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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 "basic-builders") ;; for fail-trace
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(local (in-theory (e/d (booleanp-of-rw.trace->iffp)
(forcing-booleanp-of-rw.trace->iffp))))
(defund rw.urewrite-if-specialcase-same-trace (x y a)
(declare (xargs :guard (and (rw.tracep x)
(rw.tracep y)
(logic.termp a)
(not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(equal (rw.trace->iffp x) (rw.trace->iffp y))
(equal (rw.trace->rhs x) (rw.trace->rhs y)))))
(rw.trace 'urewrite-if-specialcase-same
(rw.trace->hypbox x)
(logic.function 'if (list a (rw.trace->lhs x) (rw.trace->lhs y)))
(rw.trace->rhs x)
(rw.trace->iffp x)
(list x y)
nil))
(encapsulate
()
(local (in-theory (enable rw.urewrite-if-specialcase-same-trace)))
(defthm rw.trace->method-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->method (rw.urewrite-if-specialcase-same-trace x y a))
'urewrite-if-specialcase-same))
(defthm rw.trace->hypbox-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->hypbox (rw.urewrite-if-specialcase-same-trace x y a))
(rw.trace->hypbox x)))
(defthm rw.trace->lhs-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->lhs (rw.urewrite-if-specialcase-same-trace x y a))
(logic.function 'if (list a (rw.trace->lhs x) (rw.trace->lhs y)))))
(defthm rw.trace->rhs-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->rhs (rw.urewrite-if-specialcase-same-trace x y a))
(rw.trace->rhs x)))
(defthm rw.trace->iffp-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->iffp (rw.urewrite-if-specialcase-same-trace x y a))
(rw.trace->iffp x)))
(defthm rw.trace->subtraces-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->subtraces (rw.urewrite-if-specialcase-same-trace x y a))
(list x y)))
(defthm rw.trace->extras-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace->extras (rw.urewrite-if-specialcase-same-trace x y a))
nil))
(defthm forcing-rw.tracep-of-rw.urewrite-if-specialcase-same-trace
(implies (force (and (rw.tracep x)
(rw.tracep y)
(logic.termp a)))
(equal (rw.tracep (rw.urewrite-if-specialcase-same-trace x y a))
t)))
(defthm forcing-rw.trace-atblp-of-rw.urewrite-if-specialcase-same-trace
(implies (force (and (rw.trace-atblp x atbl)
(rw.trace-atblp y atbl)
(logic.term-atblp a atbl)
(equal (cdr (lookup 'if atbl)) 3)))
(equal (rw.trace-atblp (rw.urewrite-if-specialcase-same-trace x y a) atbl)
t)))
(local (in-theory (disable rw.urewrite-if-specialcase-same-trace)))
(defthmd lemma-forcing-rw.urewrite-if-specialcase-same-tracep-of-rw.urewrite-if-specialcase-same-trace
(implies (force (and (not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(equal (rw.trace->iffp x) (rw.trace->iffp y))
(equal (rw.trace->rhs x) (rw.trace->rhs y))))
(equal (rw.urewrite-if-specialcase-same-tracep (rw.urewrite-if-specialcase-same-trace x y a))
t))
:hints(("Goal" :in-theory (enable rw.urewrite-if-specialcase-same-tracep))))
(defthmd lemma-forcing-rw.trace-step-okp-of-rw.urewrite-if-specialcase-same-trace
(implies (force (and (not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(equal (rw.trace->iffp x) (rw.trace->iffp y))
(equal (rw.trace->rhs x) (rw.trace->rhs y))))
(equal (rw.trace-step-okp (rw.urewrite-if-specialcase-same-trace x y a) defs)
t))
:hints(("Goal" :in-theory (enable rw.trace-step-okp
lemma-forcing-rw.urewrite-if-specialcase-same-tracep-of-rw.urewrite-if-specialcase-same-trace))))
(defthm forcing-rw.trace-okp-of-rw.urewrite-if-specialcase-same-trace
