/usr/share/acl2-7.2dfsg/books/misc/expander.lisp is in acl2-books-source 7.2dfsg-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | ; expander.lisp -- symbolic expansion utilities for ACL2
; Copyright (C) 2013, Regents of the University of Texas
; Originally written by Matt Kaufmann
; License: A 3-clause BSD license. See the LICENSE file distributed with ACL2.
; Changes by Pete Manolios Wed Jul 15 21:22:03 EDT 2009
; Changes by Daron Vroon shortly thereafter.
; Made minor modifications and added simplification
; functions at the end of the file that allow us to simplify the
; "termination checkpoints" we generate. See the end of the file
; for documentation, examples, and ideas for extending this work.
; Historical comments:
; Although some attempt has been made to bring it up to date with ACL2
; Release 2.0, this file should be viewed as a set of routines that may prove
; useful in using ACL2 but _not_ as code that can be trusted to the extent
; that the ACL2 system prover may be trusted.
; For ACL2 3.0, removed symsim-for-value (not clear that it's been used for a
; long time). And, we allow symsim to return multiple clauses.
; Top-level routines (only the first two have reasonable documentation):
; SYMSIM: See :doc string
; DEFTHM?: See :doc string
; TOOL1-FN: Takes a list of hypotheses and some hints and returns a simplified
; version, as a list of clauses. Also returns a list of all runes used and a
; list of assumptions generated by forcing.
; TOOL2-FN: Takes a term and a list of hypotheses, together with some
; hints, and returns a term that is the result of rewriting the term
; under those hypotheses, using those hints. Note that the hypotheses
; are used to build a context, using forward chaining and probably
; linear arithmetic as well, but are not simplified. This tool also
; sends back a list of runes.
; Changes by Daron Vroon on June 4, 2007:
; TOOL1-FN and TOOL2-FN have now each been split into 2 functions: a
; "front end" that calculates the ctx, ens, and wrld to use, along
; with some other calculations, and a "back end" that uses the ctx,
; ens, and wrld to do what the original function did. The
; functionality of TOOL1-FN and TOOL2-FN have not been changed, and
; users of these functions should notice no difference.
; Splitting these functions in two allowed for the definition of two
; new functions, TOOL1-FN0 and TOOL2-FN0. These perform the same task
; as TOOL1-FN and TOOL2-FN, respectively, with one difference: the
; user must supply the ctx, ens, and wrld. This is helpful to people
; who want to simplify expressions in the midst of making other
; changes that require a modified world or a user-defined ctx.
; To certify this book:
; (certify-book "expander").
(in-package "ACL2")
(include-book "xdoc/top" :dir :system)
(defxdoc expander
:parents (miscellaneous)
:short "Routines for simplifying terms."
:long "<p>The routines provided by the expander can be useful in generating
theorems and simplifying expressions, under given assumptions.</p>
<p>They were developed rather in a hurry and should be used without expecting
the usual standards of care present in development of ACL2 code. Once these
routines are used to generate theorems for you, you should check the theorems
directly with ACL2.</p>
<p>To load the expander, run:</p>
@({
(include-book \"misc/expander\" :dir :system)
})")
; We know what we are doing when using state:
(set-state-ok t)
(encapsulate
((hidden-expander-function (x) t))
(logic)
(local (defun hidden-expander-function (x) x)))
(defun silly-rec-fn-for-rewrite* (x)
(declare (xargs :verify-guards t))
(if (consp x)
(silly-rec-fn-for-rewrite* (cdr x))
x))
;; (verify-guards silly-rec-fn-for-rewrite*)
(program)
(defconst *valid-output-names-except-error*
(set-difference-eq *valid-output-names* '(error)))
(defmacro tool1 (hyps &key hints (prove-assumptions 't) inhibit-output)
`(er-progn (tool1-fn ',hyps state ',hints ',prove-assumptions
',inhibit-output
t t)
(value :invisible)))
(defun pop-clauses (pool)
(mv-let (signal pool-lst cl-set hint-settings pop-history new-pool)
(pop-clause1 pool nil)
(declare (ignore pool-lst hint-settings pop-history))
(cond
((or (eq signal 'win) (eq signal 'lose))
(mv signal cl-set))
(t
(mv-let (signal rest-clauses)
(pop-clauses new-pool)
(cond
((eq signal 'win) (mv 'win (append cl-set rest-clauses)))
(t (mv signal nil))))))))
(defun prove-loop1-clauses (pool-lst clauses pspv hints ens wrld ctx state)
; Based on prove-loop1, except returns (mv erp ttree clauses pairs
; new-pspv state), where pairs is a list of pairs (assumnotes
; . clause), suitable for the third argument of prove-loop1 starting
; with forcing round 1.
(sl-let (erp pspv jppl-flg state)
(waterfall 0 pool-lst clauses pspv hints ens wrld ctx state
(initial-step-limit wrld state))
(declare (ignore jppl-flg))
(cond
(erp (mv step-limit t nil nil nil nil state))
(t
(mv-let
(signal new-clauses)
(pop-clauses (access prove-spec-var pspv :pool))
(cond
((eq signal 'lose)
(mv step-limit t nil nil nil nil state))
(t
(mv-let
(pairs new-pspv state)
; Forcing round...
(process-assumptions 0 pspv wrld state)
(mv-let
(erp ttree state)
(accumulate-ttree-and-step-limit-into-state
(access prove-spec-var new-pspv :tag-tree)
step-limit
state)
(assert$
(null erp)
(mv step-limit nil ttree new-clauses pairs new-pspv
state)))))))))))
(defun prove-loop-clauses (clauses pspv hints ens wrld ctx state)
; We either cause an error or return a ttree. If the ttree contains
; :byes, the proof attempt has technically failed, although it has
; succeeded modulo the :byes.
(pprogn
(increment-timer 'other-time state)
(sl-let (erp ttree new-clauses pairs new-pspv state)
(prove-loop1-clauses nil
clauses
pspv
hints ens wrld ctx state)
(pprogn
(increment-timer 'prove-time state)
(cond
(erp (mv step-limit erp nil nil nil nil state))
(t (mv step-limit nil ttree new-clauses pairs new-pspv
state)))))))
(defun prove-clauses (term pspv hints ens wrld ctx state)
; Adapted from prove.
