/usr/share/acl2-7.2dfsg/linear-b.lisp is in acl2-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 | ; ACL2 Version 7.2 -- A Computational Logic for Applicative Common Lisp
; Copyright (C) 2016, Regents of the University of Texas
; This version of ACL2 is a descendent of ACL2 Version 1.9, Copyright
; (C) 1997 Computational Logic, Inc. See the documentation topic NOTE-2-0.
; This program is free software; you can redistribute it and/or modify
; it under the terms of the LICENSE file distributed with ACL2.
; This program is distributed in the hope that it will be useful,
; but WITHOUT ANY WARRANTY; without even the implied warranty of
; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
; LICENSE for more details.
; Written by: Matt Kaufmann and J Strother Moore
; email: Kaufmann@cs.utexas.edu and Moore@cs.utexas.edu
; Department of Computer Science
; University of Texas at Austin
; Austin, TX 78712 U.S.A.
(in-package "ACL2")
;=================================================================
; We continue our development of linear arithmetic. In particular,
; we define the functions add-polys and linearize.
;=================================================================
; Add-polys
(defun polys-from-type-set (term force-flag dwp type-alist ens wrld ttree)
; If possible, we create a list of polys based upon the type-set
; of term.
; Warning: This function should not be used with any terms that are
; not legitimate pot-vars. See the definition of good-pot-varp.
; Assuming that term is a legitimate pot-label --- meets all the
; invariants --- we do not have to normalize any of the polys below.
; We check that term is OK and throw an error if not. It would,
; however, not be very expensive to wrap the below in a call to
; normalize-poly-lst, and thereby avoid the potential error situation.
(if (good-pot-varp term)
(mv-let (ts ts-ttree)
(type-set term force-flag dwp type-alist ens wrld ttree nil nil)
(cond ((ts-subsetp ts *ts-zero*)
(list
;; 0 <= term
(add-linear-terms :rhs term
(base-poly ts-ttree
'<=
t
nil))
;; term <= 0
(add-linear-terms :lhs term
(base-poly ts-ttree
'<=
t
nil))))
((ts-subsetp ts *ts-positive-integer*)
(list
;; 1 <= term
(add-linear-terms :lhs *1*
:rhs term
(base-poly ts-ttree
'<=
t
nil))))
((ts-subsetp ts *ts-negative-integer*)
(list
;; term <= -1
(add-linear-terms :lhs term
:rhs ''-1
(base-poly ts-ttree
'<=
t
nil))))
((ts-subsetp ts
#-:non-standard-analysis *ts-positive-rational*
#+:non-standard-analysis *ts-positive-real*)
(list
;; 0 < term
(add-linear-terms :rhs term
(base-poly ts-ttree
'<
t
nil))))
((ts-subsetp ts
#-:non-standard-analysis *ts-negative-rational*
#+:non-standard-analysis *ts-negative-real*)
(list
;; term < 0
(add-linear-terms :lhs term
(base-poly ts-ttree
'<
t
nil))))
((ts-subsetp ts
#-:non-standard-analysis *ts-non-negative-rational*
#+:non-standard-analysis *ts-non-negative-real*)
(list
;; 0 <= term
(add-linear-terms :rhs term
(base-poly ts-ttree
'<=
t
nil))))
((ts-subsetp ts
#-:non-standard-analysis *ts-non-positive-rational*
#+:non-standard-analysis *ts-non-positive-real*)
(list
;; term <= 0
(add-linear-terms :lhs term
(base-poly ts-ttree
'<=
t
nil))))
(t
nil)))
(er hard 'inverse-polys
"A presumptive pot-label, ~x0, has turned out to be illegitimate. ~
If possible, please send a script reproducing this error ~
to the authors of ACL2."
term)))
(defun add-type-set-polys (var-lst new-pot-lst old-pot-lst
already-noted-vars
pt nonlinearp
type-alist ens force-flg wrld)
; We have just finished adding a bunch of polys to a pot-lst. In ACL2
; versions prior to 2.7, these polys were canceled against any
; type-set information on the fly. We now add the type-set
; information explicitly. This function checks which pots have been
; modified (any new polys in these pots would have been canceled
; against type-set knowledge in the past), derives polys (using
; type-set information) about the vars of the modified pots, and adds
; them to the pots.