(implies (force (and (not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(equal (rw.trace->iffp x) (rw.trace->iffp y))
(equal (rw.trace->rhs x) (rw.trace->rhs y))
(rw.trace-okp x defs)
(rw.trace-okp y defs)))
(equal (rw.trace-okp (rw.urewrite-if-specialcase-same-trace x y a) defs)
t))
:hints(("Goal"
:expand ((rw.trace-okp (rw.urewrite-if-specialcase-same-trace x y a) defs))
:in-theory (enable lemma-forcing-rw.trace-step-okp-of-rw.urewrite-if-specialcase-same-trace))))
(defthmd lemma-forcing-rw.trace-step-env-okp-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.trace-step-env-okp (rw.urewrite-if-specialcase-same-trace x y a) defs thms atbl)
t)
:hints(("Goal" :in-theory (enable rw.trace-step-env-okp))))
(defthm forcing-rw.trace-env-okp-of-rw.urewrite-if-specialcase-same-trace
(implies (force (and (rw.trace-env-okp x defs thms atbl)
(rw.trace-env-okp y defs thms atbl)))
(equal (rw.trace-env-okp (rw.urewrite-if-specialcase-same-trace x y a) defs thms atbl)
t))
:hints(("Goal"
:expand ((rw.trace-env-okp (rw.urewrite-if-specialcase-same-trace x y a) defs thms atbl))
:in-theory (enable lemma-forcing-rw.trace-step-env-okp-of-rw.urewrite-if-specialcase-same-trace))))
(defthm rw.collect-forced-goals-of-rw.urewrite-if-specialcase-same-trace
(equal (rw.collect-forced-goals (rw.urewrite-if-specialcase-same-trace x y a))
(fast-merge (rw.collect-forced-goals x)
(rw.collect-forced-goals y)))
:hints(("Goal" :expand (rw.collect-forced-goals (rw.urewrite-if-specialcase-same-trace x y a))))))
(defund rw.urewrite-if-generalcase-trace (x y z)
(declare (xargs :guard (and (rw.tracep x)
(rw.tracep y)
(rw.tracep z)
(not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(not (rw.hypbox->left (rw.trace->hypbox z)))
(not (rw.hypbox->right (rw.trace->hypbox z)))
(equal (rw.trace->iffp x) t)
(equal (rw.trace->iffp y) (rw.trace->iffp z)))))
(let ((a1 (rw.trace->lhs x))
(a2 (rw.trace->rhs x))
(b1 (rw.trace->lhs y))
(b2 (rw.trace->rhs y))
(c1 (rw.trace->lhs z))
(c2 (rw.trace->rhs z))
(iffp (rw.trace->iffp y)))
;(if (and (equal a1 a2)
; (equal b1 b2)
; (equal c1 c2))
; (rw.fail-trace (rw.trace->hypbox x) (logic.function 'if (list a1 b1 c1)) iffp)
(rw.trace 'urewrite-if-generalcase
(rw.trace->hypbox x)
(logic.function 'if (list a1 b1 c1))
(logic.function 'if (list a2 b2 c2))
iffp
(list x y z)
nil)))
(encapsulate
()
(local (in-theory (enable rw.urewrite-if-generalcase-trace)))
(defthm rw.trace->method-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->method (rw.urewrite-if-generalcase-trace x y z))
'urewrite-if-generalcase))
(defthm rw.trace->hypbox-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->hypbox (rw.urewrite-if-generalcase-trace x y z))
(rw.trace->hypbox x)))
(defthm rw.trace->lhs-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->lhs (rw.urewrite-if-generalcase-trace x y z))
(logic.function 'if (list (rw.trace->lhs x) (rw.trace->lhs y) (rw.trace->lhs z))))
:hints(("Goal" :in-theory (disable forcing-true-listp-of-logic.function-args))))
(defthm rw.trace->rhs-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->rhs (rw.urewrite-if-generalcase-trace x y z))
(logic.function 'if (list (rw.trace->rhs x) (rw.trace->rhs y) (rw.trace->rhs z))))
:hints(("Goal" :in-theory (disable forcing-true-listp-of-logic.function-args))))
(defthm rw.trace->iffp-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->iffp (rw.urewrite-if-generalcase-trace x y z))
(rw.trace->iffp y)))
(defthm rw.trace->subtraces-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->subtraces (rw.urewrite-if-generalcase-trace x y z))
(list x y z)))