(prog2$
(initialize-brr-stack state)
(sl-let (erp ttree1 clauses pairs new-pspv state)
(prove-loop-clauses (list (list term))
(change prove-spec-var pspv
:user-supplied-term term
:orig-hints hints)
hints ens wrld ctx state)
(cond
(erp (mv step-limit t nil nil nil nil state))
(t
(mv-let
(erp val state)
(chk-assumption-free-ttree ttree1 ctx state)
(declare (ignore val))
(cond
(erp (mv step-limit t nil nil nil nil state))
(t (pprogn
(let ((byes (tagged-objects :bye ttree1)))
(cond
(byes
(pprogn
; The use of ~*1 below instead of just ~&1 forces each of the defthm
; forms to come out on a new line indented 5 spaces. As is already
; known with ~&1, it can tend to scatter the items randomly -- some on
; the left margin and others indented -- depending on where each item
; fits flat on the line first offered.
(io? prove nil state
(wrld byes)
(fms "To complete this proof you should try to ~
admit the following ~
event~#0~[~/s~]~|~%~*1~%See the discussion ~
of :by hints in :DOC hints regarding the ~
name~#0~[~/s~] displayed above."
(list (cons #\0 byes)
(cons #\1
(list ""
"~|~ ~q*."
"~|~ ~q*,~|and~|"
"~|~ ~q*,~|~%"
(make-defthm-forms-for-byes
byes wrld))))
(proofs-co state)
state
nil))
state))
(t state)))
(mv step-limit erp ttree1 clauses pairs
(change prove-spec-var new-pspv
:pool nil)
state))))))))))
(defun chk-for-hidden-expander-function1 (cl)
(let ((term (car (last cl))))
(case-match term
(('hide ('hidden-expander-function &))
term)
(t
(er hard 'chk-for-hidden-expander-function1
"Expected clause to end with hidden call of ~
HIDDEN-EXPANDER-FUNCTION, but instead clause is ~p0."
cl)))))
(defun chk-for-hidden-expander-function (clauses)
(cond ((null clauses) nil)
(t (and (chk-for-hidden-expander-function1 (car clauses))
(chk-for-hidden-expander-function (cdr clauses))))))
(defun untranslate-clause-lst (cl-lst wrld)
(cond
((null cl-lst)
nil)
(t
(cons (prettyify-clause1 (car cl-lst) wrld)
(untranslate-clause-lst (cdr cl-lst) wrld)))))
(defun tool1-print (print-flg runes clauses state)
(cond
(print-flg
(fms "~%***OUTPUT OF TOOL1***~%~%Tag tree:~% ~p0~%~%List of simplified ~
hypotheses:~% ~p1~|~%"
(list (cons #\0 runes)
(cons #\1
(untranslate-clause-lst clauses (w state))))
*standard-co* state nil))
(t state)))
(defun hide-special-hyps (lst)
"We do this stuff so that equalities and SYNP hyps won't be thrown out.
Perhaps what we really need is a hyp simplifier with less aggressive
heuristics."
(cond
((null lst) nil)
(t (let ((hyp (car lst)))
(let ((new-hyp
(case-match hyp
(('equal x y)
(let ((x1 (if (variablep x)
(list 'hide x)
x))
(y1 (if (variablep y)
(list 'hide y)
y)))
(list 'equal x1 y1)))
(('synp . x) (list 'hide (cons 'synp x)))
(& hyp))))
(cons new-hyp (hide-special-hyps (cdr lst))))))))
(defun fix-special-hyps (lst)
(cond
((null lst) nil)
(t (let ((hyp (car lst)))
(let ((new-hyp
(case-match hyp
(('not ('equal ('hide x) ('hide y)))
(list 'not (list 'equal x y)))
(('not ('equal ('hide x) y))
(list 'not (list 'equal x y)))
(('not ('equal y ('hide x)))
(list 'not (list 'equal y x)))
(('not ('hide ('synp . x)))
(list 'not (cons 'synp x)))
(& hyp))))
(cons new-hyp (fix-special-hyps (cdr lst))))))))
(defun remove-hidden-terms (cl-set)
(cond
((null cl-set)
nil)
(t (cons (fix-special-hyps (butlast (car cl-set) 1))
(remove-hidden-terms (cdr cl-set))))))
(defun add-key-val-pair-to-key-val-alist (key key1 val alist)
;; adapted from ACL2 function add-to-set-equal-in-alist
(cond ((null alist) (list (list key key1 val)))
((equal key (caar alist))
(cons (list* key key1 val (cdar alist))
(cdr alist)))
(t (cons (car alist)
(add-key-val-pair-to-key-val-alist key key1 val (cdr
alist))))))
(defun remove-hidden-expander-term-from-cl (cl)
(cond ((endp cl) nil)
(t (let ((term (car cl)))
(case-match term
(('HIDE ('HIDDEN-EXPANDER-FUNCTION &))
(cdr cl))
(& (cons (car cl)
(remove-hidden-expander-term-from-cl (cdr cl)))))))))
(defun remove-hidden-expander-term-from-cl-list (cl-list)
(cond ((endp cl-list)
nil)
(t (cons (remove-hidden-expander-term-from-cl (car cl-list))
(remove-hidden-expander-term-from-cl-list (cdr cl-list))))))
(defun get-assns (ttree remove-hidden)
(cond (remove-hidden
(remove-hidden-expander-term-from-cl-list
(strip-cdrs (tagged-objects :bye ttree))))
(t
(strip-cdrs (tagged-objects :bye ttree)))))
(defun tool1-fn1 (hyps ctx ens wrld state hints prove-assumptions inhibit-output
translate-flg print-flg)
; Returns error triple with value (list* runes clauses assumptions), where
; assumptions is nil if prove-assumptions is t (because they must be proved) or
; nil (because they are ignored).