(cond ((null var-lst)
(let ((new-var-lst (changed-pot-vars new-pot-lst old-pot-lst
already-noted-vars)))
(if new-var-lst
(add-type-set-polys new-var-lst
new-pot-lst new-pot-lst
new-var-lst
pt nonlinearp
type-alist ens force-flg wrld)
(mv nil new-pot-lst))))
(t
(mv-let (contradictionp new-new-pot-lst)
(add-polys0 (polys-from-type-set (car var-lst)
force-flg
nil ;;; dwp
type-alist
ens
wrld
nil) ;;; ttree
new-pot-lst pt nonlinearp t)
(cond (contradictionp
(mv contradictionp nil))
(t
(add-type-set-polys (cdr var-lst)
new-new-pot-lst old-pot-lst
already-noted-vars
pt nonlinearp
type-alist ens force-flg wrld)))))))
(defun add-polynomial-inequalities (lst pot-lst pt nonlinearp type-alist ens
force-flg wrld)
; Wrapper for the old add-polys (now add-polys0) so that we can
; eliminate the use of cancel-poly-against-type-set from within add-poly.
; We add the polys in lst to the pot-lst, and then call add-type-set-polys
; which performs a similar function to the old calls to
; cancel-poly-against-type-set.
; Historical Note: The nearest approximation to this function in Nqthm
; was named add-equations.
(mv-let (contradictionp new-pot-lst)
(add-polys0 lst pot-lst pt nonlinearp t)
(cond (contradictionp
(mv contradictionp nil))
(t
(let ((changed-pot-vars
(changed-pot-vars new-pot-lst pot-lst nil)))
(add-type-set-polys changed-pot-vars
new-pot-lst new-pot-lst
changed-pot-vars
pt nonlinearp
type-alist ens force-flg wrld))))))
#-acl2-loop-only
(defparameter *add-polys-counter*
; This is used by dmr-string to show the cumulative number of calls of
; add-polys, as requested by Robert Krug.
0)
(defun add-polys (lst pot-lst pt nonlinearp type-alist ens force-flg wrld)
#-acl2-loop-only
(when (f-get-global 'dmrp *the-live-state*)
(return-from
add-polys
(progn
(incf *add-polys-counter*)
(pstk
(add-polynomial-inequalities lst pot-lst pt nonlinearp type-alist ens
force-flg wrld)))))
(add-polynomial-inequalities lst pot-lst pt nonlinearp type-alist ens
force-flg wrld))
;=================================================================
; Linearize
(mutual-recursion
(defun eval-ground-subexpressions (term ens wrld state ttree)
(cond
((or (variablep term)
(fquotep term)
(eq (ffn-symb term) 'hide))
(mv nil term ttree))
((flambda-applicationp term)
(mv-let
(flg args ttree)
(eval-ground-subexpressions-lst (fargs term) ens wrld state ttree)
(cond
((all-quoteps args)
(mv-let
(flg val ttree)
(eval-ground-subexpressions
(sublis-var (pairlis$ (lambda-formals (ffn-symb term)) args)
(lambda-body (ffn-symb term)))
ens wrld state ttree)
(declare (ignore flg))
(mv t val ttree)))
(flg
; We could look for just those args that are quoteps, and substitute those,
; presumably then calling make-lambda-application to create a lambda out of the
; result. But we'll put that off for another time, or even indefinitely,
; noting that through Version_2.9.4 we did not evaluate any ground lambda
; applications.
