<div class="subsection">
<h4>5.6.  <a id="SU-5.6"></a><a id="secusage"></a><a id="last"></a>General Usage for Sectional Units</h4>
<p>This describes the content model in the GELLMU didactic document type
for the “whole” sectional units <em>Section</em>,
<em>Subsection</em>, … as fully tagged.
</p>
<div class="subsubsection">
<h5>5.6.1.  <a id="SU-5.6.1"></a><a id="seccontent"></a>The Content Model</h5>
<p>The content model for sectional units is:
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>((sopt)?,(sprefix)?,(sunit)?,(shead),(%UnitContent)*)</kbd></td></tr></tbody></table></div>
<p>
where:
</p>
<dl>
<dt><b>%UnitContent</b></dt>
<dd> refers to the subsections, loose paragraphs, and other general content
that is allowed inside a section.
</dd>
<dt><b>shead</b></dt>
<dd> is the required<sup><a id="revfnote30" href="#fnote30">30</a></sup>
section header or title.
</dd>
<dt><b>sopt</b></dt>
<dd> is an optional title for use in the table of
contents<sup><a id="revfnote31" href="#fnote31">31</a></sup>.
</dd>
<dt><b>sprefix</b></dt>
<dd> is optional markup for text that is to precede the sectional unit
sequence notation. For example, if the sectional unit sequence is
“B” and <em>sprefix</em> is the markup string
“<kbd>Appendix </kbd>” (ending with a blank space), then the visible
indicator for the sectional unit, when consistent with the setting of
<em>secnumdepth</em>, is “Appendix B” both at the beginning
of the section and in the table of contents. Or if the sequence is
“3” and the <em>sprefix</em> is “A”, then the
visible indicator is “A3”.
</dd>
<dt><b>sunit</b></dt>
<dd> is an optional setting for the sectional unit sequence. The GELLMU
didactic document type has an attribute “sid” for the
sectional units <em>Section</em>, <em>Subsection</em>, … that is
optional (and rare for author usage) in the SGML version but
required in the XML version. The translator from SGML to XML
computes it in the standard way. For example subsubsection 1 of
subsection 3 in section 2 acquires the <em>sid</em> “2.3.1”.
It is expected that formatters will use this value for the visible
sectional unit indicator, preceded, as previously described, by
any <em>sprefix</em>, unless the user provides <em>sunit</em>. While
<em>sunit</em> is intended to override the visible indicator, it is
not provided to override the <em>sid</em> attribute itself which a
formatter should see as describing logical structure. </dd>
</dl>
<p>
</p>
</div>
<div class="subsubsection">
<h5>5.6.2.  <a id="SU-5.6.2"></a><a id="ltxsecusage"></a>The <em>LaTeX</em>-Like Form of General Usage</h5>
<p>Corresponding <em>LaTeX</em>-like <em>argument</em>/<em>option</em> syntax can be used, as previously
indicated, in GELLMU source with <em>section</em>, <em>subsection</em>,
… . If, however, <em>argument</em>/<em>option</em> syntax is used, one must be mindful of
the ordering of the options, and use empty option brackets, as
necessary, to indicate the position in the sequence of an option with
content. For example, a sole option is understood as <em>sopt</em>, the
version of the sectional unit title to be used in the table of
contents. To provide only <em>sprefix</em> with <em>argument</em>/<em>option</em> syntax one
precedes the bracket sequence for <em>sprefix</em> with an empty pair
“<kbd>[]</kbd>” of option brackets<sup><a id="revfnote32" href="#fnote32">32</a></sup>
for <em>sopt</em>.
</p>
</div>
</div>
<div class="subsection">
<h4>5.7.  <a id="SU-5.7"></a><a id="verb"></a><em>verbatim</em>, <em>verblist</em>, and
<em>manmac</em></h4>
<p>The ordinary notion of “verbatim” is complicated in the
context of a document type that is intended for processing toward
multiple output formats. There is no special provision for verbatim
markup under <em>basic</em> GELLMU<sup><a id="revfnote33" href="#fnote33">33</a></sup>,
but there are two layers, one simplistic and one sophisticated, in the
didactic production system with each layer having provision for both inline and block-level
verbatim markup. </p>
<p>The simplistic approach involves the provision of an inline element
<em>verb</em> and a block-level element <em>verbatim</em> in the didactic document type.
With these the author is responsible for entering special characters
in ways that are safe for input source notation, safe for syntactic translator
output, and safe for each output format that is envisioned.<sup><a id="revfnote34" href="#fnote34">34</a></sup>
In the simplistic layer the formatting program in the didactic production system for HTML
output renders <em>verb</em> as an HTML <em>kbd</em> element and
<em>verbatim</em> as an HTML <em>pre</em> element. In formatting for
regular <em>LaTeX</em> output each of these SGML elements is rendered
as its <em>LaTeX</em> namesake. Neither the <em>pre</em> element in HTML
nor the (basic) <em>verbatim</em> command in <em>LaTeX</em> is context-sensitive,
and typically are formatted with left margin justification. </p>
<p>The sophisticated layer in the syntactic translator for <em>verbatim</em> is enabled by
setting the variable <em>gellmu-verbatim-clean</em> true. If this is
the case, then a user should input verbatim material literally between
<kbd>\begin{verbatim}</kbd> and <kbd>\end{verbatim}</kbd> markers occupying whole lines
and the syntactic translator will convert each of the 33 non-alphanumeric printable
ASCII characters therein to the corresponding empty element in
the didactic document type, and render each line of the converted material as a list
item bearing the item name <em>nln</em> in a list element
<em>verblist</em>.<sup><a id="revfnote35" href="#fnote35">35</a></sup></p>
<p>Similar arrangements pertain to the sophisticated inline analogue
of <em>verb</em>, which is enabled in the syntactic translator by setting the variable
<em>gellmu-manmac-bar-name</em> to a non-empty string value that is
to become the name of the element, such as <em>quostr</em>, to contain
the content, which should be delimited in source by successive
‘<kbd>|</kbd>’ characters. By default the user must enter a
verbatim string in “safe” form, but may enter it,
apart from any occurrence of the character ‘<kbd>|</kbd>’, literally
if the variable <em>gellmu-manmac-literal</em> is true. The term
“manmac” is derived from an old plain <em>TeX</em> package for
writing documentation by that name in which the character ‘<kbd>|</kbd>’
is used to delimit inline literal material for verbatim presentation.
Moreover, consistent with usage observed in <em>LaTeX</em> documentation
markup of the form
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\</kbd><em>name</em><kbd>|</kbd><em>literal-text</em><kbd>|</kbd></td></tr></tbody></table></div>
<p>
is translated by the syntactic translator to an element named as with simple
“<kbd>|...|</kbd>” having a setting for its attribute
with name the value of the string variable
<em>gellmu-manmac-attribute</em>, which for <em>quostr</em> in the didactic document type
would appropriately be its attribute <em>inv</em>. </p>
<p>Variable settings to provide for the use of literal input both for
<em>verbatim</em> as a metacommand front for the list element
<em>verblist</em> and <em>manmac</em> configuration for the element
<em>quostr</em>, as described, are default when the syntactic translator is begun with
the non-default function <em>gellmu-latex-faq</em>. This function also
sets the variable <em>gellmu-squophrase-name</em>, which otherwise
defaults to the empty string, to the value “<kbd>squophrase</kbd>”.
This causes the syntactic translator to attempt to interpret balancing
character pairs consisting of the character ‘<kbd>‘</kbd>’ and the
character ‘<kbd>’</kbd>’ as delimiters for the element
<em>squophrase</em>, an alternate form along with <em>quophrase</em>,
for “quoted phrase”, with odd instances of the character
‘<kbd>’</kbd>’ set as the empty element <em>apos</em>, which represents
an apostrophe.
</p>
</div>
<div class="subsection">
<h4>5.8.  <a id="SU-5.8"></a><a id="accents"></a>Accents</h4>
<p>Traditional <em>LaTeX</em> markup employs accent commands for modifying
ASCII characters in order to produce non-ASCII
characters. On the other hand characters from 16
“byte-planes” of Unicode are now available in HTML
and XML as ordinary characters, with treatment as the atoms of
ordinary strings of text not requiring any special attention or notice
from the viewpoint of markup. It may happen that this will affect
development in the <em>LaTeX</em> project, and it is, therefore, unclear what
the long term role might be of <em>LaTeX</em>'s accent commands. </p>
<p>Nonetheless, the didactic document type provides element names corresponding to the
14 classical <em>LaTeX</em> accents although it does not provide classical
markup notations such as “<kbd>\'</kbd>”,
“<kbd>\"</kbd>”, “<kbd>\~</kbd>”, … inasmuch
as names are required in syntactic translator output.<sup><a id="revfnote36" href="#fnote36">36</a></sup>
The names for the accents may be seen by locating the word
“accent” in the didactic production system file <kbd>gellmu.dtd</kbd> and reading
the following 14 lines. </p>
<p>An author, particularly an author residing in an English language
locale, may introduce, for example, the character é in
several ways:
</p>
<ol class="decimal">
<li><p> by using an algorithmic accent command — in this case
<kbd>\acute{e}</kbd>: é. </p>
</li>
<li><p> by direct Unicode-based entity reference – in this case
<kbd>&#xE9;</kbd>: é. </p>
</li>
<li><p> by simple direct entry of the Unicode point in a file
having the UTF-8 text encoding. </p>
</li>
</ol>
<p>
Note that Unicode values are numbers represented in hexadecimal
notation (base 16); the digits are 0–9 and A–F. Thus, E9 is
233, and one could also use the entity reference <kbd>&#233;</kbd>. </p>
<p>While for the long term, the largely equivalent<sup><a id="revfnote37" href="#fnote37">37</a></sup>
second or third methods are superior,
there are caveats for their use in 2007:
</p>
<ul>
<li><p> One's <em>LaTeX</em> back end must have a suitably robust way
of handling Unicode, presumably via the <em>inputenc</em>
package or possibly via <em>Omega/Lambda</em>.
</p>
</li>
<li><p> Even when fonts are available, some web browsers
seem only to handle Unicode via entity references. </p>
</li>
</ul>
<p>
</p>
</div>
<div class="subsection">
<h4>5.9.  <a id="SU-5.9"></a><a id="tabular"></a>Tabular Environment Emulation</h4>
<p>At this point (2006-7) the didactic document type is able to accomodate emulation
of <em>LaTeX</em>'s <em>tabular</em> environment with “<kbd>l</kbd>”, “<kbd>c</kbd>”,
“<kbd>r</kbd>”, and “<kbd>p</kbd>” column cell specifiers with, where
robust CSS support is available for HTML, “<kbd>|</kbd>” indicators
for vertical cell rules and “<kbd>\hline</kbd>” commands for horizontal
rules between rows. While <em>multicol</em>, and <em>multirow</em> are not
modeled, cells may contain other <em>tabular</em>s recursively. </p>
<p>A “<kbd>p</kbd>” column specifier optionally takes a decimal argument
that represents the fraction of available width to be made available
for the cells in that column. When is no fractional width specifier,
the default fractional width is <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mfrac
><mn>1</mn><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow
></mfrac
></math
> where <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mi>n</mi></math
> is the
total of number of columns. </p>
<p>What may be viewed as a shortcoming of the <em>tabular</em> emulation
is that in each <em>tabular</em> row the first cell must contain
some markup in order for the document to be structurally correct.
