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|
; RP-REWRITER
; Note: The license below is based on the template at:
; http://opensource.org/licenses/BSD-3-Clause
; Copyright (C) 2019, Regents of the University of Texas
; All rights reserved.
; Copyright (C) 2022 Intel Corporation
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions are
; met:
; o Redistributions of source code must retain the above copyright
; notice, this list of conditions and the following disclaimer.
; o Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
; o Neither the name of the copyright holders nor the names of its
; contributors may be used to endorse or promote products derived
; from this software without specific prior written permission.
; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
; "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
; LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
; A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
; HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
; SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
; LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
; DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
; THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
; OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
; Original Author(s):
; Mertcan Temel <mert@utexas.edu>
(in-package "RP")
(include-book "../aux-functions")
(make-flag include-fnc-fn :defthm-macro-name defthm-include-fnc)
(make-flag rp-termp :defthm-macro-name defthm-rp-termp)
(make-flag beta-search-reduce :defthm-macro-name defthm-beta-search-reduce)
#|(make-flag all-falist-consistent :defthm-macro-name
defthm-all-falist-consistent)||#
#|(make-flag rp-syntaxp :defthm-macro-name defthm-rp-syntaxp)||#
(make-flag lambda-exp-free-p :defthm-macro-name defthm-lambda-exp-free-p)
(make-flag get-lambda-free-vars :defthm-macro-name defthm-get-lambda-free-vars)
(make-flag ex-from-rp-all2 :defthm-macro-name defthm-ex-from-rp-all2)
(local
(make-flag get-lambda-free-vars :defthm-macro-name
defthm-get-lambda-free-vars))
(local
(in-theory (enable falist-consistent)))
(make-event
`(defthm is-lambda-implies
(implies (is-lambda term)
,(beta-search-reduce (caddar (caddr (meta-extract-formula
'is-lambda state)))
1000))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda) ())))))
(make-event
`(defthm is-lambda-strict-implies
(implies (is-lambda-strict x)
,(beta-search-reduce (caddar (caddr (meta-extract-formula
'is-lambda-strict state)))
1000))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda is-lambda-strict) ())))))
(defthm get-lambda-free-vars-implies
(implies
(and (mv-nth 0 (get-lambda-free-vars term))
(is-lambda term))
(b* (((mv valid sub-vars) (get-lambda-free-vars (caddr (car term))))
(lambda-vars (cadr (car term)))
((mv valid-2 &) (get-lambda-free-vars-lst (cdr term))))
(and valid
valid-2
(equal (remove-vars sub-vars lambda-vars) nil))))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda is-lambda-strict get-lambda-free-vars)
()))))
(set-ignore-ok t)
(make-event
`(defthm rp-termp-implies
(implies (rp-termp term)
,(caddr (meta-extract-formula
'rp-termp state)))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda is-lambda-strict) ())))))
(make-event
`(defthm lambda-exp-free-p-implies
(implies (lambda-exp-free-p term)
,(caddr (meta-extract-formula
'lambda-exp-free-p state)))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda is-lambda-strict lambda-exp-free-p )
())))))
(make-event
`(defthm LAMBDA-EXP-FREE-LISTP-implies
(implies (LAMBDA-EXP-FREE-LISTP subterms)
,(caddr (meta-extract-formula
'LAMBDA-EXP-FREE-LISTP state)))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda is-lambda-strict lambda-exp-free-p LAMBDA-EXP-FREE-LISTP )
())))))
(defret rp-termp-dumb-negate-lit2
(implies (rp-termp term)
(rp-termp new-term))
:fn dumb-negate-lit2
:hints (("goal" :in-theory (enable rp-term-listp
dumb-negate-lit2))))
#|(defthm-remove-return-last
(defthm rp-termp-remove-return-last
(implies (rp-termp term)
(rp-termp (remove-return-last term)))
:flag remove-return-last)
(defthm rp-term-listp-remove-return-last-subterms
(implies (rp-term-listp subterms)
(rp-term-listp (remove-return-last-subterms subterms)))
:flag remove-return-last-subterms)
:hints (("Goal" :in-theory (enable rp-term-listp
rp-termp))))||#
(defthm-rp-termp
(defthm rp-termp-implies-pseudo-termp
(implies (rp-termp term)
(pseudo-termp term))
:flag rp-termp)
(defthm rp-term-list-implies-pseudo-term-listp
(implies (rp-term-listp lst)
(pseudo-term-listp lst))
:flag rp-term-listp)
:hints (("Goal"
:in-theory (e/d (is-rp
falist-consistent)
()))))
(defthm strip-cdrs-pseudo-termlistp2
(implies
(and (rp-term-listp (strip-cdrs alist))
(cdr (assoc-equal key alist)))
(rp-termp (cdr (assoc-equal key alist)))))
(defthm rp-termp-bindings-lemma1
(implies (and (rp-term-listp (strip-cdrs bindings))
(consp (assoc-equal term bindings)))
(cdr (assoc-equal term bindings))))
(defthm rp-term-listp-is-true-listp
(implies (rp-term-listp lst)
(true-listp lst))
:hints (("Goal" :expand (rp-term-listp lst))))
(encapsulate
nil
(local
(in-theory (enable is-rp)))
;; Removed in July 2021 by Matt Kaufmann since the right-hand sides of the
;; generated rules are now all constants, due to enhancements to
;; remove-guard-holders.