(mv t (cons-term (ffn-symb term) args) ttree))
(t (mv nil term ttree)))))
((eq (ffn-symb term) 'if)
(mv-let
(flg1 arg1 ttree)
(eval-ground-subexpressions (fargn term 1) ens wrld state ttree)
(cond
((quotep arg1)
(if (cadr arg1)
(mv-let
(flg2 arg2 ttree)
(eval-ground-subexpressions (fargn term 2) ens wrld state ttree)
(declare (ignore flg2))
(mv t arg2 ttree))
(mv-let
(flg3 arg3 ttree)
(eval-ground-subexpressions (fargn term 3) ens wrld state ttree)
(declare (ignore flg3))
(mv t arg3 ttree))))
(t (mv-let
(flg2 arg2 ttree)
(eval-ground-subexpressions (fargn term 2) ens wrld state ttree)
(mv-let
(flg3 arg3 ttree)
(eval-ground-subexpressions (fargn term 3) ens wrld state ttree)
(mv (or flg1 flg2 flg3)
(if (or flg1 flg2 flg3)
(fcons-term* 'if arg1 arg2 arg3)
term)
ttree)))))))
(t (mv-let
(flg args ttree)
(eval-ground-subexpressions-lst (fargs term) ens wrld state ttree)
(cond
; The following test was taken from rewrite with a few modifications
; for the formals used.
((and (logicalp (ffn-symb term) wrld) ; maybe fn is being admitted
(all-quoteps args)
(enabled-xfnp (ffn-symb term) ens wrld)
; We don't mind disallowing constrained functions that have attachments,
; because the call of ev-fncall below disallows the use of attachments (last
; parameter, aok, is nil).
(not (getpropc (ffn-symb term) 'constrainedp nil wrld)))
(mv-let
(erp val latches)
(pstk
(ev-fncall (ffn-symb term)
(strip-cadrs args)
state nil t nil))
(declare (ignore latches))
(cond
(erp
(cond (flg
(mv t (cons-term (ffn-symb term) args) ttree))
(t (mv nil term ttree))))
(t (mv t
(kwote val)
(push-lemma (fn-rune-nume (ffn-symb term) nil t wrld)
ttree))))))
(flg (mv t (cons-term (ffn-symb term) args) ttree))
(t (mv nil term ttree)))))))
(defun eval-ground-subexpressions-lst (lst ens wrld state ttree)
(cond ((null lst) (mv nil nil ttree))
(t (mv-let
(flg1 x ttree)
(eval-ground-subexpressions (car lst) ens wrld state ttree)
(mv-let
(flg2 y ttree)
(eval-ground-subexpressions-lst (cdr lst) ens wrld state ttree)
(mv (or flg1 flg2)
(if (or flg1 flg2)
(cons x y)
lst)
ttree))))))
)
(defun poly-set (op poly1 poly2)
; Suppose linearize is called on some term, term. The output of
; linearize is either nil, (list (list poly1 poly2)), or (list (list
; poly1) (list poly2)). An answer of the first form means "no
; arithmetic information can be extracted from the assumption that
; term is true." An answer of the second form means "both poly1 and
; poly2 are true if term is true." An answer of the third form means
; "either poly1 or poly2 is true if term is true."
; This functions takes two polys and an operation, op, and constructs
; the answer returned by linearize. Op is either 'and or 'or and
; determines whether we construct (list (list poly1 poly2)), when
; op='and, or (list (list poly1) (list poly2)), when op='or.
; However, there are two special cases.
; First, it is sometimes the case that we want to construct an 'and
; but only have one poly, the other one being nil. This may happen
; when we were going to construct an 'or but noticed that one branch
; is contradictory. When this happens it is always poly1 that is nil
; and poly2 that we want to return.
; Second, it may happen that either or both of the polys are silly in
; the sense that they are based on false assumptions. Since silly polys
; are logically true, we act accordingly. Thus, if we are to return
; a conjunction and one of the polys is silly we return the other.
; But if we are to return a disjunction and one is silly, we return nil,
; meaning we could extract no arithmetic information. For example,
; suppose poly2 is silly and we are to return (list (list poly1) (list poly2)).
; Then the silliness of poly2 means the second disjunct is true, which
; is represented here as (list (list poly1) nil). That, by the way, was
; nqthm's answer in this case. However, this disjunct gives the caller
; no help because it means either poly1 is true or T is true. So we
; just tell the caller "no information".
; Note about Nqthm: As remarked above, nqthm's linearize can return
; (list (list poly1) nil). How is this used? It is put on the
; split-lst when we start adding polynomials to the pot. We then see if
; we can get a contradiction from one side and if so, we assume the other.
