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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 "trace-okp")
(include-book "urewrite-if-lemmas")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(local (in-theory (enable rw.trace-conclusion-formula rw.trace-formula)))
(defund rw.compile-urewrite-if-specialcase-same-trace (x proofs)
(declare (xargs :guard (and (rw.tracep x)
(rw.urewrite-if-specialcase-same-tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x))))
:verify-guards nil))
(let* ((lhs (rw.trace->lhs x)) ;; (if a b c)
(a (first (logic.function-args lhs)))
;; This is sort of goofy. Basically, our builder function is set up to handle assumptions
;; for the conditional rewriter. But we don't use assumptions, so we need to fake having an
;; assumption about the condition.
(test-proof (build.iff-reflexivity a))
(then-proof (build.expansion (logic.pnot (logic.pequal (logic.function 'not (list a)) ''nil))
(first proofs)))
(else-proof (build.expansion (logic.pnot (logic.pequal a ''nil))
(second proofs))))
(if (rw.trace->iffp x)
(rw.iff-of-if-x-y-y-bldr test-proof then-proof else-proof)
(rw.equal-of-if-x-y-y-bldr test-proof then-proof else-proof))))
(defobligations rw.compile-urewrite-if-specialcase-same-trace
(build.iff-reflexivity
build.expansion
rw.iff-of-if-x-y-y-bldr
rw.equal-of-if-x-y-y-bldr))
(encapsulate
()
(local (in-theory (enable rw.urewrite-if-specialcase-same-tracep rw.compile-urewrite-if-specialcase-same-trace)))
(verify-guards rw.compile-urewrite-if-specialcase-same-trace)
(defthm rw.compile-urewrite-if-specialcase-same-trace-under-iff
(iff (rw.compile-urewrite-if-specialcase-same-trace x proofs)
t)
:hints(("Goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthm logic.appealp-of-rw.compile-urewrite-if-specialcase-same-trace
(implies (force (and (rw.urewrite-if-specialcase-same-tracep x)
(rw.tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x)))))
(equal (logic.appealp (rw.compile-urewrite-if-specialcase-same-trace x proofs))
t)))
(defthm logic.conclusion-of-rw.compile-urewrite-if-specialcase-same-trace
(implies (force (and (rw.urewrite-if-specialcase-same-tracep x)
(rw.tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x)))))
(equal (logic.conclusion (rw.compile-urewrite-if-specialcase-same-trace x proofs))
(rw.trace-formula x)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm@ logic.proofp-of-rw.compile-urewrite-if-specialcase-same-trace
(implies (force (and (rw.urewrite-if-specialcase-same-tracep x)
(rw.tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x)))
;; ---
(rw.trace-atblp x atbl)
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'iff atbl)) 2)
(equal (cdr (lookup 'not atbl)) 1)
(@obligations rw.compile-urewrite-if-specialcase-same-trace)))
(equal (logic.proofp (rw.compile-urewrite-if-specialcase-same-trace x proofs) axioms thms atbl)
t))))
(defund rw.compile-urewrite-if-generalcase-trace (x proofs)
(declare (xargs :guard (and (rw.tracep x)
(rw.urewrite-if-generalcase-tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x))))
:verify-guards nil))
(let* ((rhs (rw.trace->rhs x)) ;; (if a2 b2 c2)
(a2 (first (logic.function-args rhs)))
(test-proof (first proofs))
(then-proof (build.expansion (logic.pnot (logic.pequal (logic.function 'not (list a2)) ''nil))
(second proofs)))
(else-proof (build.expansion (logic.pnot (logic.pequal a2 ''nil))
(third proofs))))
(if (rw.trace->iffp x)
(rw.iff-implies-iff-if-bldr test-proof then-proof else-proof)
(rw.iff-implies-equal-if-bldr test-proof then-proof else-proof))))
(defobligations rw.compile-urewrite-if-generalcase-trace
(build.expansion
rw.iff-implies-iff-if-bldr
rw.iff-implies-equal-if-bldr))
(encapsulate
()
(local (in-theory (enable rw.urewrite-if-generalcase-tracep rw.compile-urewrite-if-generalcase-trace)))
(verify-guards rw.compile-urewrite-if-generalcase-trace)
(defthm rw.compile-urewrite-if-generalcase-trace-under-iff
(iff (rw.compile-urewrite-if-generalcase-trace x proofs)