(er-let* ((hints (if (alistp hints)
(value (add-key-val-pair-to-key-val-alist
"Goal"
;; only preprocess and simplify are allowed
:do-not
(list 'quote '(generalize
eliminate-destructors
fertilize
eliminate-irrelevance))
hints))
(er soft ctx
"The hints must be an alist, but ~p0 is not."
hints)))
(thints (translate-hints 'tool1 hints ctx wrld state))
(thyps0
(if translate-flg
(translate-term-lst hyps t t t ctx wrld state)
(value hyps)))
(thyps
(value (hide-special-hyps thyps0)))
(vars
(value (all-vars1-lst thyps nil)))
(tconc
(translate (list 'hide
(list 'hidden-expander-function
(cons 'list vars)))
t t t ctx wrld state))
(tterm (value (implicate (conjoin thyps) tconc))))
(sl-let
(erp ttree clauses pairs new-pspv state)
(prove-clauses tterm
(make-pspv ens wrld state
:displayed-goal
(untranslate tterm t wrld)
:otf-flg t)
thints ens wrld ctx state)
(prog2$
(chk-for-hidden-expander-function clauses)
(cond
(erp
(mv erp nil state))
(prove-assumptions
(er-let* ((thints
(if (eq prove-assumptions t)
(value thints)
(translate-hints 'tool1
*bash-skip-forcing-round-hints*
ctx wrld state))))
(state-global-let*
((inhibit-output-lst
(if (eq prove-assumptions t)
(@ inhibit-output-lst)
(if (eq inhibit-output :prove)
(remove1-eq 'prove (@ inhibit-output-lst))
(@ inhibit-output-lst)))))
(er-let*
((new-ttree
(prove-loop1 1 nil pairs new-pspv
thints ens wrld ctx state)))
(let ((runes (all-runes-in-ttree
new-ttree
(all-runes-in-ttree ttree nil)))
(assumptions (get-assns new-ttree t)))
(pprogn
(tool1-print print-flg runes clauses state)
(value (list* runes
(dumb-negate-lit-lst-lst
(remove-hidden-terms clauses))
assumptions))))))))
(t (let ((runes (all-runes-in-ttree ttree nil)))
(pprogn
(tool1-print print-flg runes clauses state)
(value (list* runes
(dumb-negate-lit-lst-lst
(remove-hidden-terms clauses))
nil))))))))))
(defun tool1-fn (hyps state hints prove-assumptions inhibit-output
translate-flg print-flg)
; Returns error triple with value (list* runes clauses assumptions), where
; assumptions is nil if prove-assumptions is t (because they must be proved) or
; nil (because they are ignored).
(state-global-let*
((ld-skip-proofsp nil)
(inhibit-output-lst
(if inhibit-output
(if (eq inhibit-output :prove)
(union-eq '(proof-tree prove) (@ inhibit-output-lst))
*valid-output-names-except-error*)
(@ inhibit-output-lst))))
(with-ctx-summarized
"( TOOL1 ...)"
(let ((wrld (w state))
(ens (ens state)))
(tool1-fn1 hyps ctx ens wrld state hints prove-assumptions inhibit-output
translate-flg print-flg)))))
(defun tool1-fn0 (hyps ctx ens wrld state hints prove-assumptions inhibit-output
translate-flg print-flg)
; same as tool1-fn, except the user must supply their own wrld, ens, and ctx.
(state-global-let*
((ld-skip-proofsp nil)
(inhibit-output-lst
(if inhibit-output
(if (eq inhibit-output :prove)
(union-eq '(proof-tree prove) (@ inhibit-output-lst))
*valid-output-names-except-error*)
(@ inhibit-output-lst))))
(tool1-fn1 hyps ctx ens wrld state hints prove-assumptions inhibit-output
translate-flg print-flg)))
;;;;;;; Tool 2
(defmacro tool2 (term hyps
&key
hints equiv (prove-assumptions 't) inhibit-output
(must-rewrite-flg 't))
`(tool2-fn ',term ',hyps ',equiv state ',hints ',prove-assumptions
',inhibit-output t t ,must-rewrite-flg))
(defun tool2-print (print-flg runes rewritten-term state)
(cond
(print-flg
(fms "~%***OUTPUT OF TOOL2***~%~%Tag tree:~% ~p0~%~%Rewritten term:~% ~
~p1~|~%"
(list (cons #\0 runes)
(cons #\1 (untranslate rewritten-term nil (w state))))
*standard-co* state nil))
(t state)))
(defun expander-repeat-limit (state)
(if (f-boundp-global 'expander-repeat-limit state)
(f-get-global 'expander-repeat-limit state)
3))
(defun rewrite* (term hyps ctx
repeat-limit
completed-iterations
;; alist bkptr
;; &extra formals
type-alist
;; obj
geneqv wrld state
;; fnstack ancestors backchain-limit
step-limit
simplify-clause-pot-lst
rcnst gstack ttree
;;DARON: added must-rewrite-flg, which is T if we want to
;;throw an error if the term fails to rewrite, and NIL
;;otherwise.
must-rewrite-flg)
; Rewrite term repeatedly, (- repeat-limit completed-iterations) times. Note
; that hyps is T after the first time through.
(sl-let (val new-ttree)
(rewrite-entry (rewrite term nil 1)
:obj '?
:fnstack
; We want to fool rewrite-fncall on lambdas.
'(silly-rec-fn-for-rewrite*)
:pre-dwp nil ;; RBK:
:ancestors nil
:backchain-limit 500
:step-limit step-limit ; explicit to avoid decrement
:rdepth (rewrite-stack-limit wrld)
:pequiv-info nil)
(cond
((equal val term)
(cond
;; DARON: if must-rewrite-flg is NIL, we just return the term.
((or (not must-rewrite-flg)
(eq hyps t))
(mv step-limit term ttree state))
;; otherwise, we throw the error.
(t (prepend-step-limit
(erp val state)
(er soft ctx
"The term~% ~p0~%failed to rewrite to a new term under ~
hypotheses~% ~p1."
(untranslate val nil wrld)
(untranslate-lst hyps t wrld))))))
((= repeat-limit completed-iterations)
(pprogn
;; DARON: wrapped this fms in an io? so we can inhibit it if we
;; want.
(io? prove nil state
(completed-iterations)
(fms "OUT OF PATIENCE! Completed ~n0 iterations."
(list (cons #\0 (list completed-iterations)))
*standard-co* state nil))
(mv step-limit val new-ttree state)))
(t (pprogn (if (eql completed-iterations 0)
state
;; DARON: wrapped this fms in an io? so we can inhibit
;; output if we want.
(io? prove nil state
(completed-iterations)
(fms "NOTE: Starting ~n0 repetition of rewrite.~%"
(list (cons #\0 (list (1+ completed-iterations))))
*standard-co* state nil)))
(rewrite* val t ctx
repeat-limit
(1+ completed-iterations)
type-alist geneqv wrld state step-limit
simplify-clause-pot-lst rcnst gstack
new-ttree
;; DARON: we must pass must-rewrite-flg to
;; subsequent iterations.
must-rewrite-flg))))))
(defun tool2-fn1
(term hyps equiv ctx ens wrld state thints prove-assumptions
inhibit-output translate-flg print-flg must-rewrite-flg)
; Returns error triple with value (list* runes rewritten-term assumptions).