This arises from a rule associated with SGML document types
that might be overcome if GELLMU source were processed by a
monolithic program. Instead, however, it is an
assemby of <a href="#flow">separate components</a> (appendix 7.5.2) in which the first stage
has knowledge of syntax but not of the markup vocabulary. </p>
<p>One thing to keep in mind with <em>tabular</em> is that in the current,
though probably not future, design of HTML tables are not allowed
in paragraph content. The didactic production system works hard to deal with this. In most
web browsers there will be a line break before an HTML table and
again after an HTML table. (One way to finesse that is to place a
table in a cell in a sur-table, which is abuse of markup.) This
author generally places a <em>tabular</em> inside a <em>display</em>,
which is the GELLMU object corresponding to <em>LaTeX</em>'s <em>center</em>. </p>
<p>The document type does not offer “floating” objects, and, therefore,
the name <em>table</em> is not used as as in <em>LaTeX</em>. </p>
<p>The name <em>table</em> is used for emulation in regular GELLMU
source of HTML tables. A <em>table</em>, like a <em>tabular</em>,
takes a required argument consisting of column specifiers.
In the didactic production system at the point where an article is spun to the elaborated
XML version of <em>article</em>, there is no longer a distinction
between <em>tabular</em> and <em>table</em>. </p>
<p>There is also <em>array</em>, which, as in <em>LaTeX</em>, is the in-math
version of <em>tabular</em>, except that in GELLMU its emulation of
<em>LaTeX</em>'s array survives translation to the XML version of
<em>article</em>. An <em>array</em> has only “<kbd>l</kbd>”, “<kbd>r</kbd>”,
and “<kbd>c</kbd>” cells. </p>
<p><b>Example:</b> The markup for the <a href="#dtdfiles">table of DTD's</a>
in Appendix B.2.2 is this:
</p>
<dl class="verblist">
<dd><kbd>
\begin{display}</kbd></dd>
<dd><kbd>
\begin{tabular}{l|cc}</kbd></dd>
<dd><kbd>
~                       & Latin-1              & \abbr{UTF-8}          \\</kbd></dd>
<dd><kbd>
\hline</kbd></dd>
<dd><kbd>
First stage \abbr{SGML} &  \quostr{gellmu.dtd} &  \quostr{ugellmu.dtd} \\</kbd></dd>
<dd><kbd>
Author Level \abbr{XML} &  ~                   & \quostr{axgellmu.dtd} \\</kbd></dd>
<dd><kbd>
Elaborated \abbr{XML}   & \quostr{xgellmu.dtd} & \quostr{uxgellmu.dtd}</kbd></dd>
<dd><kbd>
\end{tabular}</kbd></dd>
<dd><kbd>
\end{display}</kbd></dd>
</dl>
<p>
Because the one horizontal divider and the one vertical divider rely
on CSS support in HTML, these dividers might not be seen in a web
browser with weak CSS support.
</p>
</div>
<div class="subsection">
<h4>5.10.  <a id="SU-5.10"></a><a id="graphics"></a>Graphic Inclusions</h4>
<p>There is basic support for graphics inclusions suitable for the HTML
backend and the <em>LaTeX</em> backend with both DVI and PDF outputs.
The arrangements are not unlike those required for the use of
the <em>includegraphics</em> command provided by <em>LaTeX</em>'s
<em>graphicx</em> package. This means that, apart from the didactic production system's chain
of processors, one needs to provide several different versions of a
given graphic object in order to accommodate the needs of the three
different output formats (HTML, PDF, and DVI). A reliable graphics
format converter such as that provided by <em>ImageMagick</em>
(<a href="http://www.imagemagick.org/"><kbd>http://www.imagemagick.org/</kbd></a>)
or the <em>netpbm</em> utilities
(<a href="http://netpbm.sourceforge.net/"><kbd>http://netpbm.sourceforge.net/</kbd></a>)
and a broad <em>TeX</em> support environment similar to that provided by
TUG's <a href="http://www.tug.org/texlive/"><em>TeXLive</em></a>
are essential for work with included graphics. </p>
<p>For example, if one begins with an encapsulated PostScript image
<kbd>glmy.eps</kbd> made, say, with Metapost, then one might run
the commands
</p>
<dl class="verblist">
<dd><kbd>
   epstopdf glmy.eps</kbd></dd>
<dd><kbd>
   convert glmy.pdf glmy.png</kbd></dd>
</dl>
<p>
before making PDF with <em>pdflatex</em> and PNG (for inclusion
in HTML). In this case the PDF version of the graphic should be
regarded as best for use with <em>pdflatex</em>, and so one wants to
have the PNG version out of view from <em>pdflatex</em> when
building the GELLMU source <kbd>glman.glm</kbd> for this document.
With the new <em>mmkg</em> drivers one may prepare a tiny file
<kbd>glman.prx</kbd> that is a list of names of image files, one file
per line, that should be out of view at the point in the pipeline when
<em>pdflatex</em> is active. Thus, a line in the file
<kbd>glman.prx</kbd> should contain the name <kbd>glmy.png</kbd>. </p>
<p>In <a href="glman.glm"><kbd>glman.glm</kbd></a> one has the
code:
</p>
<dl class="verblist">
<dd><kbd>
\begin{quotation}</kbd></dd>
<dd><kbd>
   Sometimes a picture is worth a thousand words.</kbd></dd>
<dd><kbd>
   \display[:frame="1.1"]{\includegraphics[:scale="0.2"]{glmy}}</kbd></dd>
<dd><kbd>
\end{quotation}</kbd></dd>
</dl>
<p>
which yields:
</p><blockquote>
<p>Sometimes a picture is worth a thousand words.
</p>
<div class="display"><table class="gdisplay" style="padding: 1ex; border: 0.3ex solid;"><tbody><tr><td>
<img src="glmy.png" alt="Image file: glmy.png" />
</td></tr></tbody></table></div>
<p></p>
</blockquote>
<p></p>
<p>In this markup one sees, first of all, two uses of SGML
attributes — <em>frame</em> and <em>scale</em>. Attribute
options are opened with “<kbd>[:</kbd>” rather than simply with
“<kbd>[</kbd>”. Whereas options generally may contain markup,
attribute options may not. </p>
<p>The meaning in this example of <em>scale</em> is that the <b>width</b>
of the graphic in DVI and PDF outputs will be the result
of multiplying the <em>scale</em> by <em>LaTeX</em>'s value of
<em>\textwidth</em>.<sup><a id="revfnote38" href="#fnote38">38</a></sup>
The HTML formatter will link to the PNG without a width
specification. Thus, the brower window width of the graphic will be
the actual width of the PNG image unless, perhaps, it's too large for
the browser's window. The meaning of <em>frame</em> is that for print
outputs the graphic image will be surrounded by a <em>LaTeX</em>
<em>framebox</em> with diameter that is <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1.1</mn></math
> times the diameter of the
<em>display</em>'s content. In the current HTML formatter no use is
made of the numeric value of <em>frame</em> although a default frame is
constructed via an HTML attribute giving values for the CSS
properties <em>border</em> and <em>padding</em>. When image framing is
desired, another approach is to incorporate framing in the graphic
itself.
</p>
</div>
</div>
<div class="section">
<h3>6.  <a id="SU-6"></a><a id="math"></a>Mathematics in <em>article</em></h3>
<div class="subsection">
<h4>6.1.  <a id="SU-6.1"></a><a id="genmath"></a>General</h4>
<p>There was previous mention of the basic mathematical container element
<em>tmath</em> in the discussion of <a href="#single">single string</a> (section 5.2.2) markup
and the <em>math</em> and <em>displaymath</em> elements in the discussion
of <a href="#certainstrings">certain strings</a> (section 5.2.3) of special markup
significance. </p>
<p>The markup used inside these containers is very similar to that
which is used in <em>LaTeX</em> although far from all of <em>LaTeX</em>'s math
markup, as extended by the <em>amsmath</em> package, has any
analogue in the didactic production system. </p>
<p>There are a few things that deserve short mention:
</p>
<dl>
<dt><b>\sum, \int, and \prod</b></dt>
<dd> are all similar to
their <em>LaTeX</em> namesakes except that each requires explicit closure.
For example,
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\[ \sum_{0}^{\infty} \frac{x^k}{k!} \sum: \]</kbd></td></tr></tbody></table></div>
produces
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" mode="display"
><mrow><munderover><mo>∑</mo><mn>0</mn><mi>∞</mi></munderover><mfrac
><mrow><msup><mi>x</mi><mi>k</mi></msup
></mrow
><mrow><mi>k</mi><mo>!</mo></mrow
></mfrac
></mrow
><mspace width="0.6em"/><mtext>.</mtext
></math>
</dd>
<dt><b>\regch, \mbox, and \text</b></dt>
<dd> The didactic document type provides <em>regch</em>,
for “regular character” that is a one character version
of <em>mbox</em> provided for separating from general
<em>mbox</em> matter the content to which a non-math
<a href="#accents">algorithmic accent</a> (section 5.8), may
be applied. For example,
<dl class="verblist">
<dd><kbd>
\newcommand{\Q}{\regch{\bold{Q}}}  % intended for use in math</kbd></dd>
<dd><kbd>
\newcommand{\galQ}{\mbox{Gal}(\ovbar{\Q}/\Q)}  % only in math</kbd></dd>
<dd><kbd>
$\galQ$\aos;</kbd></dd>
</dl>
produces
<math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mi>Gal</mi><mfenced open="(" close =")"
><mrow><mover accent="true"><mi mathvariant="bold" fontweight="bold" fontstyle="normal">Q</mi><mo>¯</mo></mover
><mo stretchy="true" lspace="0.3em" rspace="0.3em">⁄</mo><mi mathvariant="bold" fontweight="bold" fontstyle="normal">Q</mi></mrow></mfenced
></math
>.
<p>Both <em>regch</em> and <em>mbox</em> should be used only for symbols.
Note that “Gal” in the foregoing is a symbol. The command
\text is provided for the use of text phrases – usually conjunctive
in nature – inside math zones. For example, the markup
</p>
<dl class="verblist">
<dd><kbd>
\[ \absval{x} = \lbalbr{\begin{array}{rl}</kbd></dd>
<dd><kbd>
             x & \text{\ if\ } x \geq 0 \\</kbd></dd>
<dd><kbd>
            -x & \text{\ if\ } x < 0</kbd></dd>
<dd><kbd>
            \end{array}} \]</kbd></dd>
</dl>
<p>
produces
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block" mode="display"
><mfenced open="|" close="|"><mi>x</mi></mfenced><mo>=</mo><mfenced open="{" close =""
><mtable
><mtr><mtd columnalign="right"><mi>x</mi></mtd
><mtd columnalign="left"><mtext
> if </mtext
><mi>x</mi><mo>≥</mo><mn>0</mn></mtd
></mtr><mtr><mtd columnalign="right"><mo>−</mo><mi>x</mi></mtd
><mtd columnalign="left"><mtext
> if </mtext
><mi>x</mi><mo><</mo><mn>0</mn></mtd
></mtr></mtable
></mfenced
></math>
In this example note that the command name <em>lbalbr</em> stands for
“<b>l</b>eft <b>bal</b>anced <b>br</b>ace”. It corresponds to
the use of <kbd>\left\{  ...  \right.</kbd> in <em>LaTeX</em><sup><a id="revfnote39" href="#fnote39">39</a></sup>.
</p>
</dd>
<dt><b>\aos;, \aoc; \aoq;, and \aoe;</b></dt>
<dd> are the
named forms of the <em>LaTeX</em> space adjustment commands “<kbd>\@.</kbd>”,
“<kbd>\@,</kbd>”, “<kbd>\@?</kbd>”, and “<kbd>\@!</kbd>”, which
provide correct placement of inline punctuation immediately following
inline mathematical markup. There is now also default provision in the
didactic production system for the more <em>LaTeX</em>-like “<kbd>\@</kbd>” usage. Note that the
use of <kbd>\@</kbd> is seldom necessary.