t)
:hints(("Goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthm logic.appealp-of-rw.compile-urewrite-if-generalcase-trace
(implies (force (and (rw.urewrite-if-generalcase-tracep x)
(rw.tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x)))))
(equal (logic.appealp (rw.compile-urewrite-if-generalcase-trace x proofs))
t)))
(defthm logic.conclusion-of-rw.compile-urewrite-if-generalcase-trace
(implies (force (and (rw.urewrite-if-generalcase-tracep x)
(rw.tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x)))))
(equal (logic.conclusion (rw.compile-urewrite-if-generalcase-trace x proofs))
(rw.trace-formula x)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm@ logic.proofp-of-rw.compile-urewrite-if-generalcase-trace
(implies (force (and (rw.urewrite-if-generalcase-tracep x)
(rw.tracep x)
(logic.appeal-listp proofs)
(equal (logic.strip-conclusions proofs) (rw.trace-list-formulas (rw.trace->subtraces x)))
;; ---
(rw.trace-atblp x atbl)
(logic.proof-listp proofs axioms thms atbl)
(equal (cdr (lookup 'not atbl)) 1)
(@obligations rw.compile-urewrite-if-generalcase-trace)))
(equal (logic.proofp (rw.compile-urewrite-if-generalcase-trace x proofs) axioms thms atbl)
t))))
(defund@ rw.compile-urewrite-rule-trace (x)
(declare (xargs :guard (and (rw.tracep x)
(rw.urewrite-rule-tracep x))
:verify-guards nil))
(let* ((hypbox (rw.trace->hypbox x))
(iffp (rw.trace->iffp x))
(extras (rw.trace->extras x))
(rule (first extras))
(sigma (second extras)))
(let ((main-proof
(cond ((and iffp (equal (rw.rule->equiv rule) 'equal))
;; The rule uses equal, but we just want iff.
(@derive ((!= (equal rule-lhs rule-rhs) nil) (build.theorem (clause.clause-formula (rw.rule-clause rule))))
((= (equal rule-lhs rule-rhs) t) (build.equal-t-from-not-nil @-))
((= (equal lhs rhs) t) (build.instantiation @- sigma))
((= (iff lhs rhs) t) (build.iff-from-equal @-))))
(iffp
;; The rule uses iff and we want iff.
(@derive ((!= (iff rule-lhs rule-rhs) nil) (build.theorem (clause.clause-formula (rw.rule-clause rule))))
((= (iff rule-lhs rule-rhs) t) (build.iff-t-from-not-nil @-))
((= (iff lhs rhs) t) (build.instantiation @- sigma))))
(t
;; The rule uses equal and we want equal.
(@derive ((!= (equal rule-lhs rule-rhs) nil) (build.theorem (clause.clause-formula (rw.rule-clause rule))))
((= (equal rule-lhs rule-rhs) t) (build.equal-t-from-not-nil @-))
((= (equal lhs rhs) t) (build.instantiation @- sigma)))))))
(if (and (not (rw.hypbox->left hypbox))
(not (rw.hypbox->right hypbox)))
main-proof
(build.expansion (rw.hypbox-formula hypbox) main-proof)))))
(defobligations rw.compile-urewrite-rule-trace
(build.expansion
build.instantiation
build.iff-from-equal
build.equal-t-from-not-nil
build.iff-t-from-not-nil))
(encapsulate
()
(local (in-theory (enable logic.term-formula
rw.rule-env-okp
rw.urewrite-rule-tracep
rw.urewrite-rule-trace-env-okp
rw.compile-urewrite-rule-trace)))
(verify-guards rw.compile-urewrite-rule-trace)
(defthm rw.compile-urewrite-rule-trace-under-iff
(iff (rw.compile-urewrite-rule-trace x)
t)
:hints(("Goal" :in-theory (disable (:executable-counterpart ACL2::force)))))
(defthm forcing-logic.appealp-of-rw.compile-urewrite-rule-trace
(implies (force (and (rw.urewrite-rule-tracep x)
(rw.tracep x)))
(equal (logic.appealp (rw.compile-urewrite-rule-trace x))
t)))
(defthm forcing-logic.conclusion-of-rw.compile-urewrite-rule-trace
(implies (force (and (rw.urewrite-rule-tracep x)
(rw.tracep x)))
(equal (logic.conclusion (rw.compile-urewrite-rule-trace x))
(rw.trace-formula x))))
(defthm@ forcing-logic.proofp-of-rw.compile-urewrite-rule-trace
(implies (force (and (rw.urewrite-rule-trace-env-okp x thms atbl)
(rw.urewrite-rule-tracep x)
(rw.tracep x)
;; ---
(rw.trace-atblp x atbl)
(equal (cdr (lookup 'iff atbl)) 2)
(equal (cdr (lookup 'equal atbl)) 2)
(@obligations rw.compile-urewrite-rule-trace)))
(equal (logic.proofp (rw.compile-urewrite-rule-trace x) axioms thms atbl)
t))))
|