; But assumptions is nil if prove-assumptions is nil (we don't collect them) or
; is t (we insist that all forced assumptions be proved).
(let* ((saved-pspv (make-pspv ens wrld state
:displayed-goal term ; from, e.g., thm-fn
:user-supplied-term term ;from, e.g., prove
:orig-hints thints))) ;from, e.g., prove
(er-let*
((thyps (if translate-flg
(translate-term-lst hyps t t t ctx wrld state)
(value hyps)))
(tterm (if translate-flg
(translate term t t t ctx wrld state)
(value term))))
(mv-let ;from waterfall1
(erp pair state)
(find-applicable-hint-settings
*initial-clause-id*
(add-literal tterm (dumb-negate-lit-lst thyps) t)
nil saved-pspv ctx
thints wrld nil state)
(cond
(erp (silent-error state))
(t
(let ((hint-settings (car pair))
(thints (cdr pair)))
(mv-let
(hint-settings state)
(cond ((null hint-settings)
(mv nil state))
(t (thanks-for-the-hint nil hint-settings state))) ;BB
(er-let* ((pspv (load-hint-settings-into-pspv
t hint-settings saved-pspv nil wrld ctx state)))
(cond
((intersectp-eq
'(:do-not-induct :do-not :induct :use :cases :by)
(strip-cars hint-settings))
(er soft ctx
"It makes no sense for TOOL2 to be given hints ~
for \"Goal\" that include any of ~
:do-not-induct, :do-not,:induct, :use, ~
:cases, or :by. The hint ~p0 is therefore ~
illegal."
(cons "Goal" hint-settings)))
(t
(pprogn
(initialize-proof-tree ;from waterfall
*initial-clause-id*
(list (list (implicate (conjoin thyps) tterm)))
ctx
state)
(let* ;from simplify-clause1
((current-clause (dumb-negate-lit-lst thyps))
(rcnst
(change rewrite-constant
(access prove-spec-var pspv :rewrite-constant)
:force-info
(if (ffnnamep-lst 'if current-clause)
'weak
t)))
(pts
;; (current-clause-pts (enumerate-elements current-clause 0))
nil))
(mv-let ;from simplify-clause1
(contradictionp type-alist fc-pair-lst)
(forward-chain current-clause
pts
(access rewrite-constant
rcnst :force-info)
nil wrld ens
(access rewrite-constant rcnst
:oncep-override)
state)
(declare (ignore fc-pair-lst))
(cond
(contradictionp
(er soft ctx
"Contradiction found in hypotheses~% ~
~p0~%using type-set reasoning!"
hyps))
(t
(sl-let ;from simplify-clause1
(contradictionp simplify-clause-pot-lst)
(setup-simplify-clause-pot-lst current-clause
(pts-to-ttree-lst
pts)
nil ; fc-pair-lst ;; RBK:
type-alist
rcnst
wrld state
(initial-step-limit
wrld state))
(cond
(contradictionp
(er soft ctx
"Contradiction found in hypotheses~% ~
~p0~%using linear reasoning!"
hyps))
(t
; We skip the call of process-equational-polys in simplify-clause1; I think
; that we can assume that by the time tool2 is called, that call wouldn't have
; any effect anyhow. By the way, we skipped remove-trivial-equivalence
; earlier.
; Now we continue as in rewrite-clause.
(mv-let
(not-flg atm)
(strip-not tterm)
(let ((local-rcnst
(change rewrite-constant rcnst
:current-literal
(make current-literal
:not-flg not-flg
:atm atm)))
(gstack (initial-gstack 'simplify-clause
nil current-clause)))
(sl-let
(val ttree state)
(rewrite* atm hyps ctx
(expander-repeat-limit state)
0
type-alist
(cadr (car (last (getprop
equiv
'congruences
nil
'current-acl2-world
wrld))))
wrld state step-limit
simplify-clause-pot-lst rcnst gstack
nil
must-rewrite-flg)
(cond
((equal val t)
(mv t nil state))
(t
(sl-let
(bad-ass ttree)
(resume-suspended-assumption-rewriting
ttree
nil
gstack
simplify-clause-pot-lst
local-rcnst
wrld
state
step-limit)
(cond
(bad-ass
(er soft ctx
"Generated false assumption, ~p0! ~
So, rewriting is aborted, just ~
as it would be in the course of ~
a regular Acl2 proof."
bad-ass))
(t
(let ((rewritten-term
(if not-flg
(dumb-negate-lit val)
val)))
(cond
(prove-assumptions
(mv-let
(pairs pspv state)
(process-assumptions
0
(change prove-spec-var saved-pspv
:tag-tree
(set-cl-ids-of-assumptions
ttree *initial-clause-id*))
wrld state)
(er-let*
((ttree
(accumulate-ttree-and-step-limit-into-state
(access prove-spec-var pspv :tag-tree)
step-limit
state))
(thints
(if (eq prove-assumptions t)
(value thints)
(translate-hints 'tool2
*bash-skip-forcing-round-hints*
ctx wrld state))))
(state-global-let*
((inhibit-output-lst
(if (or (eq prove-assumptions t)
(eq inhibit-output t))
(@ inhibit-output-lst)
(if (eq inhibit-output
:prove)
(remove1-eq
'prove
(@ inhibit-output-lst))
(@ inhibit-output-lst)))))
(er-let* ((new-ttree
(prove-loop1
1 nil pairs pspv
thints ens wrld
ctx state)))
(let* ((runes
(all-runes-in-ttree
new-ttree
(all-runes-in-ttree
ttree nil)))
(byes (get-assns
new-ttree
nil))
(val (list* runes
rewritten-term
byes)))
(pprogn (tool2-print print-flg runes
rewritten-term state)
(f-put-global 'tool2-error
nil state)
(f-put-global
'tool2-result
val
state)
(value val))))))))
(t (let* ((runes (all-runes-in-ttree
ttree nil))
(val (list* runes
rewritten-term
nil)))
(pprogn
(tool2-print print-flg runes
rewritten-term
state)
(f-put-global 'tool2-error
nil state)
(f-put-global
'tool2-result
val
state)
(value val)))))))))))))))))))))))))))))))))
(defun tool2-fn0
(term hyps equiv ctx ens wrld state hints prove-assumptions
inhibit-output translate-flg print-flg must-rewrite-flg)
; Same as tool2-fn, except the user must supply the ctx, ens, and wrld.