</dd>
</dl>
<p>
</p>
</div>
<div class="subsection">
<h4>6.2.  <a id="SU-6.2"></a><a id="assert"></a>Assertions: Near Emulation of
<em>LaTeX</em>'s Theorem-Like Environments</h4>
<div class="subsubsection">
<h5>6.2.1.  <a id="SU-6.2.1"></a>Examples</h5>
<p>The container element <em>\assertion</em> is used in the didactic document type for the
creation of its analogue under SGML of theorem-like environments. As
a first example of the near emulation of a <em>LaTeX</em> theorem-like
environment, here is markup to give <em>LaTeX</em>-like meaning to
“<kbd>\begin{theorem}</kbd>” and “<kbd>\end{theorem}</kbd>”.
</p>
<dl class="verblist">
<dd><kbd>
\newcommand{\begin{thm}}[1][]{%</kbd></dd>
<dd><kbd>
\begin{assertion}[#1][theorem]{Theorem}[\evalref{\popkey}]}</kbd></dd>
<dd><kbd>
\newcommand{\end{thm}}{\end{assertion}}</kbd></dd>
</dl>
<p>
For a first instance it is invoked without supplying the optional first
argument, which is for a label key.
<a id="AssertLabel-1"></a></p>
<dl class="assertion">
<dd>
<b>Theorem 1.</b>
  The continued fraction expansion of a real number is finite
if and only if the real number is a rational number. </dd></dl>
<p>
This is just text to follow the statement of a theorem. </p>
<p>If we do the same thing again, the theorem number should go up by
<math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
> since in the didactic production system this usage is equivalent to using the default
counter associated with a label series name <em>theorem</em>.<sup><a id="revfnote40" href="#fnote40">40</a></sup>
<a id="AssertLabel-2"></a></p>
<dl class="assertion">
<dd>
<b>Theorem 2.</b>
  The continued fraction expansion of a rational number is
eventually periodic if and only if the real number is an irrational
number that is the root of some quadratic polynomial with rational
coefficients. </dd></dl>
<p>
</p>
</div>
<div class="subsubsection">
<h5>6.2.2.  <a id="SU-6.2.2"></a><a id="assertion"></a>Usage for <em>assertion</em></h5>
<p>The general usage of <em>assertion</em> is the following:
</p>
<dl>
<dd> <kbd>\begin{assertion}[</kbd><em>key</em><kbd>][</kbd><em>series</em>
<kbd>]{</kbd><em>name</em><kbd>}[</kbd><em>id</em><kbd>]</kbd></dd>
<dd> <kbd>  .  .  .</kbd></dd>
<dd> <kbd>\end{assertion}</kbd></dd>
</dl>
<p>
The options <em>key</em> and <em>series</em> represent the same things as
the corresponding <a href="#seq"><em>label</em></a> (section 5.5.1) options. The <em>id</em>
option is for explicit customization of the visible identifier, e.g.,
theorem number, as illustrated with one of the examples later in this
section. One may use the <em>id</em> option, which must follow
the name argument, without using either of the other options. But in
order to use the <em>series</em> option, a <em>key</em> option, which may
simply be empty, must be present. </p>
<p>There is also a fully named way to proceed:
</p>
<dl>
<dd> <kbd>\begin{assertion}</kbd></dd>
<dd> <kbd>\asstkey{. . .}\asstser{. . .}\asstname{. . .}\asstid{. . .}</kbd></dd>
<dd> <kbd>  .  .  .</kbd></dd>
<dd> <kbd>\end{assertion}</kbd></dd>
</dl>
<p>
Here order is important, but any of the options may simply be omitted.
For example, we may write
</p>
<dl class="verblist">
<dd><kbd>
\newcommand{\begin{Thm}}[1]{%</kbd></dd>
<dd><kbd>
\begin{assertion}\asstser{#1}\asstname{Theorem}%</kbd></dd>
<dd><kbd>
\asstid{\sref;.\evalref{\popkey}}%</kbd></dd>
<dd><kbd>
}</kbd></dd>
<dd><kbd>
\newcommand{\end{Thm}}{\end{assertion}}</kbd></dd>
<dd><kbd>
\begin{Thm}{XXseries}</kbd></dd>
<dd><kbd>
If $[ n_1, n_2, \ldots ]$ is an infinite continued fraction, then</kbd></dd>
<dd><kbd>
its sequence of convergents always has a limit.</kbd></dd>
<dd><kbd>
\end{Thm}</kbd></dd>
</dl>
<p>
to obtain:
<a id="AssertLabel-3"></a></p>
<dl class="assertion">
<dd>
<b>Theorem 6.2.2.1.</b>
  If <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mfenced open="[" close ="]"
><mrow><msub><mi>n</mi><mn>1</mn></msub
><mo>,</mo><msub><mi>n</mi><mn>2</mn></msub
><mo>,</mo><mi>…</mi></mrow></mfenced
></math
> is an infinite continued fraction, then
its sequence of convergents always has a limit. </dd></dl>
<p>
Notice that the <em>asstid</em> argument is merging the reference value
for (the new) series <em>XXseries</em> with the visible id of the
current sectional unit.
</p>
</div>
</div>
<div class="subsection">
<h4>6.3.  <a id="SU-6.3"></a><a id="eqn"></a>Equations and Equation Arrays</h4>
<p>The general usage for <em>equation</em> is the following:
</p>
<dl>
<dd> <kbd>\begin{equation}[</kbd><em>key</em><kbd>][</kbd><em>series</em><kbd>]</kbd></dd>
<dd> <kbd>  .  .  . </kbd></dd>
<dd> <kbd>\end{equation}</kbd></dd>
</dl>
<p>
The options <em>key</em> and <em>series</em> represent the same things as
the corresponding <a href="#seq"><em>label</em></a> (section 5.5.1) options. In order to use
the <em>series</em> option, a <em>key</em> option, which may simply be
empty, must be present. The use of “<kbd>equation*</kbd>” as a name for an
equation display that is not numbered is
not permitted, but one may instead use the <em>nonum</em> attribute
as follows:
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\begin{equation}[:nonum="true"] . . . \end{equation}</kbd> .</td></tr></tbody></table></div>
<p></p>
<p>General usage for an equation array (name <em>eqnarray</em>) is:
</p>
<dl>
<dd> <kbd>\begin{eqnarray}[</kbd><em>key</em><kbd>][</kbd><em>series</em><kbd>]</kbd></dd>
<dd> <kbd>  .  .  . </kbd></dd>
<dd> <kbd>\end{eqnarray}</kbd></dd>
</dl>
<p>
where the content is an <em>eqnabody</em> consisting of <em>eqnrow</em>'s,
each row may be terminated in <em>LaTeX</em>-like markup, as in <em>LaTeX</em>, with the
string “<kbd>\\</kbd>” and consists of three parts, corresponding to elements
<em>eqnleft</em>, <em>eqncenter</em>, and <em>eqnright</em>, that may
be separated in <em>LaTeX</em>-like markup with the character ‘<kbd>&</kbd>’. </p>
<p>Support for numbering in eqnarrays is only minimally developed
although there is suggestive sketching in the didactic document type that is not
supported in the formatters. By default the equations in equation
arrays are numbered consecutively throughout an article. This
behavior can be altered by using the <em>series</em> attribute of an
<em>eqnarray</em>. If that is done, then, as things have been sketched,
numbering applies to whole arrays rather than to the equations within
arrays. Numbering in an equation array may be suppressed by setting
its attribute <em>nonum</em> to the string “<kbd>true</kbd>”.
</p>
</div>
<div class="subsection">
<h4>6.4.  <a id="SU-6.4"></a><a id="mathsym"></a>The \mathsym Metacommand</h4>
<p><em>mathsym</em> is a macro substitution metacommand that is
available in the didactic production system for enabling an author to declare that a macro
name represents a mathematical symbol. It is a formal way of
recording statements commonly made by authors in introducing notation. </p>
<p>Unlike regular metacommands, which may appear at any point in
GELLMU source, <em>mathsym</em> may only appear in the <em>preamble</em>
of an <em>article</em>, or, equivalently with defaults in the
syntactic translator, <em>mathsym</em> may only appear before the <em>LaTeX</em>-like
“<kbd>\begin{document}</kbd>”. </p>
<p>Its usage is:
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>\mathsym{</kbd>
<em>symbol-name</em>
<kbd>}{</kbd>
<em>symbol-rendering</em>
<kbd>}[</kbd><em>symbol-meta-info</em>
<kbd>]</kbd> . </td></tr></tbody></table></div>
<p></p>
<p>Here <em>symbol-name</em> is an alphanumeric string (case-sensitive)
beginning with a letter. The second argument is the presentation
rendering of the symbol in GELLMU markup. It is like the definition
of a <em>newcommand</em> except that it may not involve
arguments.<sup><a id="revfnote41" href="#fnote41">41</a></sup>
The optional third argument <em>symbol-meta-info</em> is an
alpha-numeric string that might also include possibly a few other
string characters such as ‘<kbd>/</kbd>’, ‘<kbd>-</kbd>’, ‘<kbd>,</kbd>’,
‘<kbd>.</kbd>’, ‘<kbd>*</kbd>’, etc. Its exact structure depends on the
typing system. (No typing system is part of the didactic production system.) For example,
it might consist of (name, value) pairs for conveying meta-information
about the symbol. </p>
<p>The syntactic translator replaces each invocation of a given
<em>mathsym</em> with the specified rendering and writes for each
<em>mathsym</em> definition a corresponding element in the SGML output
whose content consists solely of the declared symbol name if there is
no meta information but otherwise consists of the symbol name followed
by a blank space and then whatever string of meta information is
provided in the optional argument. Additionally, each invocation is
wrapped in a rendering-inert <em>Sym</em> element whose <em>key</em>
attribute reveals the name given to the symbol at the point of
declaration (and by which the symbol is invoked). This makes it
possible for a downstream authoring platform processor that has
remembered the list of declared symbol names to match each invocation
of a declared symbol with its associated meta information, if any,
provided by the author in the symbol declaration. </p>
<p>A related feature in the didactic GELLMU document type is the
<em>mlg</em> tag for marking mathematical logical groups. This is
somewhat akin to the <em>lgg</em> tag for <em>TeX</em>-like logical groups,
traditionally created in <em>TeX</em> markup with braces that are not
attached to a command.<sup><a id="revfnote42" href="#fnote42">42</a></sup>
As with <em>lgg</em> there is no obvious evidence of an <em>mlg</em> tag
in a typeset rendering, but the presence of such a tag is intended as
a signal to downstream mathematical parsers that the contents of the
tag be given grouping priority as, say, with visible parentheses.
Furthermore, the <em>mtype</em> and <em>mml</em> attributes of the
<em>mlg</em> tag may be used to pass semantic information about the
tag's contents to a processor.
</p>
</div>
</div>
<div class="section">
<h3>7.  <a id="SU-7"></a><a id="dps"></a>The Didactic Production System</h3>
<p>The didactic production system is the suite of processors and technical support files
underlying what is called regular GELLMU.
</p>
<div class="subsection">
<h4>7.1.  <a id="SU-7.1"></a>Permission</h4>
<p>The items of the didactic production system are copyrighted free software released
under the <a href="http://www.gnu.org/copyleft/">GNU General Public License</a>.
