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; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.com/
;
; License: (An MIT/X11-style license)
;
; Permission is hereby granted, free of charge, to any person obtaining a
; copy of this software and associated documentation files (the "Software"),
; to deal in the Software without restriction, including without limitation
; the rights to use, copy, modify, merge, publish, distribute, sublicense,
; and/or sell copies of the Software, and to permit persons to whom the
; Software is furnished to do so, subject to the following conditions:
;
; The above copyright notice and this permission notice shall be included in
; all copies or substantial portions of the Software.
;
; THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
; IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
; FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
; AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
; LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
; FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
; DEALINGS IN THE SOFTWARE.
;
; Original author: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "colors")
(include-book "skeletonp")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund tactic.generalize-all-okp (x)
(declare (xargs :guard (tactic.skeletonp x)))
(let ((goals (tactic.skeleton->goals x))
(tacname (tactic.skeleton->tacname x))
(extras (tactic.skeleton->extras x))
(history (tactic.skeleton->history x)))
(and (equal tacname 'generalize-all)
(consp extras)
(let ((expr (car extras)) ;; the term to generalize
(var (cdr extras)) ;; the new variable to generalize to
(prev-goals (tactic.skeleton->goals history)))
(and (consp prev-goals)
(logic.termp expr)
(logic.variablep var)
(not (memberp var (logic.term-list-list-vars prev-goals)))
(equal goals (logic.replace-subterm-list-list prev-goals expr var)))))))
(defund tactic.generalize-all-env-okp (x atbl)
(declare (xargs :guard (and (tactic.skeletonp x)
(tactic.generalize-all-okp x)
(logic.arity-tablep atbl))
:guard-hints (("Goal" :in-theory (enable tactic.generalize-all-okp)))))
(let* ((extras (tactic.skeleton->extras x))
(expr (car extras)))
(logic.term-atblp expr atbl)))
(defthm booleanp-of-tactic.generalize-all-okp
(equal (booleanp (tactic.generalize-all-okp x))
t)
:hints(("Goal" :in-theory (e/d (tactic.generalize-all-okp)
((:executable-counterpart acl2::force))))))
(defthm booleanp-of-tactic.generalize-all-env-okp
(equal (booleanp (tactic.generalize-all-env-okp x atbl))
t)
:hints(("Goal" :in-theory (e/d (tactic.generalize-all-env-okp)
((:executable-counterpart acl2::force))))))
(defund tactic.generalize-all-tac (x expr var)
;; Replace occurrences of expr with var, a new variable
(declare (xargs :guard (and (tactic.skeletonp x)
(logic.termp expr)
(logic.variablep var))))
(let ((goals (tactic.skeleton->goals x)))
(if (not (consp goals))
(ACL2::cw "~s0generalize-all-tac failure~s1: all clauses have already been proven.~%" *red* *black*)
(let* ((clause-vars (logic.term-list-list-vars goals))
(replacements (logic.replace-subterm-list-list goals expr var)))
(cond ((memberp var clause-vars)
(ACL2::cw "~s0generalize-all-tac failure~s1: we need to use a fresh variable, but ~x2 ~
is already mentioned in some clause.~%" *red* *black* var))
((equal replacements goals)
(ACL2::cw "~s0generalize-all-tac failure~s1: the clauses did not change due to this ~
generalization.~%" *red* *black*))
(t
(tactic.extend-skeleton replacements
'generalize-all
(cons expr var)
x)))))))
(defthm forcing-tactic.skeletonp-of-tactic.generalize-all-tac
(implies (and (tactic.generalize-all-tac x expr var)
(force (logic.variablep var))
(force (tactic.skeletonp x)))
(equal (tactic.skeletonp (tactic.generalize-all-tac x expr var))
t))
:hints(("Goal" :in-theory (enable tactic.generalize-all-tac))))
(defthm forcing-tactic.generalize-all-okp-of-tactic.generalize-all-tac
(implies (and (tactic.generalize-all-tac x expr var)
(force (logic.termp expr))
(force (logic.variablep var))
(force (tactic.skeletonp x)))
(equal (tactic.generalize-all-okp (tactic.generalize-all-tac x expr var))
t))
:hints(("Goal" :in-theory (enable tactic.generalize-all-tac
tactic.generalize-all-okp))))
(defthm forcing-tactic.generalize-all-env-okp-of-tactic.generalize-all-tac
(implies (and (tactic.generalize-all-tac x expr var)
(force (logic.termp expr))
(force (logic.term-atblp expr atbl))
(force (logic.variablep var))
(force (tactic.skeletonp x)))
(equal (tactic.generalize-all-env-okp (tactic.generalize-all-tac x expr var) atbl)
t))
:hints(("Goal" :in-theory (enable tactic.generalize-all-tac
tactic.generalize-all-env-okp))))
(defund tactic.generalize-all-compile (x proofs)
(declare (xargs :guard (and (tactic.skeletonp x)
(tactic.generalize-all-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs)))
:verify-guards nil))
(let* ((extras (tactic.skeleton->extras x))
(expr (car extras))
(var (cdr extras)))
(build.instantiation-list proofs (list (cons var expr)))))
(defobligations tactic.generalize-all-compile
(build.instantiation-list))
(encapsulate
()
(local (in-theory (enable tactic.generalize-all-okp
tactic.generalize-all-env-okp
tactic.generalize-all-compile)))
(defthm forcing-logic.substitute-of-logic.replace-subterm-list-list-with-fresh-variable-free
(implies (and (equal y (logic.replace-subterm-list-list x old new))
(not (memberp new (logic.term-list-list-vars x)))
(logic.variablep new)
(force (logic.term-list-listp x)))
(equal (logic.substitute-list-list y (list (cons new old)))
(list-list-fix x))))
(verify-guards tactic.generalize-all-compile)
(defthm forcing-logic.appeal-listp-of-tactic.generalize-all-compile
(implies (force (and (tactic.skeletonp x)
(tactic.generalize-all-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs))))
(equal (logic.appeal-listp (tactic.generalize-all-compile x proofs))
t)))
(defthm forcing-logic.strip-conclusions-of-tactic.generalize-all-compile
(implies (force (and (tactic.skeletonp x)
(tactic.generalize-all-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs))))
(equal (logic.strip-conclusions (tactic.generalize-all-compile x proofs))
(clause.clause-list-formulas (tactic.skeleton->goals (tactic.skeleton->history x))))))
(defthm@ forcing-logic.proof-listp-of-tactic.generalize-all-compile
(implies (force (and (tactic.skeletonp x)
(tactic.generalize-all-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs))
;; ---
(tactic.skeleton-atblp x atbl)
(tactic.generalize-all-env-okp x atbl)
(logic.proof-listp proofs axioms thms atbl)
(@obligations tactic.generalize-all-compile)))
(equal (logic.proof-listp (tactic.generalize-all-compile x proofs) axioms thms atbl)
t))))
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