; DARON: added must-rewrite-flg to formals of tool2-fn0.
(state-global-let*
((inhibit-output-lst
(if inhibit-output
(if (eq inhibit-output :prove)
(union-eq '(proof-tree prove) (@ inhibit-output-lst))
*valid-output-names-except-error*)
(@ inhibit-output-lst))))
(prog2$
(initialize-brr-stack state)
(er-let*
((thints (translate-hints 'tool2 hints ctx wrld state)))
(tool2-fn1 term hyps equiv ctx ens wrld state thints prove-assumptions
inhibit-output translate-flg print-flg must-rewrite-flg)))))
(defun tool2-fn
(term hyps equiv state hints prove-assumptions inhibit-output translate-flg
print-flg must-rewrite-flg)
; Returns error triple with value (list* runes rewritten-term assumptions).
; But assumptions is nil if prove-assumptions is nil (we don't collect them) or
; is t (we insist that all forced assumptions be proved).
; DARON: there was a bunch of duplicated code here, so I simplified tool2-fn to
; call tool2-fn0. Note that the signature of tool2-fn is still the same. By
; default it sets the must-rewrite-flg to T, which gives it the same behavior
; as before. (Matt K. mod: Now must-rewrite-flg is passed explicitly here.)
(let ((ctx 'TOOL2)
(wrld (w state))
(ens (ens state)))
(tool2-fn0 term hyps equiv ctx ens wrld state hints prove-assumptions
inhibit-output translate-flg print-flg must-rewrite-flg)))
;;;;;;; Hooking them together
(defun tool2-fn-lst
(term runes hyps-lst assns equiv state hints prove-assumptions inhibit-output
print-flg must-rewrite-flg)
; Returns the result of mapping tool2-fn over the list hyps-lst, pairing each
; result with the corresponding member of hyps-lst. Assumes hyps-lst is
; already translated. The value returned is actually a list of tuples
; (list* runes hyps rewritten-term assumptions).
(cond
((null hyps-lst)
(value nil))
(t
(mv-let
(erp x state)
(tool2-fn term (car hyps-lst) equiv state hints prove-assumptions
inhibit-output nil print-flg must-rewrite-flg)
(cond
(erp
(tool2-fn-lst term runes (cdr hyps-lst) assns equiv state
hints prove-assumptions inhibit-output print-flg
must-rewrite-flg))
(t
(er-let*
((rst (tool2-fn-lst term runes (cdr hyps-lst) assns equiv
state
hints prove-assumptions inhibit-output print-flg
must-rewrite-flg)))
(value (cons (list* (union-equal runes (car x))
(car hyps-lst)
(cadr x)
(union-equal assns (cddr x)))
rst)))))))))
(defun simplify-hyps
(remaining-hyps rewritten-previous-hyps-rev runes assns equiv state hints
prove-assumptions inhibit-output print-flg must-rewrite-flg)
; Returns the result of mapping tool2-fn over each hyp in remaining-hyps, where
; the hyps in rewritten-previous-hyps-rev and (cdr remaining-hyps) are assumed.
; Assumes all hyps are already translated. The value returned is actually a
; list (list* runes (list rewritten-hyp-list) assumptions).
(cond
((null remaining-hyps)
(value (list* runes (list (reverse rewritten-previous-hyps-rev)) assns)))
(t (er-let*
((x (tool2-fn (car remaining-hyps)
(revappend rewritten-previous-hyps-rev
(cdr remaining-hyps))
equiv state hints prove-assumptions
inhibit-output nil print-flg must-rewrite-flg)))
(simplify-hyps (cdr remaining-hyps)
(cons (cadr x) rewritten-previous-hyps-rev)
(union-equal (car x) runes)
(union-equal (cddr x) assns)
equiv state hints prove-assumptions inhibit-output
print-flg must-rewrite-flg)))))
(defun tool-fn
(term hyps simplify-hyps-p equiv state hints prove-assumptions inhibit-output
print-flg must-rewrite-flg ctx)
; Term and hyps are in translated form. Returns a list of tuples
; (list* runes hyps rewritten-term assumptions).
(er-let* ((runes-hyps-assns
(cond
((eq simplify-hyps-p :no-split)
(simplify-hyps hyps nil nil nil equiv state hints
prove-assumptions inhibit-output print-flg
must-rewrite-flg))
((eq simplify-hyps-p t)
(tool1-fn hyps state hints prove-assumptions inhibit-output
nil print-flg))
(simplify-hyps-p
(value (er hard 'tool-fn
"Bad :simplify-hyps-p argument (should be ~v0): ~x1"
(list t nil :no-split)
simplify-hyps-p)))
(t (value (list* nil (list hyps) nil))))))
(cond
((null (cdr runes-hyps-assns))
(er soft ctx
"It does not make sense to simplify the term ~p0, because the ~
hypothesis list ~p1 is contradictory."
(untranslate term nil (w state))
(untranslate-lst hyps t (w state))))
(t
(pprogn
(cond (print-flg
(fms "***NOTE***: Starting TOOL2.~%" nil *standard-co* state nil))
(t state))
(er-let*
((x (tool2-fn-lst term
(car runes-hyps-assns)
(cadr runes-hyps-assns)
(cddr runes-hyps-assns)
equiv state hints prove-assumptions
inhibit-output print-flg must-rewrite-flg)))
(cond
((not (= (length x) (length (cadr runes-hyps-assns))))
(er soft ctx
"Unable to successfully simplify term~% ~p0~%and ~
hypotheses~% ~p1 in every case generated."
(untranslate term nil (w state))
(untranslate-lst hyps t (w state))))
(x (value x))
(t (er soft ctx
"No theorems were suggested for term~% ~p0~%and ~
hypotheses~% ~p1.")))))))))
(defxdoc defthm?
:parents (expander)
:short "Generate a theorem."
:long "<p>Example:</p>
@({
(defthm? app-simplify
(implies (true-listp x)
(equal (append x y)
?))
:hints ((\"Goal\" :expand ((true-listp x)
(true-listp (cdr x))
(append x y))))
; show some output
:print-flg t)
})
<p>General Forms:</p>
@({
(DEFTHM? name
(IMPLIES hyps (equiv term ?))