</p>
</div>
<div class="subsection">
<h4>7.2.  <a id="SU-7.2"></a><a id="materials"></a>Materials</h4>
<p>The release contains everything originating with the author that is
currently used in “building” GELLMU documents. </p>
<p>It also contains a slightly <a href="../perllib/SGMLS.pm">modified version</a>
of David Megginson's <em>Perl</em> module “<kbd>SGMLS.pm</kbd>” based on
another slightly modified version that was furnished to me by Dave
Holden in a very quick early 1999 response to my posted request for a
modification that handles the labels provided (optionally) by
<em>nsgmls</em> for SGML elements that are defined empty. A similar
slight modification was also supplied a few days later by Vassilii
Kachaturov and had been available at his web site. </p>
<p>Although the materials offered in this package aside from the syntactic translator
pertain only to the didactic document type and the didactic production system, it should be understood that
the larger design for GELLMU envisions other parties, on the one
hand, building in various ways to extend the functionality of the
didactic system, and, on the other hand, applying the methods of the
didactic system to other document types and other formatting programs
for those document types. </p>
<p>The basic items originating with the author, aside from the document
type definition <a href="#dtdfiles">files</a> (section B.2.2) are:
</p>
<dl>
<dt><b><a href="../gellmu.el"><kbd>gellmu.el</kbd></a></b></dt>
<dd>the GELLMU syntactic translator, which makes SGML</dd>
<dt><b><a href="../xplaingart.pl"><kbd>xplaingart.pl</kbd></a></b></dt>
<dd>converts SGML to
author-level XML</dd>
<dt><b><a href="../xmlgart.pl"><kbd>xmlgart.pl</kbd></a></b></dt>
<dd>converts author-level XML
to elaborated XML</dd>
<dt><b><a href="../ltxgart.pl"><kbd>ltxgart.pl</kbd></a></b></dt>
<dd>translates elaborated XML
to <em>LaTeX</em></dd>
<dt><b><a href="../htmlgart.pl"><kbd>htmlgart.pl</kbd></a></b></dt>
<dd>translates elaborated XML
to classical HTML and translates specially prepared XML to XHTML+MathML</dd>
<dt><b><a href="../mathcdata.pl"><kbd>mathcdata.pl</kbd></a></b></dt>
<dd>first of two special
preparations for translation toward XHTML+MathML</dd>
<dt><b><a href="../mathprep.pl"><kbd>mathprep.pl</kbd></a></b></dt>
<dd>second of two special
preparations for translation toward XHTML+MathML</dd>
<dt><b><a href="../mval.pl"><kbd>mval.pl</kbd></a></b></dt>
<dd>check for certain types of MathML errors</dd>
</dl>
<p></p>
<p>Since some users will only be interested in the syntactic translator, additional
description of these materials is found below in
<a href="#usingdps">“Using the didactic production system”</a> (section 7.5) and in the
<a href="#release">Release Notes</a> (appendix B).
</p>
</div>
<div class="subsection">
<h4>7.3.  <a id="SU-7.3"></a><a id="requiredsoftware"></a>Other Required Software</h4>
<p>To make use of the GELLMU syntactic translator a user must have or separately acquire
<a href="http://www.gnu.org/software/emacs/"><em>Emacs</em></a>.<sup><a id="revfnote43" href="#fnote43">43</a></sup>
(“Windows” users should look at the special
<a href="http://www.gnu.org/software/emacs/windows">FAQ</a>.) <em>Emacs</em> is
commonly found on GNU/Linux systems and on *ix systems. It may be
found on other systems when provided by system managers.<sup><a id="revfnote44" href="#fnote44">44</a></sup></p>
<p>To make use of the didactic production system beyond the syntactic translator a user must have or acquire
the following items of free cross-platform software
</p>
<ul>
<li><p> an ESIS
generating SGML parser such as found in the cross-platform package
<a href="http://www.jclark.com/sp/"><em>SP</em></a> by James Clark,
which has stood the test of years, or the newer variant
<a href="http://openjade.sourceforge.net/"><em>OpenSP</em></a>, which
is internationalized, from the <em>OpenJade</em> Team.
</p>
</li>
<li><p> <a href="http://www.cpan.org/"><em>Perl</em> at CPAN</a>.
</p>
</li>
<li><p> a complete <em>TeX</em> system, for which one may look to
<a href="http://www.tug.org">The <em>TeX</em> Users Group (TUG)</a> or
The Comprehensive <em>TeX</em> Archive Network
(<a href="http://www.ctan.org">CTAN</a>).
</p>
</li>
<li><p> <em>xmlwf</em> — a basic utility that is part of the release of
James Clark's <a href="http://expat.sourceforge.net/"><em>expat</em></a>.
</p>
</li>
</ul>
<p>
</p>
</div>
<div class="subsection">
<h4>7.4.  <a id="SU-7.4"></a>Using the syntactic translator</h4>
<p>This explains how to use the syntactic translator, which is the Emacs Lisp program
contained in the file <a href="../gellmu.el"><kbd>gellmu.el</kbd></a>.
</p>
<div class="subsubsection">
<h5>7.4.1.  <a id="SU-7.4.1"></a>Operation in Batch Mode</h5>
<p>For linux and the other *ix a script like <a href="../bin/linux/g2s"><kbd>bin/linux/g2s</kbd></a> will be
adequate if your working directory is the distribution directory<sup><a id="revfnote45" href="#fnote45">45</a></sup>.
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
Usage: <kbd>g2s  </kbd><em>stem-name</em>
<kbd>  [ </kbd><em>function-call</em><kbd> ]</kbd> </td></tr></tbody></table></div>
<p>
For example, if “<kbd>foo.glm</kbd>” is the name of the source file, then
the first argument should be “<kbd>foo</kbd>”. The optional second
argument <em>function-call</em> is the name of the function in the Emacs
Lisp package “<kbd>gellmu.el</kbd>” that is to be used. The function
call defaults to “<kbd>gellmu-trans</kbd>”, which is the correct name for
<em>LaTeX</em>-like usage under the <a href="#ddt">didactic document type</a> (section 5). </p>
<p>There are also parallel scripts “<kbd>g2h</kbd>” and “<kbd>g2x</kbd>”. </p>
<p>“<kbd>g2s</kbd>” will byte compile “<kbd>gellmu.el</kbd>” if
“<kbd>gellmu.elc</kbd>” is not present. </p>
<p>“<kbd>g2h</kbd>” runs the function <em>gellmu-html</em> for the case
where the GELLMU file has been written directly for HTML.
The file <a href="ghtml.glm"><kbd>ghtml.glm</kbd></a> and the derived file <a href="ghtml.html"><kbd>ghtml.html</kbd></a>
are examples. </p>
<p>“<kbd>g2x</kbd>” runs the function <em>gellmu-xml</em> for the case
where the GELLMU file has been written directly for XML. </p>
<p>The directory “<kbd>bin/win32</kbd>” contains parallel, though more
complicated, batch files for use in a “DOS” command line
under “Windows”.
</p>
</div>
<div class="subsubsection">
<h5>7.4.2.  <a id="SU-7.4.2"></a>Interactive Operation</h5>
<p>Open GNU <em>Emacs</em> interactively on the GELLMU source file. When
finished editing the source, save it but keep <em>Emacs</em> open. Then do
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>M-x load-file gellmu.el</kbd></td></tr></tbody></table></div>
<p>
and
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>M-x gellmu-trans</kbd> . </td></tr></tbody></table></div>
<p></p>
<p>(It is better to have byte-compiled “<kbd>gellmu.el</kbd>” and if the
byte-compiled version “<kbd>gellmu.elc</kbd>” is in your <em>Emacs</em>
<em>load-path</em>, then
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>M-x load-library gellmu</kbd></td></tr></tbody></table></div>
<p>
is faster.)</p>
<p>The SGML output should come up in a second buffer. Save that buffer
to save the output. </p>
<p>Make any corrections or changes in the GELLMU source buffer and re-run
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<kbd>M-x gellmu-trans</kbd> . </td></tr></tbody></table></div>
<p></p>
<p>As with batch operation the functions <em>gellmu-html</em> and
<em>gellmu-xml</em>, may be handled parallel to <em>gellmu-trans</em>. </p>
<p>There are a number of other functions besides these three for
obtaining syntactic translation from GELLMU source to SGML. Each of
these is, in fact, a front for calling <em>gellmu-trans</em> with
various combinations of variable settings. There are a great many
user configurable variables in the syntactic translator. Notable
among these for <a href="#regular"><em>regular</em> GELLMU</a> (section 4.1) are (1)
<em>gellmu-parb-nogo</em> and (2) <em>gellmu-autoclose-list</em>.
See the variable documentation text, available interactively when the
GELLMU library is loaded in <em>Emacs</em> with the key combination
qquostrC-h C-h v, for more information. For a list of the names of
all user configurable variables see the variable documentation for
<em>gellmu-public-vars</em>. </p>
<p>For example, setting <em>gellmu-verblist</em> true causes a sequence of lines
beginning with the line “<kbd>\begin{verbatim}</kbd>” and ending
with the line “<kbd>\end{verbatim}</kbd>” to be considered
<em>verbatim</em> as in <em>LaTeX</em>, i.e., without requiring escaped forms
of special characters, and then to be set as a simple <em>verblist</em>,
which is in most circumstances superior to GELLMU's version of
pre-historic <em>verbatim</em>.<sup><a id="revfnote46" href="#fnote46">46</a></sup>
</p>
</div>
<div class="subsubsection">
<h5>7.4.3.  <a id="SU-7.4.3"></a><a id="interrupt"></a>Interrupting the Syntactic
Translator</h5>
<p>Interruption of the GELLMU syntactic translator will be necessary in the event that the
combined use of <em>newcommand</em>, <em>macro</em>, <em>Macro</em>,
and <em>mathsym</em> (advanced mode only) leads to infinite recursive
loops. Users should avoid the use of <em>macro</em> and <em>Macro</em>
unless such use is absolutely necessary since these metacommands
present greater looping risks. </p>
<p>Inasmuch as there are two ways to invoke the syntactic translator, there are two
different procedures for interrupting it should that be necessary.
</p>
<dl>
<dt><b>
Batch mode invocation</b></dt>
<dd>This is the case when GNU <em>Emacs</em> is launched
in batch processing mode to run the syntactic translator. To interrupt the syntactic translator in this
case one must interrupt the <em>Emacs</em> process. The author does not
know of any case when <em>Emacs</em> does not respond to standard interrupts.
For example, on <em>linux</em> systems pressing “Control-C”
when the process was launched from a shell provides a standard interrupt.
If the processed was launched in some other way, a normal “<kbd>kill</kbd>”
addressed to the process should have the same effect.
</dd><dt><b>
Interactive invocation</b></dt>
<dd>This is the case when the syntactic translator is launched
from within the GNU <em>Emacs</em> editing interface. Use the standard <em>Emacs</em>
function “quit”, accessed with the key “<kbd>C-g</kbd>” (Control-G)
to interrupt the syntactic translator.
</dd></dl>
<p>
</p>
</div>
</div>
<div class="subsection">
<h4>7.5.  <a id="SU-7.5"></a><a id="usingdps"></a>Using the didactic production system</h4>
<div class="subsubsection">
<h5>7.5.1.  <a id="SU-7.5.1"></a>Staged Design</h5>
<p>The items in the didactic production system are components for use with staged processing.
The document type may be used with any SGML system. Of course, one
may not use a parser that is limited to XML with the SGML version of
the document type. Moreover, if one makes use of features in the
SGML version such as the positional argument and option elements,
then one might want to provide translation to the XML version of the
document type. </p>
<p>No particular processing system is required for the XML version of
the document type. For example, one might profitably write an
<a href="http://www.w3.org/TR/xslt">XSLT</a> sheet for translation to some
other format and then submit the document and the XSLT sheet
to an XSLT engine such as <em>xt</em>, <em>xsltproc</em>, or
<em>saxon</em>.