#||
(defthm is-synp-implies
(implies (is-synp term)
(CASE-MATCH TERM (('SYNP & & &) T)
(& NIL)))
:hints (("Goal" :in-theory (enable is-synp))))
||#
(defthm pseudo-termlistp-extract-from-rp
(implies (and (rp-termp term)
(not (quotep (ex-from-rp term))))
(rp-term-listp (cdr (ex-from-rp term))))
:hints (("Goal"
:Expand (rp-termp term)
:in-theory (e/d (is-rp) ()))))
(defthm rp-termp-extract-from-rp
(implies (and (rp-termp term))
(rp-termp (ex-from-rp term))))
(defthm extract-from-synp-to-ex-from-rp
(equal (extract-from-synp term)
(ex-from-synp term))
:hints (("Goal" :in-theory (enable is-synp ex-from-synp extract-from-synp))))
(defthm pseudo-termp-extract-from-synp
(implies (rp-termp term)
(rp-termp (ex-from-synp term)))
:hints (("Goal" :in-theory (enable extract-from-synp))))
(defthm atom-rp-termp-is-symbolp
(implies (and (atom x) (rp-termp x)) (symbolp x)))
(defthm rp-termp-context-from-rp
(implies (and (rp-termp term)
(rp-term-listp context))
(rp-term-listp (context-from-rp term context)))
:hints (("goal"
:in-theory (e/d (context-from-rp ex-from-rp is-rp) ())
:expand (rp-termp term))))
(defthm put-term-in-cons-is-pseudo-termp
(rp-termp (put-term-in-cons term))
:hints (("goal" :in-theory (enable is-rp put-term-in-cons))))
(defthm extract-from-rp-with-context-to-no-context
(equal (mv-nth 1 (extract-from-rp-with-context term context))
(ex-from-rp term))
:hints (("goal" :in-theory (enable extract-from-rp-with-context
is-rp
ex-from-rp))))
(defthm extract-from-rp-with-context-context
(equal (mv-nth 0 (extract-from-rp-with-context term context))
(context-from-rp term context))
:hints (("goal" :in-theory (enable extract-from-rp-with-context
is-rp
context-from-rp
ex-from-rp))))
(defthm cons-consp-context-from-rp
(implies (cons-consp context)
(cons-consp (context-from-rp term context)))
:hints (("Goal"
:induct (context-from-rp term context)
:in-theory (enable cons-consp is-rp context-from-rp))))
(defthm symbolp-ex-from-rp
(implies (and (rp-termp term)
(not (consp (ex-from-rp term))))
(symbolp (ex-from-rp term))))
(defthm ex-from-rp-x2
(equal (ex-from-rp (ex-from-rp term))
(ex-from-rp term))
:hints (("Goal" :in-theory (enable ex-from-rp is-rp))))
(defthm ex-from-synp-ex-from-rpx2
(equal (EX-FROM-SYNP
(EX-FROM-RP (EX-FROM-SYNP (EX-FROM-RP term))))
(EX-FROM-SYNP (EX-FROM-RP term)))
:hints (("Goal" :in-theory (enable ex-from-rp
ex-from-synp
is-rp
is-synp)))))
(defthm append-of-two-context
(implies (and (context-syntaxp c1)
(context-syntaxp c2))
(context-syntaxp (append c1 c2)))
:hints (("Goal" :in-theory (enable rp-term-listp
context-syntaxp))))
;; acl2::beta-eval-to-beta-reduce-lambda-expr
(defthm-beta-search-reduce
(defthm eval-of-beta-search-reduce
(implies (pseudo-termp term)
(equal (acl2::beta-eval (beta-search-reduce term limit) a)
(acl2::beta-eval term a)))
:flag beta-search-reduce)
(defthm eval-of-beta-search-reduce-subterms
(implies (pseudo-term-listp subterms)
(equal (acl2::beta-eval-list (beta-search-reduce-subterms subterms limit) a)
(acl2::beta-eval-list subterms a)))
:flag beta-search-reduce-subterms)
:hints (("Goal" :in-theory (enable acl2::beta-eval-constraint-0))))
(defthm eval-of-beta-search-reduce-fixed-lim