:hints hints
:prove-assumptions prove-flg ; t or nil, default t
:print-flg print-flg ; t or nil, default nil
:simplify-hyps-p flg ; t, nil, or :no-split; default t
)
(DEFTHM? name
(equiv term ?)
:hints hints
:prove-assumptions prove-flg ; t or nil, default t
:print-flg print-flg ; t or nil, default nil
:simplify-hyps-p flg ; t, nil, or :no-split; default t
)
})
<p>where @('name') is a new symbolic name (see @(see name)), @('term') is a
term to be simplified assuming @('hyps') is true, and @(see hints) is as
described in its @(see documentation). The four keyword arguments above are
all optional, and behave as you might expect. In particular, set
@(':simplify-hyps-p') to @('nil') if you do not want the @('hyps') to be
simplified; otherwise, case splitting may occur in the course of their
simplification.</p>
<p>If the given @('term') cannot be simplified, then the event fails.
Otherwise, the result is an @(see encapsulate) event with one or more @(see
defthm) events of the form of the theorem, except with @('hyps')
simplified (and even omitted if simplified to @('t')) and @('term') simplified
under the assumption that @('hyps') is true. The reason that there can be more
than one @(see defthm) event is that @('hyps') may simplify to an expression
that generates a case split, for example if it simplifies to an @(see if)
expression that does not represent a conjunction.</p>
<p>In general, simplification may generate assumptions because of @(see force).
By default, an attempt is made to prove these assumptions, which must succeed
or else this event fails. However, if @(':prove-assumptions') is @('nil'),
then roughly speaking, no proof of forced hypotheses is attempted until after
simplification is complete. The documentation of :prove-assumptions is
admittedly weak here; feel free to experiment.</p>
<p>Also see @(see symsim).</p>
<p>Here are some examples, including the one above. Try them out and see what
happens.</p>
@({
; Doesn't simplify, so fails:
(defthm? app-simplify
(implies (true-listp x)
(equal (append x y)
?))
:hints ((\"Goal\" :expand (true-listp x))))
:pbt 0
; The following creates one event, but maybe we'd prefer cases to be
; broken out into separate events. That comes next.
(defthm? app-simplify
(implies (true-listp x)
(equal (append x y)
?))
:hints ((\"Goal\" :expand (append x y))))
:pbt 0
:pe :here
:pe APP-SIMPLIFY
:u
(defthm? app-simplify
(implies (true-listp x)
(equal (append x y)
?))
:hints ((\"Goal\" :expand ((true-listp x)
(true-listp (cdr x))
(append x y))))
; show some extra output; this is optional
:print-flg t)
:pe :here
:u
})")
(defmacro defthm?
(name term &key hints (prove-assumptions 't) (simplify-hyps-p 't) print-flg)
(let* ((form0
`(defthm?-fn ',name ',term ',simplify-hyps-p ',hints
',prove-assumptions ',print-flg (w state) state))
(form `(er-let* ((val ,form0))
(pprogn (f-put-global 'defthm?-result val state)
(value :invisible)))))
`(state-global-let*
((defthm?-result nil))
(er-progn (ld '(,form)
:ld-pre-eval-print nil
:ld-prompt nil)
(value (f-get-global 'defthm?-result state))))))
; This is new in 8/97. If we don't include executable counterparts of some
; functions, one of the examples in the documentation fails to simplify.
; Try the following. If you define *adjust-hints-exec-theory* to be nil
; instead, the defthm? will still fail, but it will get more stuck in the
; final proof attempt than it should.
#|
(defthm true-listp-expand-append
(implies (and (force (true-listp x))
x)
(equal (append x y)
(cons (car x) (append (cdr x) y)))))
(defthm? foo (implies (consp x) (equal (append X Y) ?))
:prove-assumptions nil)
|#
(defconst *adjust-hints-exec-theory*
'(definition-runes
(union-eq '(iff) *expandable-boot-strap-non-rec-fns*)
t
world))
(defun adjust-hints-with-runes1 (hint runes)
; hint is an alternating list of keywords and hints, e.g.,
; (:expand (foo x) :in-theory *s-prop-theory*)
(cond
((null hint)
(list :in-theory
(list 'union-theories
*adjust-hints-exec-theory*
(list 'quote runes))))
((eq (car hint) :in-theory)
(list* :in-theory
(list 'union-theories
*adjust-hints-exec-theory*
`(intersection-theories ',runes ,(cadr hint)))
(cddr hint)))
(t
(list* (car hint)
(cadr hint)
(adjust-hints-with-runes1 (cddr hint) runes)))))
(defun adjust-hints-with-runes (hints runes top-goal-seen-p)
; We know that only runes were used in the proof, and we want to adjust hints
; correspondingly.
(cond
((null hints)
(if top-goal-seen-p
nil
`(("Goal" :in-theory (union-theories
,*adjust-hints-exec-theory*
',runes)))))
(t (cons (cons (caar hints) (adjust-hints-with-runes1 (cdar hints) runes))
(adjust-hints-with-runes (cdr hints) runes
(or top-goal-seen-p
(equal (caar hints) "Goal")))))))
(defconst *fake-runes*
(list *fake-rune-for-anonymous-enabled-rule*
*fake-rune-for-type-set*
*fake-rune-for-linear*))
(defun defthm-?-fn-forms1-lst (name index x equiv lhs hints wrld)
; x is from the output of tool-fn: a list of elements of the form
; (list* runes hyps rewritten-term assumptions)
; If there is only one lemma, it has the name <name>, else we create
; <name>$0, ... <name>$n etc.
(cond
((null x)
nil)
(t (let ((runes (set-difference-equal (car (car x))
*fake-runes*))
(hyps (cadr (car x)))
(rhs (caddr (car x)))
(assumptions (cdddr (car x))))
(cons `(defthm
,(if (and (zerop index) (null (cdr x)))
name
(packn (list name '$ index)))
,(untranslate (implicate (conjoin (append assumptions hyps))
(fcons-term* equiv lhs rhs))
t wrld)
:hints ,(adjust-hints-with-runes hints runes nil))
(defthm-?-fn-forms1-lst name (1+ index) (cdr x) equiv lhs hints wrld))))))
(defun defthm?-fn-forms
(name form simplify-hyps-p hints prove-assumptions inhibit-output print-flg wrld state)
(with-ctx-summarized
(cons 'defthm? name)
(er-let*
((tform (translate form t t t ctx wrld state)))
(let* ((x (unprettyify tform))
(hyps (car (car x)))
(concl (cdr (car x))))
(cond
((and (null (cdr x))
(not (variablep concl))
(not (fquotep concl))
(variablep (fargn concl 2)))
(cond
((equivalence-relationp (ffn-symb concl) wrld)
(er-let*
((x (tool-fn (fargn concl 1) hyps simplify-hyps-p (ffn-symb concl)
state hints prove-assumptions inhibit-output print-flg
t ctx)))
(value (defthm-?-fn-forms1-lst name 0 x (ffn-symb concl)
(fargn concl 1) hints wrld))))
(t (er soft ctx
"The form supplied to DEFTHM? must be of the form ~p0 or ~p1, ~
where equiv is an equivalence relation. However, ~p2 is not ~
an equivalence relation in the current world."