</p>
</div>
<div class="subsubsection">
<h5>7.5.2.  <a id="SU-7.5.2"></a>Default Staging</h5>
<p>The release includes <a href="../bin/linux/lmkg"><kbd>bin/linux/lmkg</kbd></a> and
<a href="../bin/linux/mmkg"><kbd>bin/linux/mmkg</kbd></a> as example driver scripts for running the
following sequence. (The <a href="../bin/win32"><kbd>bin/win32</kbd></a> directory contains
old driver scripts for the MS Windows command line that might someday
be worth updating.) The behavior of these driver scripts depends
on the way they are called though the specific of this are somewhat
different for <kbd>lmkg</kbd> than for <kbd>mmkg</kbd>. The older
<kbd>lmkg</kbd> scripts do not generate XHTML+MathML at this point they are
provided primarily for backward compatibility. </p>
<p>The <kbd>mmkg</kbd> scripts by default make XHTML+MathML but not if called by
a name, e.g., via a symbolic link, without the substring “<kbd>mm</kbd>”.
If an <kbd>mmkg</kbd> script is called with a name ending in the string
“<kbd>froms</kbd>” or “<kbd>fromx</kbd>”, then it will take as starting
point, respectively, an SGML, i.e., “<kbd>.sgml</kbd>”, or author-level
XML, i.e., “<kbd>.xml</kbd>”, version of the document. Thus, for
example, <kbd>mmkgfromx</kbd> might be used to operate on a document
that is an author-level XML translation from a non-GELLMU source. </p>
<p><b>Caution.</b> These scripts, like all shell scripts, should be
examined for file system locations, system environmental variables,
and other platform-specific and location-specific issues. The user
who introduces a script on a platform should understand the script.
A user who does not understand a script should not attempt to
introduce it on a local platform. </p>
<p><a id="flow"></a> Flow in the didactic production system is portrayed in the following diagram:
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<img src="gcompst.png" alt="Image file: gcompst.png" />
</td></tr></tbody></table></div>
<p></p>
<p>These are the stages in the didactic production system pipeline:
</p>
<ol class="decimal">
<li><p> Prepare GELLMU source using a text editor.
</p>
</li>
<li><p> Process the source with the syntactic translator to obtain an SGML document under
the didactic document type.
</p>
</li>
<li><p> Use <em>nsgmls</em> to validate the SGML document and obtain an
ESIS for it as output.
</p>
</li>
<li><p> Submit the SGML ESIS as input<sup><a id="revfnote47" href="#fnote47">47</a></sup>
to the <em>Perl</em>
program <em>sgmlspl</em> with the script <a href="../xplaingart.pl"><kbd>xplaingart.pl</kbd></a>
as file argument, obtaining an author-level XML document.
</p>
</li>
<li><p> Use <em>nsgmls</em> to validate the author-level XML document
and then submit its ESIS as input to to <em>sgmlspl</em>
with the script <a href="../xmlgart.pl"><kbd>xmlgart.pl</kbd></a>, obtaining an elaborated
XML document. This document, which is accompanied by several
auxiliary files<sup><a id="revfnote48" href="#fnote48">48</a></sup>,
has things such as sectional unit numbers and cross references
fully resolved so that there will be consistency in these across
the various output formats.
</p>
</li>
<li><p> Use <em>nsgmls</em> to validate the elaborated XML document and
submit its ESIS as input multiply to <em>sgmlspl</em>:
</p>
<ol class="lower-alpha">
<li><p> with the script <a href="../htmlgart.pl"><kbd>htmlgart.pl</kbd></a> to obtain a
classical HTML document that then will be validated if an
HTML validation program is identified in the driver script.
</p>
</li>
<li><p> with the script <a href="../ltxgart.pl"><kbd>ltxgart.pl</kbd></a>
as file argument, obtaining a <em>LaTeX</em> document. The <em>LaTeX</em>
document is then built with <em>latex</em> to make a DVI
file and with <em>pdflatex</em> to make a PDF file.
</p>
</li>
<li><p> for a pipeline using successive runs of <em>sgmlspl</em> with
3 scripts, <a href="../mathcdata.pl"><kbd>mathcdata.pl</kbd></a>, <a href="../mathprep.pl"><kbd>mathprep.pl</kbd></a>,
and <a href="../htmlgart.pl"><kbd>htmlgart.pl</kbd></a> (called in a special way) to make
a XHTML+MathML file that is then checked for XML well-formedness
using <em>xmlwf</em>, checked for certain kinds of MathML
errors using <em>sgmlspl</em> with <a href="../mval.pl"><kbd>mval.pl</kbd></a>, and
validated if a suitable validation program is
identified in the driver script.
</p>
</li>
</ol>
</li>
</ol>
<p>
</p>
</div>
<div class="subsubsection">
<h5>7.5.3.  <a id="SU-7.5.3"></a>Parsing with <em>nsgmls</em></h5>
<p>The program <em>nsgmls</em> is part of the
<a href="http://www.jclark.com/sp/">SP</a> package, which includes
extensive documentation. Those familiar with it will want to ignore
these hints. </p>
<p>Since for both the SGML and the XML versions of the didactic document type SP
requires non-default SGML declarations, it is recommended that the user
employ SGML catalogs, one for SGML and another for XML.
The file system location of a catalog is conveyed to <em>nsgmls</em>
as the value of its command line argument immediately following the
argument “-c”. </p>
<p>Each catalog should contain an SGMLDECL directive that is the
file system location of an SGML declaration. Aside from that a catalog
may contain a number of three string lines of either of the following
forms
</p>
<dl>
<dd> PUBLIC  <em>formal-public-identifier</em>  <em>quoted-pathname</em></dd>
<dd> SYSTEM  <em>quoted-system-identifier</em>  <em>quoted pathname</em></dd>
</dl>
<p>
where the quoted pathname, which may be relative to the location of the
catalog, should for this context in each case be that of a
DTD file. </p>
<p>It is recommended in each case that <em>nsgmls</em> be run with
arguments “-l” (for propagating line number references) and
“-oempty” (for flagging defined-empty elements). For
processing the XML version of the didactic document type one should additionally use
the argument “-wxml”. </p>
<p>Additionally, a user may wish to make locally-specific arrangements
for the handling of character sets.
</p>
</div>
<div class="subsubsection">
<h5>7.5.4.  <a id="SU-7.5.4"></a>Processing with <em>sgmlspl</em></h5>
<p>The program <em>sgmlspl</em> is part of David Megginson's
SGMLSPM package. Megginson's extensive documentation for it
may be found in the (December 1995) release found at
<a href="http://www.cpan.org/">CPAN</a>.<sup><a id="revfnote49" href="#fnote49">49</a></sup></p>
<p>One uses <em>sgmlspl</em> by calling the Perl program <em>sgmlspl</em>
with an ESIS as input and a script as argument. Additional
arguments become arguments for the script. </p>
<p>Although some operating systems provide a way for dealing with a Perl
program, which is stored in a text file, as an executable object, in
other cases one must explicitly call the Perl engine as a program with
an ESIS as input, the system name of <em>sgmlspl</em> as first
argument, and (the system name of) a script as second argument. In
both cases one will want to arrange, perhaps with an environmental
variable or perhaps with the “-I” argument to the Perl engine,
for the directory containing “<kbd>SGMLS.pm</kbd>” and its supporting
module “<kbd>SGMLS/Output.pm</kbd>” to be in its path array
<kbd>@INC</kbd>.
</p>
</div>
<div class="subsubsection">
<h5>7.5.5.  <a id="SU-7.5.5"></a><a id="environmentals"></a>Environmental Variables</h5>
<p>There are a number of environmental variables that affect processing
in the didactic production system. The names all begin with the string “<kbd>GELLMU_</kbd>”.
Of course, the names are case-sensitive. </p>
<p>Many of these variables are set in the distributed driver scripts.
When that is the case, the distributed driver scripts commonly check
for a previous setting (which may, therefore, be easily placed in a
fronting script that makes a setting and then just calls the
distributed driver). </p>
<p>Setting environmentals can be difficult in a non-Unix-like
operating system environment. This is one reason why the author
generally recommends that Windows users install GELLMU under
<a href="http://www.cygwin.com/"><em>Cygwin</em></a>.
</p>
<dl>
<dt><b><kbd>GELLMU_Dir</kbd></b></dt>
<dd> The top of the directory tree where GELLMU is installed.
</dd>
<dt><b><kbd>GELLMU_StyleDir</kbd></b></dt>
<dd> URI or directory location of CSS and XSLT style
sheets that is used by the didactic production system in writing links in XML,
HTML and XHTML+MathML files.
The value usually has a different meaning under the eye of a
web server than in a local file system. A relative URI or
path is usually best. A value like “<kbd>../webstyle</kbd>”
can often be made to work both ways.
</dd>
<dt><b><kbd>GELLMU_CSSName</kbd></b></dt>
<dd> Name, relative if given relative syntax, to the value of
<kbd>GELLMU_StyleDir</kbd>, of the CSS stylesheet written by the
didactic production system in HTML and XHTML+MathML files.
</dd>
<dt><b><kbd>GELLMU_XhtmlSuffix</kbd></b></dt>
<dd> Suffix given to XHTML or XHTML+MathML files written
by <kbd>htmlgart.pl</kbd>.
</dd>
<dt><b><kbd>GELLMU_NoUMSS</kbd></b></dt>
<dd> Value <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>0</mn></math
> or <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>: if <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>, signals to <kbd>htmlgart.pl</kbd>
that it should not link to W3C's
<a href="http://www.w3.org/Math/XSL/">UMSS</a> XSLT
stylesheets.
</dd>
<dt><b><kbd>GELLMU_UTF8</kbd></b></dt>
<dd> Value <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>0</mn></math
> or <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>: signals to <em>sgmlspl</em> scripts that
Perl's handling of the UTF-8 text encoding should be invoked.
The meaning is subtly different between Perl versions 5.6
and 5.8.
</dd>
<dt><b><kbd>GELLMU_Encoding</kbd></b></dt>
<dd> String value for text encoding that is set by the
<kbd>xplaingart.pl</kbd> in writing author-level XML and by
<kbd>xmlgart.pl</kbd> in writing elaborated XML. (HTML,
XHTML, and XHTML+MathML are always written with the UTF-8
encoding.)
</dd>
<dt><b><kbd>GELLMU_LaTeXUTF8</kbd></b></dt>
<dd> Value <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>0</mn></math
> or <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>: signals to <em>latex</em> and
<em>pdflatex</em> to expect the UTF-8 encoded text in
their input.
</dd>
<dt><b><kbd>GELLMU_LaTeXStyle</kbd></b></dt>
<dd> Pathname for <em>LaTeX</em> stylesheets that <em>latex</em>
and <em>pdflatex</em> should use when such stylesheets are
not properly positioned for <em>TeX</em> system KPSE-based
location. (It's better to use a local or personal
TDS tree.)
</dd>
<dt><b><kbd>GELLMU_PAPER</kbd></b></dt>
<dd> String value for the paper used in printing; becomes an
option for the <em>documentclass</em> command in the output
<em>LaTeX</em> file.
</dd>
<dt><b><kbd>GELLMU_Memoir</kbd></b></dt>
<dd> Value <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>0</mn></math
> or <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>: if <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>, use the <em>memoir</em>, rather
than <em>article</em>, documentclass in the output <em>LaTeX</em> file.