(implies (pseudo-termp (car cl))
(equal (acl2::beta-eval (beta-search-reduce (car cl) *big-number*) a)
(acl2::beta-eval (car cl) a))))
(defthm falist-consistent-implies-falist-syntaxp
(implies (and (rp-termp term)
(falist-consistent-aux falist term))
(falist-syntaxp falist)))
(defthm extract-from-rp-with-context-to-context-from-rp
(equal (mv-nth 0 (extract-from-rp-with-context term context))
(context-from-rp term context))
:hints (("Goal" :in-theory (enable context-from-rp is-rp))))
(defthm remove-from-alist-returns-alistp
(implies (alistp x)
(alistp (remove-from-alist x key))))
;; (defthm rp-stat-add-to-rules-used-returns-rp-stat-p
;; (implies (rp-stat-p stat)
;; (rp-stat-p (rp-stat-add-to-rules-used rule stat failed)))
;; :hints (("Goal" :in-theory (enable rp-stat-p
;; rp-stat-add-to-rules-used))))
;; (defthm rp-stat-add-to-rules-used-returns-rp-stat-p2
;; (implies (rp-stat-p stat)
;; (rp-stat-p (rp-stat-add-to-rules-used-ex-cnt rule stat)))
;; :hints (("Goal" :in-theory (enable rp-stat-p
;; rp-stat-add-to-rules-used-ex-cnt))))
#|(defthm all-falist-consistent-bindings-lemma1
(implies (all-falist-consistent-bindings bindings)
(all-falist-consistent (cdr (assoc-equal term bindings)))))||#
#|(encapsulate
nil
(local
(defthm is-rpl-is-not-is-falist
(implies (is-rp term)
(not (is-falist term)))
:hints (("Goal" :in-theory (enable is-rp is-falist)))))
(local
(defthm lemma2
(implies (is-rp term)
(and (not (EQUAL (CAR TERM) 'QUOTE))
(CONSP TERM)))
:hints (("Goal" :in-theory (enable is-rp is-falist)))))
(defthm all-falist-consistent-ex-from-rp
(implies (all-falist-consistent term)
(all-falist-consistent (ex-from-rp term)))
:hints (("Goal"
:induct (ex-from-rp term)
:expand ((all-falist-consistent term))
:in-theory (e/d (ex-from-rp)
(IS-FALIST all-falist-consistent)))))
(defthm all-falist-consistent-put-term-in-cons
(implies (all-falist-consistent term)
(all-falist-consistent (put-term-in-cons term)))
:hints (("Goal" :in-theory (enable put-term-in-cons))))
(defthm all-falist-consistent-lst-context-from-rp
(implies (and (all-falist-consistent-lst context)
(all-falist-consistent term))
(all-falist-consistent-lst (context-from-rp term context)))
:hints (("Goal"
:induct (context-from-rp term context)
:expand ((ALL-FALIST-CONSISTENT-LST (CDDR TERM))
(ALL-FALIST-CONSISTENT-LST (CDR TERM)))
:in-theory (e/d (context-from-rp is-rp)))))
(defthm cdr-term-is-all-falist-consistent-lst
(implies (and (not (quotep term))
(all-falist-consistent term))
(all-falist-consistent-lst (cdr term)))
:hints (("Goal"
:expand ((ALL-FALIST-CONSISTENT TERM)
(ALL-FALIST-CONSISTENT-LST (CDR TERM)))
:in-theory (enable all-falist-consistent
all-falist-consistent-lst
is-falist)))))||#
#|(defthm all-falist-consistent-lst-cdr-term-lemma
(implies (and (all-falist-consistent term)
(not (equal (car term) 'quote)))
(all-falist-consistent-lst (cdr term)))
:hints (("Goal"
:do-not-induct t
:expand ((all-falist-consistent term)
(FALIST-CONSISTENT TERM)
(ALL-FALIST-CONSISTENT (CADR TERM))
(ALL-FALIST-CONSISTENT-LST (CDR TERM)))
:in-theory (enable is-falist all-falist-consistent-lst))))||#
#|(defthm-all-falist-consistent
(defthm not-include-falist-all-falist-consistent