'(implies hyps (equiv lhs var))
'(equiv lhs var)
(ffn-symb concl)))))
(t (er soft ctx
"The form supplied to DEFTHM? must be of the form ~p0 or ~p1,~
where var is a variable. But ~p2 is not of this form."
'(implies hyps (equiv lhs var))
'(equiv lhs var)
form)))))))
(defun defthm?-fn
(name term simplify-hyps-p hints prove-assumptions print-flg wrld state)
(state-global-let*
((inhibit-output-lst
(if (boundp-global 'defthm?-inhibit-output-lst state)
; Suggestion: '(warning observation prove event summary proof-tree)
(f-get-global 'defthm?-inhibit-output-lst state)
(@ inhibit-output-lst))))
(er-let* ((forms (defthm?-fn-forms name term simplify-hyps-p hints
prove-assumptions nil print-flg wrld state)))
(er-progn (encapsulate-fn nil (cons '(logic) forms) state nil)
(value (list* 'encapsulate () forms))))))
(defxdoc symsim
:parents (expander)
:short "Simplify given term and hypotheses."
:long "<p>Example:</p>
@({
(symsim (append x y)
((not (atom x)) (not (cdr x)))
:hints ((\"Goal\" :expand
((true-listp x)
(true-listp (cdr x))
(append x y)))))
})
<p>yields</p>
@({
Simplified term:
(CONS (CAR X) Y)
Simplified hyps:
((CONSP X) (NOT (CDR X)))~/
General Form:
(symsim term hyps
:hints hints
:inhibit-output inhibit-flg ; t, :prove, or nil, default t
:prove-assumptions prove-flg ; t, nil, or (default) any other value
:print-flg print-flg ; t or nil, default nil
:simplify-hyps-p flg ; t, nil, or :no-split; default t
)
})
<p>where @('term') is a term to be simplified assuming that each @('hyp') in
the list @('hyps') is true, and @(see hints) is as described in its @(see
documentation). The keyword arguments above are all optional, and behave as
you might expect. In particular, set @(':simplify-hyps-p') to @('nil') if you
do not want the @('hyps') to be simplified; otherwise, case splitting may occur
in the course of their simplification.</p>
<p>Prover output is inhibited if @(':inhibit-output') is @('t') (the default).
Only proof output is inhibited if @(':inhibit-output') is @(':prover') (so for
example, summaries and warnings are printed), and all prover output is shown if
@(':inhibit-output') is @('nil').</p>
<p>Also see @(see defthm?), which has a related functionality and is a bit more
thoroughly documented. Here are some examples that should help give an idea of
how @('symsim') works. (The name, by the way, is short for \"symbolically
simulate\".) Try these, as well as the examples shown above.</p>
@({
(symsim (append x y)
nil
:hints ((\"Goal\" :expand
((true-listp x)
(append x y)
(append (cdr x) y)))))
; Generates three cases:
(symsim (append x y)
((true-listp x))
:hints ((\"Goal\" :expand
((true-listp x)
(true-listp (cdr x))
(append x y)
(append (cdr x) y)))))
; Let's illustrate the role of FORCE. The following rule
; forces append to open up, and comes into play below.
(defthm true-listp-expand-append
(implies (and (force (true-listp x))
x)
(equal (append x y)
(cons (car x) (append (cdr x) y)))))
; Generates assumption forced by preceding rule.
(symsim (append x y)
((not (atom x))))
; But now we fail; but why? See next form.
(symsim (append x y)
((consp x))
:prove-assumptions t)
; Let's not inhibit output. Then we can see the failed forcing round.
(symsim (append x y)
((consp x))
:prove-assumptions t
:inhibit-output nil)
; As above, but doesn't deal with generated forced assumptions at all (just
; drops them on the floor).
(symsim (append x y)
((consp x))
:prove-assumptions nil)
})")
(defmacro symsim
(term hyps &key
hints (prove-assumptions 'try) (inhibit-output 't) (simplify-hyps-p 't)
print-flg)
`(symsim-fn ',term ',hyps ',simplify-hyps-p ',hints ',prove-assumptions
',inhibit-output ',print-flg (w state) state))
(defun symsim-fn-print-lst (tuples n total wrld state)
(cond ((null tuples)
(fms "========================================~%~%"
(list (cons #\0 n))
*standard-co* state nil))
(t
(let ((tuple (car tuples)))
(pprogn
(fms "========== Generated case #~x0 of ~x1 ==========~%"
(list (cons #\0 n)
(cons #\1 total))
*standard-co* state nil)
(fms "Runes:~% ~p0~%Simplified hyps:~% ~p1~%Simplified term:~% ~p2~%Simplified ~
assumptions:~% ~p3~%"
(list (cons #\0 (car tuple))
(cons #\1 (untranslate-lst (cadr tuple) t wrld))
(cons #\2 (untranslate (caddr tuple) nil wrld))
(cons #\3 (prettyify-clause-lst
(cdddr tuple)
(let*-abstractionp state)
wrld)))
*standard-co* state nil)
(symsim-fn-print-lst (cdr tuples) (1+ n) total wrld state))))))
(defun symsim-fn (term hyps simplify-hyps-p hints prove-assumptions
inhibit-output print-flg wrld state)
; Returns a list of tuples of the form (list* runes hyps rewritten-term
; assumptions), after doing some appropriate printing.