</dd>
<dt><b><kbd>GELLMU_DefaultEmptyEqncenter</kbd></b></dt>
<dd> <em>Experimental.</em> String value
consisting of a small bit of <em>LaTeX</em> wrapped as a Perl
string to use in tweeking the <em>LaTeX</em>-rendered appearance of
a GELLMU <em>eqnarray</em> (which is rendered in <em>LaTeX</em> using
either <em>align</em> or <em>aligned</em>, depending on
numbering arrangments) in the case of an empty middle cell
(<em>eqncenter</em>). The current default value used in
<kbd>ltxgart.pl</kbd> is the string “<kbd> \qquad </kbd>”. Be
mindful of how such a string can be entered as a literal
string in Perl or as part of an on-the-fly environmental
setting from a command line shell.
</dd>
<dt><b><kbd>GELLMU_XLink</kbd></b></dt>
<dd> Value <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>0</mn></math
> or <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>. How to handle links in MathML output
when writing XHTML+MathML. Such links, which are currently
illegal inside XHTML+MathML math zones, are confined to
<kbd>\text{...}</kbd> areas in GELLMU. If the value is <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mn>1</mn></math
>, use
XLink; otherwise, switch into the HTML namespace and
write an HTML anchor. (<em>Firefox</em> handles both,
while more of the other browsers seem to choke on the
namespace switch than choke on the necessarily cumbersome
use of XLink.)
</dd>
<dt><b><kbd>GELLMU_OriginLabel</kbd></b></dt>
<dd> Name for an automatic label key, chiefly of occasional
value for HTML and XHTML+MathML outputs, that, when this
variable is present in the environment, places a link target,
with id the value of this variable, at the top of the document.
</dd>
</dl>
<p>
</p>
</div>
</div>
</div>
<div class="section">
<h3>Appendix A.  <a id="SU-8"></a><a id="KEY-5"></a><a id="archive"></a>The GELLMU Archive</h3>
<p>The GELLMU Archive is the web site
<a href="http://www.albany.edu/~hammond/gellmu/"><kbd>http://www.albany.edu/~hammond/gellmu/</kbd></a>. </p>
<p>It is the source for late breaking information about GELLMU.
Among other things, it houses a largely uncommented
<a href="http://www.albany.edu/~hammond/gellmu/examples">archive of examples</a>. This is provided
in the belief that the study of examples is one of the quickest
ways to learn a markup language. </p>
<p>Of course, this document, which is furnished with the release,
is also an example. </p>
<p>Another item, also an example, that is housed in the archive
is <a href="http://www.albany.edu/~hammond/gellmu/examples/gfaq.html">The GELLMU FAQ</a>.
</p>
</div>
<div class="section">
<h3>Appendix B.  <a id="SU-9"></a><a id="KEY-6"></a><a id="release"></a>Release Notes</h3>
<p>This version of the manual was prepared for release 0.8.5 in
July 2007. The <a href="#materials">GELLMU materials</a> (section 7.2) consist of:
</p>
<ol class="decimal">
<li><p> The manual, which is this document.
</p>
</li>
<li><p> The GELLMU syntactic translator, a <em>Emacs</em> Lisp program, which is the only
item of software required for those who simply wish to use GELLMU
markup for the conscious preparation of HTML documents or documents
under some other classical SGML or XML document type for which the
user is otherwise equipped.
</p>
</li>
<li><p> The GELLMU didactic production system, which consists of
an SGML document type called <em>article</em>, an XML document type
also called <em>article</em>, and three separate collections of <em>Perl</em>
functions for the well-known <em>Perl</em> SGML processing framework
<em>sgmlspl</em> by <a href="http://www.megginson.com/">David Megginson</a>.
A very slightly modified version of Megginson's <em>Perl</em> library
<em>SGMLSpm</em> that provides a method for detecting defined-empty
SGML elements, as flagged in an SGML parse stream in ESIS
format, is included as part of the didactic production system.
Since it is by size 60% of the software content of the
Megginson package on <a href="http://www.cpan.org/">CPAN</a>, the rest of the
package, licensed under the GNU
<a href="http://www.gnu.org/copyleft/gpl.html">General Public License</a>
is distributed with the didactic production system as well, though without its
documentation. The distribution includes 7 scripts for use with
<em>sgmlspl</em> in the didactic production system pipeline. For more
on this see <a href="#usingdps">“Using the didactic production system”</a> (section 7.5).
</p>
</li>
</ol>
<p>
</p>
<div class="subsection">
<h4>B.1.  <a id="SU-9.1"></a>Comments on the Syntactic Translator</h4>
<p>The GELLMU syntactic translator is more mature than the other components. The following
comments pertain to it.
</p>
<dl>
<dt><b>internationalization</b></dt>
<dd>
<p>Internationalization has a considerable and evolving
level of support in <em>Emacs</em>. The concept is that an author resides in
a locale. When the author enters a character from a locale, it gives
rise in <em>Emacs</em> to a somewhat complicated multibyte entity that can have
“properties”. Particularly relevant variables in <em>Emacs</em>
are: <kbd>coding-system-for-write</kbd> and
<kbd>buffer-file-coding-system</kbd>. GELLMU provides the user
variable <kbd>gellmu-sgml-default-coding</kbd>, which should be properly
coordinated via driver script settings with one's SGML parser.
</p>
</dd>
<dt><b>inclusions</b></dt>
<dd>
<p>It is not actually a limitation that a GELLMU source file cannot
be included in another. The primary reason is that one should
make use of the inclusion mechanism of SGML. For that one needs
to define the included pieces as entities in the direct internal
subset <sup><a id="revfnote50" href="#fnote50">50</a></sup>
of the source file and then reference each as an entity, e.g.,
“<kbd>&sect2;</kbd>” at the appropriate location in the source
file where it is to be included. Because the inclusion happens
at the SGML level there are two points to observe:
</p>
<ol class="decimal">
<li><p> Macro information is local to each source file. </p>
</li>
<li><p> The situation is optimal for the location of validation
errors provided that one's parser reports such errors by
filename and line number since the syntactic translator
provides line number alignment between source and generated
SGML. </p>
</li>
</ol>
<p></p>
<p>A second reason is that source inclusion would disturb
line number alignment between source and SGML output. This
is important for the interpretation of SGML validation error
messages. Such validation is considered routine, and plays an
important role in detecting an author's mistakes. Some author errors
are diagnosed in the syntactic translator. </p>
<p>A third reason, which at the same time might be considered also
a disadvantage, is that all of GELLMU's macro facilities are
local to each source file. This adds both robustness and flexibility
at the price of the inconvenience of physical inclusion of common
macro definitions.
</p>
</dd>
<dt><b>variable management</b></dt>
<dd>
<p>This refers to the management of user variables in the syntactic
translator. These are <em>Elisp</em> variables. One who is familiar with
<em>Elisp</em> should be able to provide values in batch mode without
making changes in the <em>Elisp</em> source.<sup><a id="revfnote51" href="#fnote51">51</a></sup>
Setting values interactively in the Emacs editing interface can be
done easily using “<kbd>M-x set-variable</kbd>”. </p>
<p>With a future release it is likely that additionally a user resource
file for custom variable settings without the need for writing <em>Elisp</em>
code will be provided.
</p>
</dd>
<dt><b>Bugs</b></dt>
<dd>
<p>No serious existing problem is known in the GELLMU syntactic translator at the time of this
release. Of course, as stated in source code comments, there is no
warranty of any kind. Please report bugs to the author:
<a href="mailto:hammond@math.albany.edu"><kbd>hammond@math.albany.edu</kbd></a>.
</p>
<ul>
<li><p> <b>Reserved element names.</b>
The GELLMU syntactic translator reserves for its own internal use all SGML or XML element
names in which the first numeric character in the range
“0–9” is the character “0”.
</p>
</li>
<li><p> <b>Limitation on braces in macros.</b>
Unbalanced braces are not permitted in either the name or the value
field of any form of macro metacommand.
</p>
</li>
<li><p> <b>First cell limitation.</b>
In the <em>LaTeX</em>-like emulation of an <em>array</em> or <em>tabular</em>
environment the first cell in each row must have something other than
whitespace. Of course, sometimes no content is wanted, and then
<kbd>\empty</kbd> (for nil markup, not to be confused with the mathematical
<kbd>\emptyset</kbd>) is one way to handle it, but this author usually uses
something that is mostly inconsequential like “<kbd>~</kbd>” or
“<kbd>\,</kbd>”. Another way to handle it is to invoke the names
of the SGML elements, i.e., <kbd>\firstcell{}</kbd> for <em>tabular</em> or
<kbd>\firstacell{}</kbd> for <em>array</em>.
</p>
</li>
<li><p> <b>Concept of advanced GELLMU immature.</b>
Inasmuch as didactic article is the only document type for
which the idea of advanced GELLMU has been implemented, the general
concept of advanced GELLMU is not fully developed in the GELLMU syntactic translator.
Basic GELLMU is characterized in the GELLMU syntactic translator by the evaluation of
the Boolean variable <em>gellmu-straight-sgml</em> to “true”.
This automatically make the Boolean variable
<em>gellmu-regular-sgml</em> true.
Full LaTeX-like support for the didactic production system is realized only by both
of these Booleans being false. Thus, advanced GELLMU will
need to evolve in the space in between, probably after the
introduction of further such Boolean variables, some public and
some private. This technique will make it possible for the
code to continue performing as now when the variable
<em>gellmu-straight-sgml</em>, the flag for basic GELLMU, is true
and also when both of these flags are false.
</p>
</li>
<li><p> <b>Reserved strings.</b>
The strings “<kbd><<</kbd>” and “<kbd>>></kbd>” have been reserved
as future notation for mathematical objects. Although it might seem
at first glance that this type of short hand has no place apart from
the fully <em>LaTeX</em>-like environment of the GELLMU syntactic translator in the context of the didactic production system, in
which they have not yet been used, it is actually not so clear that
one could not make sensible use of such notation in the context of
“XHTML plus MathML” under advanced GELLMU along with
other features such as blank lines for new paragraphs and many other
mathematical shortcuts. It awaits the further development of advanced
GELLMU, and reserving this notation is necessary to ensure backward
compatibility.
</p>
<p>Consequently, for example, entering “<kbd><<a>></kbd>” is
problematical, because only the first “<kbd><</kbd>” or “<kbd>></kbd>”
will be converted to something appropriate. In basic mode
“<kbd>&lt;</kbd>” and “<kbd>&gt;</kbd>” are one-step ways of
circumventing this when these entities are available, which is
guaranteed for any form of HTML as well as for any form of XML. In
the didactic production system one should use “<kbd>\ltc;</kbd>” and
“<kbd>\gtc;</kbd>”. For other cases the one-step circumvention is
to use entity references to the numeric character codes, e.g., in
ASCII “<kbd>&#3C;</kbd>” and “<kbd>&#3E;</kbd>”, and for
convenience these may be brought up as macros, perhaps
“<kbd>\lt</kbd>” and “<kbd>\gt</kbd>”.
</p>
</li>
</ul>
<p>
</p>
</dd>
</dl>
<p>
</p>
</div>
<div class="subsection">
<h4>B.2.  <a id="SU-9.2"></a>Comments on the Didactic Production System</h4>
<p>The didactic production system is to be understood as a potential base for development.
As such it is not intended ever to offer everything that might
be imagined. The following comments pertain to it.
</p>
<div class="subsubsection">
<h5>B.2.1.  <a id="SU-9.2.1"></a>Internationalization</h5>
<p>Internationalization has been a concern of the project. It is
possible, for example, to use the ISO-Latin-1
character ‘é’ in the name of an element. The
didactic <em>article</em> document type offers, for example, an element
<em>étale</em>, which is a style, parallel to <em>bold</em>.