; We certainly can't get a contradiction from the nil side. Suppose
; we got a contradiction from the other. Then we'd assume the other
; side, which is a no-op. The end result is that returning such an
; answer causes work but is guaranteed to have no effect.
; It is unlikely that we can generate a silly poly2 without generating a
; silly poly1, since silliness stems from requiring a false rationalp
; assumption. However, rather than convince ourselves that they are
; both silly if either is, we'll just check both.
(cond ((eq op 'and)
(cond ((or (eq poly1 nil)
(silly-polyp poly1))
(cond ((silly-polyp poly2) nil)
(t (list (list poly2)))))
((silly-polyp poly2)
(list (list poly1)))
(t (list (list poly1 poly2)))))
((or (silly-polyp poly1)
(silly-polyp poly2))
nil)
((impossible-polyp poly1)
(list (list (change poly poly2
:ttree
(cons-tag-trees (access poly poly1 :ttree)
(access poly poly2 :ttree))
:parents
(marry-parents (access poly poly1 :parents)
(access poly poly2 :parents))))))
((impossible-polyp poly2)
(list (list (change poly poly1
:ttree
(cons-tag-trees (access poly poly1 :ttree)
(access poly poly2 :ttree))
:parents
(marry-parents (access poly poly1 :parents)
(access poly poly2 :parents))))))
(t (list (list poly1) (list poly2)))))
;; RAG - I changed complex-rational to complex, and rational to real,
;; to stand for the non-zero numbers.
(defun linearize1 (term positivep type-alist ens force-flg wrld ttree state)
; See the comment in linearize. Linearize1 does all the work of linearize
; except that the latter maps normalize-poly over the former.
(mv-let (flg temp ttree)
(eval-ground-subexpressions term ens wrld state ttree)
(declare (ignore flg))
(mv-let
(not-flg atm)
(strip-not temp)
; Let us pause for a moment here. Term is the original term we are to
; linearize and is preserved for the use of add-linear-assumption. Temp is
; the result of replacing all ground subexpressions in term by their
; values, and atm is temp with any 'not stripped off. Recall that we
; are attempting to derive a contradiction by assuming either (1) that
; term is true if positivep is true, or (2) that term is false if
; positivep is false. Since not-flg tells us whether atm is the
; negation of term/temp, we use it to reset positivep to reflect its
; new role with respect to atm.
(let ((positivep (if not-flg (not positivep) positivep)))
(cond
((inequalityp atm)
(let ((lhs (fargn atm 1))
(rhs (fargn atm 2)))
(mv-let (ts-lhs ts-ttree)
(type-set lhs force-flg nil type-alist ens wrld ttree nil nil)
(mv-let (ts-rhs ts-ttree)
(type-set rhs force-flg nil type-alist ens wrld ts-ttree nil
nil)
(if positivep ; (< lhs rhs)
(cond
((and (ts-integerp ts-lhs)
(ts-integerp ts-rhs))
; (implies (and (< lhs rhs)
; (integerp lhs)
; (integerp rhs))
; (<= (1+ lhs) rhs))
(poly-set 'and
nil
(add-linear-terms
:lhs lhs
:lhs *1*
:rhs rhs
(base-poly ts-ttree
'<=
t
nil))))
(t ; still (< lhs rhs), but not both integerp
(poly-set 'and
nil
(add-linear-terms
:lhs lhs
:rhs rhs
(let ((rationalp-flg
(and (ts-real/rationalp ts-lhs)
(ts-real/rationalp ts-rhs))))
(base-poly0 (if rationalp-flg
ts-ttree
ttree)
; :Parent wart:
; In a slight break from tradition (here and in three other places below that
; refer to this comment), we use the parents from the original ttree. When
; fixing a (probably long-standing) bug in Version_3.0.1 by recording ts-ttree
; above in the case that rationalp-flg is true, we found that the regression
; suite broke in three places without this tweak on the parents. Since
; rationalp-flg is only used in non-linear arithmetic, this seems like a minor
; break from our traditional propagation of parent trees. We considered making
; a similar change for all calls of base-poly in this function, but that led to
; a proof failure in community book
; books/workshops/2004/schmaltz-borrione/support/routing_defuns.lisp that
; looked like it would be painful to fix, and we took that as a sign that such
; loss of backward compatibility could be painful for other users, and
; potentially even a bad heuristic.