(er-let*
((tterm (translate term t t t 'top-level wrld state))
(thyps (translate-term-lst hyps t t t 'top-level wrld state))
(tuples-lst (tool-fn tterm thyps simplify-hyps-p 'equal state
hints prove-assumptions
inhibit-output
print-flg t (cons 'symsim-fn term))))
(pprogn (if print-flg
(symsim-fn-print-lst tuples-lst 1 (length tuples-lst) wrld
state)
state)
(value tuples-lst))))
; DARON: added the new function to streamline calls to normalize:
(defun normalize-no-ttree (term iff-flg type-alist ens wrld)
(mv-let (x ttree)
(normalize term iff-flg type-alist ens wrld nil)
(declare (ignore ttree))
x))
; PETE: new functions for ccg analysis.
; DARON: altered functions below to take ctx, ens, and wrld.
(defun simp-hyps-aux
(hyps-remaining hyps-init hyps-res ctx ens wrld state hints
inhibit-output print-flg simp-flg)
(cond
((null hyps-remaining)
(value (reverse hyps-res)))
(t (let* ((hyp0 (car hyps-remaining))
(hyp (normalize-no-ttree hyp0 t nil ens wrld))
(other-hyps (remove1-equal hyp0 hyps-init)))
;; DARON: changed this er-let* to an mv-let so we can catch any
;; errors. If there are errors, we simply use the original term.
(mv-let
(erp x state)
(tool2-fn0 hyp
other-hyps
'iff ctx ens wrld state hints nil
inhibit-output nil print-flg nil)
(let* ((res (if erp
hyp
(normalize-no-ttree (cadr x) t nil ens wrld)))
(simplified-to-t? (equal res ''t))
(simplified-to-nil? (equal res ''nil))
(simplified? (term-order res hyp))
(always-simp? (and (not (equal simp-flg :t))
(not (equal simp-flg :term-order))))
(nhyps-init
(cond (simplified-to-t?
other-hyps)
((or always-simp?
(and simplified? (not (equal simp-flg :t))))
(append (flatten-ands-in-lit res)
other-hyps))
(t (append (flatten-ands-in-lit hyp)
other-hyps))))
(nhyps-res
(cond (simplified-to-t? hyps-res)
((or always-simp?
(and simplified? (not (equal simp-flg :t))))
(append (flatten-ands-in-lit res)
hyps-res))
(t
(append (flatten-ands-in-lit hyp)
hyps-res)))))
(if simplified-to-nil?
(value nil)
(simp-hyps-aux (cdr hyps-remaining)
nhyps-init
nhyps-res
ctx ens wrld state hints
inhibit-output print-flg simp-flg))))))))
; DARON: changed simp-hyps to simp-hyps0, requiring ctx, ens, and wrld from the
; user, and then wrote a new simp-hyps which simply calls simp-hyps0 with these
; values provided.
(defun simp-hyps0 (hyps ctx ens wrld state hints inhibit-output print-flg simp-flg)
"See the documentation for simp-hyps. This function has the same
functionality, but requires the user to provide the ctx, ens, and wrld."
(let ((nd-hyps (remove-duplicates hyps)))
(er-let*
((t-nd-hyps
(simp-hyps-aux nd-hyps nd-hyps nil ctx ens wrld state hints
inhibit-output print-flg :t)))
(if (equal simp-flg :t)
(value t-nd-hyps)
(simp-hyps-aux
t-nd-hyps t-nd-hyps nil ctx ens wrld state hints
inhibit-output print-flg simp-flg)))))
(defun simp-hyps (hyps state hints inhibit-output print-flg simp-flg)
"Given a list of terms (hyps), return a list that is a subset
of hyps. The conjunction of hyps should be equal to the
conjuction of the returned list. If simp-flg is :t, all we do
is to remove elements of hyps that can be proven to simplify to
t, assuming the rest of the elements in hyps hold. If simp-flg
is :term-order, then we replace elements of hyps with what they
simplify to (again, assuming the rest of the elements in hyps
hold) if we wind up with a smaller term (as determined by the
function term-order). Otherwise, we replace elements of hyps
with whatever they simplify to (again, assuming the rest of the
elements in hyps hold). Some care is taken to deal with
duplicates, and the like. For example, we always try with
simp-flg set to :t first since this tends to return results
that depend less on the order of arguments. To see this, note
that if you give ((natp x) (integerp x)) as input, you would get
different results when you change the order of the hyps (if you
didn't try :t first). "
(simp-hyps0 hyps 'SIMP-HYPS (ens state) (w state)
state hints inhibit-output print-flg simp-flg))
#|
Testing code
(simp-hyps '((natp x) (natp x)) state nil t nil :t)
(simp-hyps '((natp x) (natp x)) state nil t nil :term-order)
(simp-hyps '((natp x) (natp x)) state nil t nil nil)
(simp-hyps '((natp x) (integerp x)) state nil t nil :t)
(simp-hyps '((natp x) (integerp x)) state nil t nil :term-order)
(simp-hyps '((natp x) (integerp x)) state nil t nil nil)
(simp-hyps '((integerp x) (natp x) (integerp x) (natp x)) state nil t nil :t)
(simp-hyps '((integerp x) (natp x) (integerp x) (natp x)) state nil t nil :term-order)
(simp-hyps '((integerp x) (natp x) (integerp x) (natp x)) state nil t nil nil)
(simp-hyps '((not (stringp x)) (integerp x) (natp x) (posp x)) state nil t nil :t)
(simp-hyps '((not (stringp x)) (integerp x) (natp x) (posp x)) state nil t nil :term-order)
(simp-hyps '((not (stringp x)) (integerp x) (natp x) (posp x)) state nil t nil nil)
(simp-hyps '((natp x) (integerp x) (< x 1)) state nil t nil :t)
(simp-hyps '((natp x) (integerp x) (< x 1)) state nil t nil :term-order)
(simp-hyps '((natp x) (integerp x) (< x 1)) state nil t nil nil)
(simp-hyps '((natp x) (integerp x) (< x 1)) state nil t nil :t)
(simp-hyps '((natp x) (integerp x) (< x 1)) state nil t nil :term-order)
(simp-hyps '((integerp x) (natp x) (< x 1)) state nil t nil nil)
(simp-hyps '((natp x) (stringp x)) state nil t nil :t)
(simp-hyps '((natp x) (stringp x)) state nil t nil :term-order)
(simp-hyps '((natp x) (stringp x)) state nil t nil nil)
|#
#|
For possible future work.
Consider
(simp-hyps '((natp x) (< x 1)) state nil t nil nil)
This doesn't lead to simplifications, but we can figure out that
x=0. Maybe we should think about how to do this and do it.
|#
|