Use of the character ‘é’ as a raw word character
data with the didactic production system is less robust than the more careful
“<kbd>\acute{e}</kbd>”<sup><a id="revfnote52" href="#fnote52">52</a></sup>
construction, which is desirable for translation of <em>article</em>
to formats that do not support latin1. For that matter, the
exact extent of <em>LaTeX</em>'s support of latin1 is a bit tricky, and
the whole matter of internationalization is currently under
review in the <em>LaTeX</em> project.<sup><a id="revfnote53" href="#fnote53">53</a></sup>
</p>
</div>
<div class="subsubsection">
<h5>B.2.2.  <a id="SU-9.2.2"></a><a id="doctypes"></a>Document Type Definitions</h5>
<p>Currently the project has one SGML document type definition
and two XML document type definitions. Files under the
various document types are suffixed as follows:
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<table><tbody>
<tr><td align="left">First stage SGML</td><td align="left"><kbd>.sgml</kbd></td></tr
><tr><td align="left">Author Level XML</td><td align="left"><kbd>.xml</kbd></td></tr
><tr><td align="left">Elaborated XML</td><td align="left"><kbd>.exml</kbd></td></tr
></tbody></table>
</td></tr></tbody></table></div>
<p></p>
<p>Additionally, in the three steps of processing to generate an
XHTML+MathML file from an elaborated XML file there are two intermediate
XML files generated, the first with suffix “<kbd>.yml</kbd>”, which
lives under the document type definition for an elaborated XML
document, and the second with suffix “<kbd>.zml</kbd>”, an XML file
for which there is no extant formal document type
definition.<sup><a id="revfnote54" href="#fnote54">54</a></sup></p>
<p>The author-level XML document type is formalized by the
DTD "axgellmu.dtd", while the elaborated XML document
type is formalized by a modification that is found in the DTD
"uxgellmu.dtd". (The latter was the only XML document type
used with the regular GELLMU production stream prior to
October, 2006.)</p>
<p>The document type represented by "uxgellmu.dtd" is now called the
elaborated XML document type. </p>
<p>The author-level XML document type is suitable as a translation
target from other markups. The elaborated XML document type
should not be used as a translation target other than from the
GELLMU author-level XML document type. </p>
<p>All document type definitions are available under the UTF-8
text encoding. The two older document type definitions will continue
to exist for a while under the Latin-1 (ISO-8859-1) text
encoding. The text encoding of a so-called DTD file (not
quite the same thing as a document type definition) is significant
in regard to the names of SGML/XML entities and
elements rather than in regard to document instances which might
be processed. The names of the DTD files are:
<a id="dtdfiles"></a>
</p>
<div class="display"><table class="gdisplay"><tbody><tr><td>
<table><tbody>
<tr class="bruled"><td class="rruled" align="left"> </td><td class="lruled" align="center">Latin-1</td><td align="center">UTF-8</td></tr
><tr class="truled"><td class="rruled" align="left">First stage SGML</td><td class="lruled" align="center"><kbd>gellmu.dtd</kbd></td><td align="center"><kbd>ugellmu.dtd</kbd></td></tr
><tr><td class="rruled" align="left">Author Level XML</td><td class="lruled" align="center"> </td><td align="center"><kbd>axgellmu.dtd</kbd></td></tr
><tr><td class="rruled" align="left">Elaborated XML</td><td class="lruled" align="center"><kbd>xgellmu.dtd</kbd></td><td align="center"><kbd>uxgellmu.dtd</kbd></td></tr
></tbody></table>
</td></tr></tbody></table></div>
<p>
</p>
</div>
<div class="subsubsection">
<h5>B.2.3.  <a id="SU-9.2.3"></a>Translation to XML</h5>
<p>Presently the author-level XML files link to a CSS stylesheet that
provides primitive rendering. One could go further in this direction,
but the rendering of mathematics will be limited without more development
in that direction of CSS.
</p>
</div>
<div class="subsubsection">
<h5>B.2.4.  <a id="SU-9.2.4"></a>Translation to HTML</h5>
<dl>
<dt><b>
Math in classic HTML</b></dt>
<dd>The classic HTML output does not use graphic images for mathematical
zones in the manner of programs like <em>latex2html</em>. Instead it
uses pseudo-<em>TeX</em> notation for math.
There are a
number of reasons:
<ol class="decimal">
<li><p> Well typeset mathematics is available in the modern form of
HTML that is more precisely called XHTML+MathML. </p>
</li>
<li><p> Graphical images completely block accessibility in the
sense of the World Wide Web Consortium's
<a href="http://www.w3.org/WAI/">Web Accesibility Initiative</a>. </p>
</li>
<li><p> The present classical HTML output files may be deciphered
in terminal window browsers. </p>
</li>
<li><p> The present classical HTML output files may be “dumped” to
plain text using a program such as <em>lynx</em> or <em>w3m</em>
for various sometimes useful purposes. </p>
</li>
</ol>
</dd><dt><b>
Style.</b></dt>
<dd>HTML and XHTML+MathML made with the didactic production system now rely on CSS, even, for
some things, level 2 CSS.
</dd></dl>
</div>
<div class="subsubsection">
<h5>B.2.5.  <a id="SU-9.2.5"></a>Translation to <em>LaTeX</em></h5>
<p>This translator writes <em>LaTeX</em><sub>2E</sub>. A number of packages, including
<em>graphicx</em>, <em>amsmath</em>, <em>amssymb</em>, <em>amsfonts</em>,
<em>bm</em>, <em>url</em> (not <em>hyperref</em> for the standard track
where the focus is on printed output), and <em>inputenc</em> for UTF-8
(which may be needed even if the GELLMU source or, otherwise, the
author-level XML source is not UTF-8 encoded).
Apart from current font availability issues, the author would have
preferred to invoke the T1 font encoding. </p>
<p>Even though GELLMU source uses the names <em>equation</em> and
<em>eqnarray</em>, in the <em>LaTeX</em> formatting <em>amsmath</em> constructions
are used. </p>
<p>A small modification of this translator can be used to write
Adobe's Portable Document Format (PDF) with pages sized for screens
rather than for paper.
</p>
</div>
<div class="subsubsection">
<h5>B.2.6.  <a id="SU-9.2.6"></a>Future Plans</h5>
<p>This is a very limited list.
</p>
<dl>
<dt><b>A literate document type definition.</b></dt>
<dd>
<p>Capable of spawning not only the 5 DTD's but type definitions
under other mechanisms such as, for example, <em>RelaxNG</em>.
</p>
</dd>
<dt><b>Mathematical Semantics</b></dt>
<dd>
<p>Provision for optional semantic tightening sufficient for authors
wishing to be able to export mathematical markup into computer algebra
systems.
</p>
</dd>
</dl>
<p>
</p>
</div>
</div>
</div>
<hr />
<h3>Footnotes</h3>
<ol>
<li><a id="fnote1" href="#revfnote1">*</a> The syntactic translator does, however, have some facilities for
classifying the names in a list in regard to common syntactic
behavior. See, in particular, the <em>Elisp</em> variables
<em>gellmu-autoclose-list</em> and <em>gellmu-parb-hold</em>, both
of which are not significant in basic GELLMU.</li>
<li><a id="fnote2" href="#revfnote2">*</a> With several minor exceptions, one related to the direct writing of
SGML attributes (which cannot contain markup and which do not have
many parallels in <em>LaTeX</em>) and another related to the way of escaping
the character ‘<kbd>\</kbd>’, everything about basic mode also
applies to advanced mode.</li>
<li><a id="fnote3" href="#revfnote3">*</a> There is a way, with the setting of several
variables for the syntactic translator in advanced mode, to have blank lines begin
new paragraphs in basic input for HTML</li>
<li><a id="fnote4" href="#revfnote4">*</a> This means that it is a relatively slow form of processing, but
the author believes that it is a good match for the intuitive
expectations of most <em>LaTeX</em> users. </li>
<li><a id="fnote5" href="#revfnote5">*</a> In a future release an alternative metacommand
called <em>frontcommand</em> may be provided which could be used, for
example, if one wishes to have a macro name of some kind match the
name of an actual SGML element. </li>
<li><a id="fnote6" href="#revfnote6">*</a> In the prototype production system based on
the didactic <em>article</em> document type the output from each
stage is available for examination and, where necessary, intervention.
However, such use of intervention is intended only for temporary
expedient use while a GELLMU system is being designed or enhanced.
As with <em>LaTeX</em>, enhancement is an ongoing process. </li>
<li><a id="fnote7" href="#revfnote7">*</a> In handling GELLMU source markup one could provide
a more elaborate processor that can be configured to know for each
such command the list of names for its positional arguments and
options. It was decided that this goes somewhat beyond syntactic
handling but that the question of whether a list of arguments and options
corresponds to sole content might be regarded as a syntactic matter. </li>
<li><a id="fnote8" href="#revfnote8">*</a> Its use is optionally permitted in basic mode as well. </li>
<li><a id="fnote9" href="#revfnote9">*</a> Indeed, <em>LaTeX</em> usage allows markup in options, but (element level)
markup is not permitted in SGML attributes. Note, however, that
in the didactic document type the SGML content model for an option is more restrictive
than that for an argument. Also in the didactic document type some options, such as
that for <em>anch</em>, which is described later in this section, are
practically required. </li>
<li><a id="fnote10" href="#revfnote10">*</a> To say <em>seldom</em> is not to say <em>not</em>. Two important
instances in the didactic production system are the <em>series</em> attribute for the
<em>label</em> command, which stands in, to the extent possible, for the
notion of <em>counter</em> in <em>LaTeX</em>, and the <em>type</em> attribute for
the <em>series</em> command, which provides emulation of counter
conversion from, say, number values to letter values. </li>
<li><a id="fnote11" href="#revfnote11">*</a> In the XML version of <em>article</em> the option becomes the element
<em>anchref</em> and the anchored text becomes the element <em>anchv</em>.
One may use these names directly in GELLMU source, but option/argument
notation is more familiar and more succinct. </li>
<li><a id="fnote12" href="#revfnote12">*</a> There was no list
of this type in early pre-release versions of the syntactic translator. </li>
<li><a id="fnote13" href="#revfnote13">*</a> The <em>LaTeX</em> concept of document class has only a loose correspondence
with the SGML concept of document type. </li>
<li><a id="fnote14" href="#revfnote14">*</a> It is not inconceivable that at some future point conscious writing
for some XML document types using <em>LaTeX</em>-like markup might be
subsumed in the <em>LaTeX</em> project, but in saying this, the author is
neither predicting it nor assessing the merits of the idea. He has no
affiliation with the <em>LaTeX</em> project other than as a user. </li>
<li><a id="fnote15" href="#revfnote15">*</a> Strict discussion of an SGML document type would not allow use of the
word <em>handled</em>. In this instance a coordinated pair of document
types is being described, one SGML and the other an XML translation.
For most purposes the SGML document type is the richer of the two.