(defthm rw.trace->extras-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace->extras (rw.urewrite-if-generalcase-trace x y z))
nil))
(defthm forcing-rw.tracep-of-rw.urewrite-if-generalcase-trace
(implies (force (and (rw.tracep x)
(rw.tracep y)
(rw.tracep z)))
(equal (rw.tracep (rw.urewrite-if-generalcase-trace x y z))
t)))
(defthm forcing-rw.trace-atblp-of-rw.urewrite-if-generalcase-trace
(implies (force (and (rw.trace-atblp x atbl)
(rw.trace-atblp y atbl)
(rw.trace-atblp z atbl)
(equal (cdr (lookup 'if atbl)) 3)))
(equal (rw.trace-atblp (rw.urewrite-if-generalcase-trace x y z) atbl)
t)))
(local (in-theory (disable rw.urewrite-if-generalcase-trace)))
(defthmd lemma-forcing-rw.trace-step-okp-of-rw.urewrite-if-generalcase-trace
(implies (force (and (not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(not (rw.hypbox->left (rw.trace->hypbox z)))
(not (rw.hypbox->right (rw.trace->hypbox z)))
(equal (rw.trace->iffp x) t)
(equal (rw.trace->iffp y) (rw.trace->iffp z))))
(equal (rw.trace-step-okp (rw.urewrite-if-generalcase-trace x y z) defs)
t))
:hints(("Goal" :in-theory (enable rw.trace-step-okp rw.urewrite-if-generalcase-tracep))))
(defthm forcing-rw.trace-okp-of-rw.urewrite-if-generalcase-trace
(implies (force (and (not (rw.hypbox->left (rw.trace->hypbox x)))
(not (rw.hypbox->right (rw.trace->hypbox x)))
(not (rw.hypbox->left (rw.trace->hypbox y)))
(not (rw.hypbox->right (rw.trace->hypbox y)))
(not (rw.hypbox->left (rw.trace->hypbox z)))
(not (rw.hypbox->right (rw.trace->hypbox z)))
(equal (rw.trace->iffp x) t)
(equal (rw.trace->iffp y) (rw.trace->iffp z))
(rw.trace-okp x defs)
(rw.trace-okp y defs)
(rw.trace-okp z defs)))
(equal (rw.trace-okp (rw.urewrite-if-generalcase-trace x y z) defs)
t))
:hints(("Goal"
:expand ((rw.trace-okp (rw.urewrite-if-generalcase-trace x y z) defs))
:in-theory (enable lemma-forcing-rw.trace-step-okp-of-rw.urewrite-if-generalcase-trace))))
(defthmd lemma-forcing-rw.trace-step-env-okp-of-rw.urewrite-if-generalcase-trace
(equal (rw.trace-step-env-okp (rw.urewrite-if-generalcase-trace x y z) axioms thms atbl)
t)
:hints(("Goal" :in-theory (enable rw.trace-step-env-okp rw.urewrite-if-generalcase-tracep))))
(defthm forcing-rw.trace-env-okp-of-rw.urewrite-if-generalcase-trace
(implies (force (and (rw.trace-env-okp x defs thms atbl)
(rw.trace-env-okp y defs thms atbl)
(rw.trace-env-okp z defs thms atbl)))
(equal (rw.trace-env-okp (rw.urewrite-if-generalcase-trace x y z) defs thms atbl)
t))
:hints(("Goal"
:expand ((rw.trace-env-okp (rw.urewrite-if-generalcase-trace x y z) defs thms atbl))
:in-theory (enable lemma-forcing-rw.trace-step-env-okp-of-rw.urewrite-if-generalcase-trace))))
(defthm rw.collect-forced-goals-of-rw.urewrite-if-generalcase-trace
(equal (rw.collect-forced-goals (rw.urewrite-if-generalcase-trace x y z))
(fast-merge (rw.collect-forced-goals x)
(fast-merge (rw.collect-forced-goals y)
(rw.collect-forced-goals z))))
:hints(("Goal" :in-theory (enable definition-of-rw.collect-forced-goals)))))
(defund rw.try-urewrite-rule (hypbox term rule iffp control)
(declare (xargs :guard (and (rw.hypboxp hypbox)
(logic.termp term)
(rw.rulep rule)
(booleanp iffp)
(rw.controlp control))))
(and
;; The rule must be unconditional
(not (rw.rule->hyps rule))
;; The equivalence relation must be acceptable
(let ((equiv (rw.rule->equiv rule)))
(or (equal equiv 'equal)
(and (equal equiv 'iff) iffp)))
;; Note: we ignore esigmas completely for urewrite rules
(let ((match-result (logic.patmatch (rw.rule->lhs rule) term nil)))
(and
;; We must have a match
(not (equal 'fail match-result))
;; The syntactic restrictions must be satisfied.