(collect-parents ttree)
'<
rationalp-flg
nil))))))
; The (not positivep) case. Note:
; (implies (not (< lhs rhs))
; (<= rhs lhs))
(poly-set 'and
nil
(add-linear-terms
:lhs rhs
:rhs lhs
(let ((rationalp-flg
(and (ts-real/rationalp ts-lhs)
(ts-real/rationalp ts-rhs))))
(base-poly0 (if rationalp-flg ts-ttree ttree)
; See the "break from tradition" comment above for a discussion of the
; parents.
(collect-parents ttree)
'<=
rationalp-flg
nil)))))))))
((equalityp atm)
(let ((lhs (fargn atm 1))
(rhs (fargn atm 2)))
(mv-let (ts-lhs ts-ttree)
(type-set lhs force-flg nil type-alist ens wrld ttree nil nil)
(mv-let (ts-rhs ts-ttree)
(type-set rhs force-flg nil type-alist ens wrld ts-ttree nil
nil)
; Here is the one place that we can construct a poly which is derived
; from a negated equality. Note that the final argument to base-poly
; is 'T.
(if positivep
; (implies (equal lhs rhs)
; (and (<= lhs rhs) (<= rhs lhs)))
(let ((rationalp-flg (and (ts-real/rationalp ts-lhs)
(ts-real/rationalp ts-rhs))))
(poly-set 'and
(add-linear-terms
:lhs lhs
:rhs rhs
(base-poly0 (if rationalp-flg ts-ttree ttree)
; See the "break from tradition" comment above for a discussion of the
; parents.
(collect-parents ttree)
'<=
rationalp-flg
t))
(add-linear-terms
:lhs rhs
:rhs lhs
(base-poly0 (if rationalp-flg ts-ttree ttree)
; See the "break from tradition" comment above for a discussion of the
; parents.
(collect-parents ttree)
'<=
rationalp-flg
t))))
; Other case: (not (equal lhs rhs)). But we need additional (type) information
; in order to derive inequalities.
(cond ((and (ts-subsetp ts-lhs *ts-integer*)
(ts-subsetp ts-rhs *ts-integer*))
; (implies (and (not (equal lhs rhs))
; (integerp lhs)
; (integerp rhs))
; (or (<= (1+ lhs) rhs)
; (<= (1+ rhs) lhs)))
(poly-set 'or
(add-linear-terms
:lhs lhs
:lhs *1*
:rhs rhs
(base-poly ts-ttree
'<=
t
nil))
(add-linear-terms
:lhs rhs
:lhs *1*
:rhs lhs
(base-poly ts-ttree
'<=
t
nil))))
((if (ts-subsetp ts-lhs *ts-acl2-number*)
(or (ts-subsetp ts-rhs *ts-acl2-number*)
(ts-disjointp ts-lhs *ts-zero*))
(and (ts-subsetp ts-rhs *ts-acl2-number*)
(ts-disjointp ts-rhs *ts-zero*)))
; (implies (and (not (equal lhs rhs))
; (or (and (acl2-numberp lhs)
; (acl2-numberp rhs))
; (and (acl2-numberp lhs)
; (not (equal lhs 0)))
; (and (acl2-numberp rhs)
; (not (equal rhs 0)))))
; (or (< lhs rhs)
; (< rhs lhs)))
(let ((rationalp-flg
(and (ts-real/rationalp ts-lhs)
(ts-real/rationalp ts-rhs))))
(poly-set 'or
(add-linear-terms
:lhs lhs
:rhs rhs
(base-poly ts-ttree
'<
rationalp-flg
nil))
(add-linear-terms
:lhs rhs
:rhs lhs
(base-poly ts-ttree
'<
rationalp-flg
nil)))))
((and (ts-acl2-numberp ts-lhs)
force-flg
(ts-intersectp ts-rhs *ts-acl2-number*))
; (implies (and (not (equal lhs rhs))
; (acl2-numberp lhs)
; (force (acl2-numberp rhs)))
; (or (< lhs rhs)
; (< rhs lhs)))
(mv-let (flg new-ttree)
(add-linear-assumption
term
`(acl2-numberp ,rhs)
type-alist ens
(immediate-forcep nil ens)
force-flg wrld ts-ttree)
; We strongly suspect that add-linear-assumption will succeed with flg =
; :added, since (ts-intersectp ts-rhs *ts-acl2-number*). But we do not depend
; on this without checking it. Indeed, it fails for the following example,
; sent to us by Sol Swords.