However, because of its use of a handful of generic elements (in its
reserved namespace consisting of names that contain ‘<kbd>0</kbd>’ (zero)
as first numeric character) for modeling certain convenience features
of <em>LaTeX</em>, it is possible for a correct translation of a valid SGML
article to yield an XML version that fails validation because the
content models of the generic elements are necessarily loose. </li>
<li><a id="fnote16" href="#revfnote16">*</a> The variable
<em>gellmu-xml-strict</em> is by default unset in advanced mode. </li>
<li><a id="fnote17" href="#revfnote17">*</a> The correct <em>LaTeX</em> markup is “<kbd>\LaTeX{} document</kbd>”. In the didactic production system the
name of <em>LaTeX</em> is “latex”, which is a defined-empty
element, that for the SGML version of <em>article</em> may be marked up
safely either as “<kbd>\latex;</kbd>” or as “<kbd>\latex{}</kbd>”. </li>
<li><a id="fnote18" href="#revfnote18">*</a> In math ‘<kbd>[</kbd>’ sometimes needs to be escaped to prevent confusion
between its markup use and its ordinary use in an instance such as
the markup for <math xmlns="http://www.w3.org/1998/Math/MathML" mode="inline"
><mi mathvariant="double-struck" mathcolor="#b00">Z</mi
><mo stretchy="true">[</mo><mi>t</mi><mo stretchy="true">]</mo></math
>. The syntactic translator would need to know
vocabulary — at least the argument/option pattern for
<em>mathbb</em> — in order to elude the syntactic ambiguity. </li>
<li><a id="fnote19" href="#revfnote19">*</a> “<kbd>\~</kbd>” is an example of a markup string that is defined in <em>LaTeX</em> (for
an accent) that is not defined in the didactic document type. A <em>LaTeX</em> user may recover
a prior markup habit of this type using <em>newcommand</em> possibly in
combination with <em>macro</em>. For more information see the
<a href="#accents">discussion of accents</a> (section 5.8). </li>
<li><a id="fnote20" href="#revfnote20">*</a> It is possible to merge the inline <em>math</em> and <em>tmath</em> zones
at any level of processing beyond the syntactic translator. These are indeed the same
in <em>LaTeX</em>, but the syntactic translator resists the temptation here to
go beyond syntax and merge them. With the didactic <em>article</em>
document type the formatting to <em>LaTeX</em> inserts the <em>LaTeX</em> markup
“<kbd>\,</kbd>” for a small horizontal space before and after
<em>math</em>, but not before and after <em>tmath</em>. </li>
<li><a id="fnote21" href="#revfnote21">*</a> The syntactic translator simply outputs the SGML defined-empty element
<em>brk0</em>, which belongs to its reserved name space. The dual use of
<em>brk0</em> involves some SGML chicanery that is resolved during translation
to the XML version of the <em>article</em> document type,
where <em>tabular</em> is converted to <em>table</em> and non-tabular use of
<em>brk0</em> is converted to <em>brk</em>. See also the handling of
<em>array</em>, which is different even though the source markup, as in
<em>LaTeX</em> is similar. </li>
<li><a id="fnote22" href="#revfnote22">*</a> Alternate forms “<kbd>\aos;</kbd>”, “<kbd>\aoq;</kbd>”, “<kbd>\aoe;</kbd>” of sentence ending
punctuation are provided that may be used following inline mathematical
markup at the end of a sentence. Similarly, “<kbd>\aoc;</kbd>” is an alternate
form for a comma. </li>
<li><a id="fnote23" href="#revfnote23">*</a> Or one
could use:
<dl class="verblist">
<dd><kbd>
\Section{\sectiontitle{Some...}</kbd></dd>
<dd><kbd>
\para A para...  . . .}</kbd></dd>
</dl>
instead of using the environment-like
<em>begin</em>/<em>end</em> construction. </li>
<li><a id="fnote24" href="#revfnote24">*</a> In fact, classical SGML document types are often
even more elaborate than this.</li>
<li><a id="fnote25" href="#revfnote25">*</a> Caveats:
<dl>
<dd> No document type definition under SGML is actually a complete
language definition. A document type definition describes a document
markup structurally; in particular, it does not provide definition
for legal “field” values. </dd>
<dd> While the GELLMU syntactic translator is now considered as
“alpha” software, the document type and the accompanying
translators, which constitute the didactic production system are
developmental. These materials have some support for obsolete
practice and also contain sketch sections that are not fully robust. </dd>
</dl>
</li>
<li><a id="fnote26" href="#revfnote26">*</a> It is recommended that the characters in label key strings be
restricted to lower case ASCII letters, the digits 0–9, and
possibly the character ‘<kbd>-</kbd>’ or the character ‘<kbd>.</kbd>’ for
maximal inter-operability with current and future formattings.
For example, the ‘<kbd>_</kbd>’ is problematical in this context. </li>
<li><a id="fnote27" href="#revfnote27">*</a> Although one <em>could</em> provide SGML modeling for <em>LaTeX</em>'s
counters, it would not be very much along the lines of main track
SGML or XML document types. </li>
<li><a id="fnote28" href="#revfnote28">*</a> The value strings may contain simple markup such as, for example,
“<kbd>\tld;</kbd>” to provide robust multiple output processing of
‘<kbd>~</kbd>’ whereas an attribute option may not contain markup. </li>
<li><a id="fnote29" href="#revfnote29">*</a> A <em>klabel</em> is a
“visible key” label.</li>
<li><a id="fnote30" href="#revfnote30">*</a> It may be left empty, but it must be present.
</li>
<li><a id="fnote31" href="#revfnote31">*</a> The presence of <em>sopt</em>
does not cause a table of contents to be produced automatically.
For that one uses “<kbd>\tableofcontents</kbd>”. Moreover,
the presence of <em>sopt</em> should have no effect upon a manually
constructed “<kbd>\TableOfContents</kbd>”.</li>
<li><a id="fnote32" href="#revfnote32">*</a> The didactic production system offers a way to furnish a formally empty string, which is an
empty element called <em>empty</em> in the document type for use in
places such as the the table of contents option of a sectional unit,
where it is not otherwise possible to distinguish after parsing whether
deliberately empty content was specified by the author.
That is, the markup “<kbd>\sopt{}</kbd>” furnishes an empty
string which, in turn, signals “no <em>sopt</em>”, while
“<kbd>\sopt{\empty;}</kbd>” indicates that empty content
was specified for <em>sopt</em>. </li>
<li><a id="fnote33" href="#revfnote33">*</a> When editing for HTML one may, of course use HTML's <em>pre</em>,
which stands for “pre-formatted text”</li>
<li><a id="fnote34" href="#revfnote34">*</a> With a sufficiently long list of output format candidates each of the
33 non-alphanumeric printable ASCII characters is unsafe.
However, one might use an external character-to-string conversion
program to prepare a large amount of verbatim material for inclusion
inside the simplistic <em>verbatim</em> command in GELLMU source. </li>
<li><a id="fnote35" href="#revfnote35">*</a> To export this procedure for general <em>advanced</em> mode usage, all
of the names used need to be made user-configurable. </li>
<li><a id="fnote36" href="#revfnote36">*</a> Familiar short forms
may be introduced by a user using the <em>macro</em> facility.</li>
<li><a id="fnote37" href="#revfnote37">*</a> For the
third method one's GELLMU driver script must provide appropriately
for the text encoding of the source file.</li>
<li><a id="fnote38" href="#revfnote38">*</a> This meaning of <em>scale</em> differs
from the meaning of <em>scale</em> with <em>includegraphics</em> under
<em>LaTeX</em>'s <em>graphicx</em> package. New controls of this type
may be introduced in a future version.</li>
<li><a id="fnote39" href="#revfnote39">*</a> Note that the use of <em>lbalbr</em> in this instance is insufficiently
semantic for translation to content MathML while it is meaningful
for translation to presentation MathML. Adequate enhancement might
be had by providing <kbd>mml="cases"</kbd> (using a name from <em>amsmath</em>)
as an attribute for <em>lbalbr</em> with this example. </li>
<li><a id="fnote40" href="#revfnote40">*</a> There is also a default counter that is used when no label series name
is present. That counter simply is the position of the underlying
<em>assertion</em> in the list of all assertions. </li>
<li><a id="fnote41" href="#revfnote41">*</a> However, a declared math symbol may be invoked in
a <em>newcommand</em> that takes arguments. </li>
<li><a id="fnote42" href="#revfnote42">*</a> Such unattached braces in GELLMU markup lead to an <em>lg0</em> tag in
the output of the syntactic translator that is translated to an
<em>lgg</em> tag in the XML version of the didactic document type. </li>
<li><a id="fnote43" href="#revfnote43">*</a> Version 20 or later should be adequate. Although the author began
this project using version 19, he is no longer able to run tests
with that version.</li>
<li><a id="fnote44" href="#revfnote44">*</a> It is an embarrassment of the business world in the years since 1985
that many business computing installations do not provide general
purpose cross-platform programming systems despite the widespread
availability of excellent free robust systems such as <em>Emacs</em> (for
Lisp), <em>gcc</em> (for C), and <em>Perl</em>. This new phenomenon
apparently arises not so much from lack of organizational interest but
from the fact that the responsibility for maintenance cannot be passed
beyond the local system manager to a vendor. </li>
<li><a id="fnote45" href="#revfnote45">*</a> None of the enclosed scripts either for linux or for win32 should be used
without prior examination and verification for suitability. </li>
<li><a id="fnote46" href="#revfnote46">*</a> The main reasons that this version is not the default with a call to
<em>gellmu-trans</em> are:
<ol class="decimal">
<li><p> It breaks the paradigm under which a GELLMU command name is the
name of an SGML element. </p>
</li>
<li><p> It breaks backward compatibility with earlier versions of the
syntactic translator, i.e., breaks older documents. </p>
</li>
<li><p> It is felt that the user invoking <em>verblist</em> this way
should be aware of what is being done. </p>
</li>
</ol>
Note that direct invocation of <em>verblist</em> requires escaping
special characters. Thus, using the function call
<em>gellmu-verblist</em> converts the name <em>verbatim</em> from a
command name to a meta-command name.</li>
<li><a id="fnote47" href="#revfnote47">*</a> Specifically, this mention of “input” refers to
what is called “standard input” in a command line
situation. There may be a challenge here on platforms that do
not provide a command line. </li>
<li><a id="fnote48" href="#revfnote48">*</a> Formally, two of these auxiliary files are considered part of the
elaborated XML document. </li>
<li><a id="fnote49" href="#revfnote49">*</a> At the time of this release
there was discussion in the UseNet newsgroup
<a href="news:comp.text.sgml"><kbd>news:comp.text.sgml</kbd></a> about a proposed revision of
SGMLSPM by another party. The code for “<kbd>SGMLS.pm</kbd>”
included in this GELLMU release contains a very small modification
of Megginson's 1995 release. </li>
<li><a id="fnote50" href="#revfnote50">*</a> The direct internal subset is the content of the optional argument of
the <em>documenttype</em> metacommand that follows its required argument.
It should be noted in the didactic production system that the direct internal
subset cannot be propagated to the XML form of <em>article</em>
because it is digested by any standard SGML parser and, hence,
by any translation based on a standard parsing. Thus,
any pieces are merged in the XML form of an article although
the translator <kbd>xmlgart</kbd> might be modified to
construct an internal declaration subset there and provide
partitioning of the XML version among filesystem pieces based
on document structure. </li>
<li><a id="fnote51" href="#revfnote51">*</a> Please observe the rules of the <em>LaTeX</em> project regarding filenames
as well as the license rules of the GNU General Public License
if you wish to distribute a modified version of the <em>Elisp</em>
source. Alternatively, the author is always interested in learning
of suggestions for change.</li>
<li><a id="fnote52" href="#revfnote52">*</a> The corresponding usage in <em>LaTeX</em> would be “<kbd>\'e</kbd>”;
this could be brought into GELLMU source using <em>\macro</em>,
but it must be resolved to a name in the output of the GELLMU syntactic translator where
everything that is markup needs a name. Rather than using a
general container <em>acute</em>, the document type could have provided
a name for the specific character. </li>
<li><a id="fnote53" href="#revfnote53">*</a> Alternatively <em>LaTeX</em> source can be submitted to the program
<em>lambda</em> which is the <em>LaTeX</em> format for the program
<em>omega</em> that is now under development as a substitute for
Knuth's <em>TeX</em>, the program, with internationalization as a stated
goal.</li>
<li><a id="fnote54" href="#revfnote54">*</a> There is no formal document type definition
for a “<kbd>.zml</kbd>” file because such a file is endowed via XML
attributes with information about tree structure for
mathematical zones.</li>
</ol>
</body>
</html>
|