(rw.rule-syntax-okp rule match-result control)
;; Everything's ok; build the trace.
(rw.trace 'urewrite-rule
hypbox
term
(logic.substitute (rw.rule->rhs rule) match-result)
iffp
nil
(list rule match-result))))))
(encapsulate
()
(local (in-theory (enable rw.try-urewrite-rule)))
(defthmd lemma-forcing-rw.trace->method-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.trace->method (rw.try-urewrite-rule hypbox term rule iffp control))
'urewrite-rule)))
(defthm forcing-rw.trace->hypbox-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.trace->hypbox (rw.try-urewrite-rule hypbox term rule iffp control))
hypbox)))
(defthm forcing-rw.trace->lhs-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.trace->lhs (rw.try-urewrite-rule hypbox term rule iffp control))
term)))
(defthm forcing-rw.trace->iffp-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.trace->iffp (rw.try-urewrite-rule hypbox term rule iffp control))
iffp)))
(defthmd lemma-forcing-rw.trace->subtraces-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.trace->subtraces (rw.try-urewrite-rule hypbox term rule iffp control))
nil)))
(defthmd lemma-forcing-rw.trace->extras-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.trace->extras (rw.try-urewrite-rule hypbox term rule iffp control))
(list rule (logic.patmatch (rw.rule->lhs rule) term nil)))))
(defthm forcing-rw.tracep-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(rw.hypboxp hypbox)
(logic.termp term)
(rw.rulep rule)
(booleanp iffp)))
(equal (rw.tracep (rw.try-urewrite-rule hypbox term rule iffp control))
t)))
(defthm forcing-rw.trace-atblp-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(rw.hypbox-atblp hypbox atbl)
(logic.term-atblp term atbl)
(rw.rule-atblp rule atbl)))
(equal (rw.trace-atblp (rw.try-urewrite-rule hypbox term rule iffp control) atbl)
t)))
(defthmd lemma-forcing-rw.urewrite-rule-tracep-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(logic.termp term)
(rw.rulep rule)
(rw.controlp control)))
(equal (rw.urewrite-rule-tracep (rw.try-urewrite-rule hypbox term rule iffp control))
t))
:hints(("Goal" :in-theory (enable rw.urewrite-rule-tracep))))
(local (in-theory (disable rw.try-urewrite-rule)))
(local (in-theory (enable lemma-forcing-rw.trace->method-of-rw.try-urewrite-rule
lemma-forcing-rw.trace->subtraces-of-rw.try-urewrite-rule
lemma-forcing-rw.trace->extras-of-rw.try-urewrite-rule
lemma-forcing-rw.urewrite-rule-tracep-of-rw.try-urewrite-rule)))
(defthmd lemma-forcing-rw.trace-step-okp-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(logic.termp term)
(rw.rulep rule)
(rw.controlp control)))
(equal (rw.trace-step-okp (rw.try-urewrite-rule hypbox term rule iffp control) defs)
t))
:hints(("Goal" :in-theory (enable rw.trace-step-okp))))
(defthm forcing-rw.trace-okp-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(logic.termp term)
(rw.rulep rule)
(rw.controlp control)))
(equal (rw.trace-okp (rw.try-urewrite-rule hypbox term rule iffp control) defs)
t))
:hints(("Goal"
:expand ((rw.trace-okp (rw.try-urewrite-rule hypbox term rule iffp control) defs))
:in-theory (enable lemma-forcing-rw.trace-step-okp-of-rw.try-urewrite-rule))))
(defthmd lemma-forcing-rw.trace-step-env-okp-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(logic.termp term)