; (defstub bar-p (x) nil)
; (defstub foo (x) nil)
;
; (defaxiom type-of-foo
; (implies (force (bar-p x))
; (or (and (rationalp (foo x))
; (<= 0 (foo x)))
; (equal (foo x) nil)))
; :rule-classes :type-prescription)
;
; (thm (implies (not (rationalp (foo x))) (equal 0 (foo x))))
(cond
((and (not (eq flg :failed))
(not (eq flg :known-false)))
(poly-set 'or
(add-linear-terms
:lhs lhs
:rhs rhs
(base-poly new-ttree
'<
nil
nil))
(add-linear-terms
:lhs rhs
:rhs lhs
(base-poly new-ttree
'<
nil
nil))))
(t nil))))
((and (ts-acl2-numberp ts-rhs)
force-flg
(ts-intersectp ts-lhs *ts-acl2-number*))
; (implies (and (not (equal lhs rhs))
; (acl2-numberp rhs)
; (force (acl2-numberp lhs)))
; (or (< lhs rhs)
; (< rhs lhs)))
(mv-let (flg new-ttree)
(add-linear-assumption
term
`(acl2-numberp ,lhs)
type-alist ens
(immediate-forcep nil ens)
force-flg wrld ts-ttree)
(cond
((and (not (eq flg :failed))
(not (eq flg :known-false)))
(poly-set 'or
(add-linear-terms
:lhs lhs
:rhs rhs
(base-poly new-ttree
'<
nil
nil))
(add-linear-terms
:lhs rhs
:rhs lhs
(base-poly new-ttree
'<
nil
nil))))
(t nil))))
(t
nil)))))))
((quotep atm)
; This is a strange one. It can happen that the
; eval-ground-subexpressions can reduce the term to a constant. We
; saw this happen in a bug reported by Jun Sawada. Suppose (<= 2 (foo
; x)) is a :LINEAR lemma about foo. Suppose we wish to prove (not
; (equal 1 (foo 3))). This should be obvious. But we assume the
; negation of the conclusion and get (foo 3) = 1. We then find the
; linear lemma and instantiate it to get (<= 2 (foo 3)). We then
; rewrite-linear-concl and get (<= 2 1), which we eval to 'nil! If we
; do not recognize that we've succeeded here, we do not prove the
; theorem because all manner of other heuristics prevent us from using
; (<= 2 (foo x)) against the current literal. Not surprisingly, this
; is an example of tail biting: we've used the negation of the goal to
; prevent ourselves from proving it! One could probably construct a
; more insidious example of tail biting from this example -- an
; example that is not solved by the hack here of recognizing when eval
; solved our problem -- by arranging for rewrite-linear-concl to
; rewrite the inequality to something that we can't use but which
; doesn't eval to nil.
; Here is another curious example:
; ACL2 !>
; (thm
; (implies (and (not (consp x))
; (true-listp x))
; (equal (reverse (reverse x)) x)))
;
; But simplification reduces this to T, using the :executable-counterparts
; of EQUAL and REVERSE and linear arithmetic.
;
; Q.E.D.
;
; Summary
; Form: ( THM ...)
; Rules: ((:DEFINITION NOT)
; (:EXECUTABLE-COUNTERPART EQUAL)
; (:EXECUTABLE-COUNTERPART REVERSE)
; (:FAKE-RUNE-FOR-LINEAR NIL))
; Warnings: None
; Time: 0.01 seconds (prove: 0.01, print: 0.00, other: 0.00)
;
; Proof succeeded.
; Note the presence of (:FAKE-RUNE-FOR-LINEAR NIL).
; This oddity is due to the fact that we now rewrite all terms (not
; just the conclusion of linear lemmas) before adding them to the
; linear-pot-lst.
(if positivep
; Recall that we are hoping to derive a contradiction from assuming atm
; true. Hence, we win iff atm is 'NIL.
(if (equal atm *nil*)
(poly-set 'and
nil
(impossible-poly ttree))
nil)
; We are hoping to derive a contradiction from assuming atm false. Hence,
; we win iff atm is not 'NIL.
(if (not (equal atm *nil*))
(poly-set 'and
nil
(impossible-poly ttree))
nil)))
(t nil))))))
(defun linearize (term positivep type-alist ens force-flg wrld ttree state)
; If positivep we are to linearize term; else we are to linearize the negation
; of term. The linearization of a term is either NIL, meaning no linear
; information was extracted from the term; or else it is a list of length 1
; containing a list of polynomials ((p1...pn)) such that term implies their
; conjunction (p1&...&pn); or else it is a list of length 2, ((p1...pn)
; (q1...qn)), such that term implies the disjunction (p1&...&pn) \/
; (q1&...&qn). The claim that the term implies the polys has to be taken with
; a grain of salt: the additional 'assumptions in the ttree fields of the polys
; must be considered.
; There are two situations where this code might add an assumption to the polys
; it creates. The first is that we sometimes call type-set and may get back a
; ttree with assumptions in it, which then infect our polys. The second
; involves the linearization of negative equalities, where we insist that both
; x and y be numeric in order to derive (or (< x y) (< y x)) from (not (equal x
; y)). Otherwise, we do not add any assumptions to our polys.
; We store ttree in the ttree of the poly.
; Trace Note:
; (trace (linearize
; :entry
; (list* (car si::arglist) (cadr si::arglist) (caddr si::arglist)
; '|ens| (car (cddddr si::arglist)) '(|wrld| |ttree| |state|))
; :exit
; (cond ((null (car values)) (list nil))
; ((null (cdr (car values)))
; (list (cons 'and (show-poly-lst (car (car values))))))
; (t (list
; (list 'or
; (cons 'and (show-poly-lst (car (car values))))
; (cons 'and (show-poly-lst (cadr (car values))))))))))
(let ((temp (linearize1 term positivep type-alist ens
force-flg wrld ttree state)))
(cond ((null temp)
nil)
((null (cdr temp))
(list (normalize-poly-lst (car temp))))
(t
(list (normalize-poly-lst (car temp))
(normalize-poly-lst (cadr temp)))))))
(defun linearize-lst1
(term-lst ttrees positivep type-alist ens force-flg wrld state
poly-lst split-lst)
(cond ((null term-lst)
(mv (reverse poly-lst) (reverse split-lst)))
(t (let ((lst (linearize (car term-lst)
positivep
type-alist ens force-flg wrld
(car ttrees)
state)))
(cond
((null lst)
(linearize-lst1 (cdr term-lst)
(cdr ttrees)
positivep
type-alist ens force-flg wrld state
poly-lst split-lst))
((null (cdr lst))
(linearize-lst1 (cdr term-lst)
(cdr ttrees)
positivep
type-alist ens force-flg wrld state
(revappend (car lst) poly-lst) split-lst))
(t
(linearize-lst1 (cdr term-lst)
(cdr ttrees)
positivep
type-alist ens force-flg wrld state
poly-lst (cons lst split-lst))))))))
(defun linearize-lst
(term-lst ttrees positivep type-alist ens force-flg wrld state)
; This function linearizes every term in term-lst, using the parity
; indicated by positivep, and type-alist and wrld. This effectively
; assumes true/false (as per positivep) each term in term-lst and produces
; some polys. Ttrees is in weak 1:1 correspondence with term-lst and
; enumerates the parent trees to use for each term in all the polys
; generated for the term; if ttrees is nil, no parent tree is stored.
; We return two values, poly-lst and split-lst. The first is a list of
; polys that may be assumed true. I.e., all these polys are implied by the
; assumption of term-lst. The second is a list of doublets (lst1 lst2),
; such that each lst is a list of polys and the assumption of term-lst
; implies one of either lst1 or lst2 for each doublet.
(linearize-lst1 term-lst ttrees positivep type-alist ens force-flg wrld state
nil nil))
|