(logic.term-atblp term atbl)
(rw.rulep rule)
(rw.rule-atblp rule atbl)
(rw.rule-env-okp rule thms)
(rw.controlp control)))
(equal (rw.trace-step-env-okp (rw.try-urewrite-rule hypbox term rule iffp control) defs thms atbl)
t))
:hints(("Goal" :in-theory (enable rw.trace-step-env-okp rw.urewrite-rule-trace-env-okp))))
(defthm forcing-rw.trace-env-okp-of-rw.try-urewrite-rule
(implies (force (and (rw.try-urewrite-rule hypbox term rule iffp control)
(logic.termp term)
(logic.term-atblp term atbl)
(rw.rulep rule)
(rw.rule-atblp rule atbl)
(rw.rule-env-okp rule thms)
(rw.controlp control)))
(equal (rw.trace-env-okp (rw.try-urewrite-rule hypbox term rule iffp control) defs thms atbl)
t))
:hints(("Goal"
:expand ((rw.trace-env-okp (rw.try-urewrite-rule hypbox term rule iffp control) defs thms atbl))
:in-theory (enable lemma-forcing-rw.trace-step-env-okp-of-rw.try-urewrite-rule))))
(defthm forcing-rw.collect-forced-goals-of-rw.try-urewrite-rule
(implies (force (rw.try-urewrite-rule hypbox term rule iffp control))
(equal (rw.collect-forced-goals (rw.try-urewrite-rule hypbox term rule iffp control))
nil))
:hints(("Goal" :in-theory (enable definition-of-rw.collect-forced-goals)))))
(defund rw.try-urewrite-rule-list (hypbox term rules iffp control)
(declare (xargs :guard (and (rw.hypboxp hypbox)
(logic.termp term)
(rw.rule-listp rules)
(booleanp iffp)
(rw.controlp control))))
(if (consp rules)
(or (rw.try-urewrite-rule hypbox term (car rules) iffp control)
(rw.try-urewrite-rule-list hypbox term (cdr rules) iffp control))
nil))
(encapsulate
()
(local (in-theory (enable rw.try-urewrite-rule-list)))
(defthm forcing-rw.trace->lhs-of-rw.try-urewrite-rule-list
(implies (force (rw.try-urewrite-rule-list hypbox term rules iffp control))
(equal (rw.trace->lhs (rw.try-urewrite-rule-list hypbox term rules iffp control))
term)))
(defthm forcing-rw.trace->iffp-of-rw.try-urewrite-rule-list
(implies (force (rw.try-urewrite-rule-list hypbox term rules iffp control))
(equal (rw.trace->iffp (rw.try-urewrite-rule-list hypbox term rules iffp control))
iffp)))
(defthm forcing-rw.trace->hypbox-of-rw.try-urewrite-rule-list
(implies (force (rw.try-urewrite-rule-list hypbox term rules iffp control))
(equal (rw.trace->hypbox (rw.try-urewrite-rule-list hypbox term rules iffp control))
hypbox)))
(defthm forcing-rw.tracep-of-rw.try-urewrite-rule-list
(implies (force (and (rw.hypboxp hypbox)
(logic.termp term)
(rw.rule-listp rules)
(booleanp iffp)))
(equal (rw.tracep (rw.try-urewrite-rule-list hypbox term rules iffp control))
(if (rw.try-urewrite-rule-list hypbox term rules iffp control)
t
nil))))
(defthm forcing-rw.trace-atblp-of-rw.try-urewrite-rule-list
(implies (force (and (rw.hypbox-atblp hypbox atbl)
(logic.term-atblp term atbl)
(rw.rule-list-atblp rules atbl)))
(equal (rw.trace-atblp (rw.try-urewrite-rule-list hypbox term rules iffp control) atbl)
(if (rw.try-urewrite-rule-list hypbox term rules iffp control)
t
nil))))
(defthm forcing-rw.trace-okp-of-rw.try-urewrite-rule-list
(implies (force (and (logic.termp term)
(rw.rule-listp rules)
(rw.controlp control)))
(equal (rw.trace-okp (rw.try-urewrite-rule-list hypbox term rules iffp control) defs)
(if (rw.try-urewrite-rule-list hypbox term rules iffp control)
t
nil))))
(defthm forcing-rw.trace-env-okp-of-rw.try-urewrite-rule-list
(implies (force (and (logic.termp term)
(logic.term-atblp term atbl)
(rw.rule-listp rules)
(rw.rule-list-atblp rules atbl)
(rw.rule-list-env-okp rules thms)
(rw.controlp control)))
(equal (rw.trace-env-okp (rw.try-urewrite-rule-list hypbox term rules iffp control) defs thms atbl)
t)))
(defthm forcing-rw.collect-forced-goals-of-rw.try-urewrite-rule-list
(implies (force (rw.try-urewrite-rule-list hypbox term rules iffp control))
(equal (rw.collect-forced-goals (rw.try-urewrite-rule-list hypbox term rules iffp control))
nil))))
(defund rw.try-urewrite-rules (hypbox term type iffp control)
(declare (xargs :guard (and (rw.hypboxp hypbox)
(logic.termp term)
(or (equal type 'inside)
(equal type 'outside))
(booleanp iffp)
(rw.controlp control))))
(let* ((rulemap (rw.theory-lookup term (rw.control->theory control)))
(rules (cdr (lookup type rulemap))))
(rw.try-urewrite-rule-list hypbox term rules iffp control)))
(encapsulate
()
(local (in-theory (enable rw.try-urewrite-rules)))
(defthm forcing-rw.trace->lhs-of-rw.try-urewrite-rules
(implies (force (rw.try-urewrite-rules hypbox term type iffp control))
(equal (rw.trace->lhs (rw.try-urewrite-rules hypbox term type iffp control))
term)))
(defthm forcing-rw.trace->iffp-of-rw.try-urewrite-rules
(implies (force (rw.try-urewrite-rules hypbox term type iffp control))
(equal (rw.trace->iffp (rw.try-urewrite-rules hypbox term type iffp control))
iffp)))
(defthm forcing-rw.trace->hypbox-of-rw.try-urewrite-rules
(implies (force (rw.try-urewrite-rules hypbox term type iffp control))
(equal (rw.trace->hypbox (rw.try-urewrite-rules hypbox term type iffp control))
hypbox)))
(defthm forcing-rw.tracep-of-rw.try-urewrite-rules
(implies (force (and (rw.hypboxp hypbox)
(logic.termp term)
(booleanp iffp)
(rw.controlp control)))
(equal (rw.tracep (rw.try-urewrite-rules hypbox term type iffp control))
(if (rw.try-urewrite-rules hypbox term type iffp control)
t
nil))))
(defthm forcing-rw.trace-atblp-of-rw.try-urewrite-rules
(implies (force (and (rw.hypbox-atblp hypbox atbl)
(logic.term-atblp term atbl)
(rw.controlp control)
(rw.control-atblp control atbl)))
(equal (rw.trace-atblp (rw.try-urewrite-rules hypbox term type iffp control) atbl)
(if (rw.try-urewrite-rules hypbox term type iffp control)
t
nil))))
(defthm forcing-rw.trace-okp-of-rw.try-urewrite-rules
(implies (force (and (logic.termp term)
(rw.controlp control)))
(equal (rw.trace-okp (rw.try-urewrite-rules hypbox term type iffp control) defs)
(if (rw.try-urewrite-rules hypbox term type iffp control)
t
nil))))
(defthm forcing-rw.trace-env-okp-of-rw.try-urewrite-rules
(implies (force (and (logic.termp term)
(logic.term-atblp term atbl)
(rw.controlp control)
(rw.control-atblp control atbl)
(rw.control-env-okp control axioms thms)))
(equal (rw.trace-env-okp (rw.try-urewrite-rules hypbox term type iffp control) defs thms atbl)
t)))
(defthm forcing-rw.collect-forced-goals-of-rw.try-urewrite-rules
(implies (force (rw.try-urewrite-rules hypbox term type iffp control))
(equal (rw.collect-forced-goals (rw.try-urewrite-rules hypbox term type iffp control))
nil))))
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