(implies (not (include-fnc term 'falist))
(all-falist-consistent term))
:flag all-falist-consistent)
(defthm not-include-falist-all-falist-consistent-lst
(implies (not (include-fnc-subterms lst 'falist))
(all-falist-consistent-lst lst))
:flag all-falist-consistent-lst)
:hints (("Goal"
:in-theory (e/d (is-falist
all-falist-consistent-lst
all-falist-consistent)
(falist-consistent)))))||#
(encapsulate
nil
(local
(defthm lemma1
(implies (and (is-lambda (cons (car term) subterms))
(rp-termp term))
(is-lambda-strict term))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-lambda-strict is-lambda) ())))))
(defthm get-lambda-free-vars-of-cons-car-term-subterms
(implies (and (rp-termp term)
(mv-nth 0 (get-lambda-free-vars-lst subterms)))
(mv-nth 0 (get-lambda-free-vars (cons (car term)
subterms))))
:otf-flg t
:hints (("Goal"
:expand ((get-lambda-free-vars (cons (car term)
subterms)))
:in-theory (e/d () ())))))
(defthm-rp-termp
(defthm rp-termp-implies-get-lambda-free-vars
(implies (rp-termp term)
(mv-nth 0
(get-lambda-free-vars term)))
:flag rp-termp)
(defthm rp-term-listp-implies-get-lambda-free-vars-lst
(implies (rp-term-listp lst)
(mv-nth 0
(get-lambda-free-vars-lst lst)))
:flag rp-term-listp)
:hints (("Goal"
:in-theory (e/d (is-rp falist-consistent) ()))))
(defthm get-lambda-free-vars-of-bindings
(implies (and (rp-term-listp (strip-cdrs bindings))
(consp (assoc-equal term bindings)))
(mv-nth 0
(get-lambda-free-vars (cdr (assoc-equal term bindings))))))
(encapsulate
nil
#|(local
(defthm lemma1
(implies (and (is-lambda term)
(mv-nth 0 (get-lambda-free-vars term)))
(equal (mv-nth 1 (get-lambda-free-vars term))
(mv-nth 1 (get-lambda-free-vars-lst (cdr term)))))
:hints (("Goal"
:expand ((get-lambda-free-vars term))
:in-theory (e/d () ())))))
(local
(defthm lemma2
(implies (and (booleanp x)
x)
(equal (equal t x) t))))
#|(skip-proofs
(local
(defthm lemma3
(booleanp (mv-nth 0 (get-lambda-free-vars-lst lst))))))||#
(local
(defthm-get-lambda-free-vars
(defthm booleanp-get-lambda-free-vars
(booleanp (mv-nth 0 (get-lambda-free-vars term)))
:flag get-lambda-free-vars)
(defthm booleanp-get-lambda-free-vars-lst
(booleanp (mv-nth 0 (get-lambda-free-vars-lst lst)))
:flag get-lambda-free-vars-lst)))
(local
(defthm lemma4
(implies (and (is-lambda term)
(mv-nth 0 (get-lambda-free-vars term)))
(equal (mv-nth 0 (get-lambda-free-vars term))
(mv-nth 0 (get-lambda-free-vars-lst (cdr term)))))
:hints (("Goal"
:expand ((get-lambda-free-vars term))
:in-theory (e/d () ())))))
(local
(defthm lemma5
(implies (and (mv-nth 0 (GET-LAMBDA-FREE-VARS-LST (CDR TERM)))
(EQUAL (GET-LAMBDA-FREE-VARS-LST SUBTERMS)
(GET-LAMBDA-FREE-VARS-LST (CDR TERM))))
(MV-NTH 0 (GET-LAMBDA-FREE-VARS-LST SUBTERMS)))))||#
#|(local
;; this was used when lambda expressions were allowed
(defthm rp-termp-cons-car-term-subterms-lemma1
(implies (and (rp-termp term)
(consp term)
(consp (car term))
(equal (len subterms)
(len (cdr term)))
;(mv-nth 0 (get-lambda-free-vars-lst subterms)) ; ;
#|(lambda-exp-free-listp subterms)||#
(rp-term-listp subterms))
(rp-termp (cons (car term) subterms)))
:otf-flg t
:hints (("Goal"
:do-not-induct t
:expand ((rp-termp term)
(GET-LAMBDA-FREE-VARS (CONS (CAR TERM) SUBTERMS))
(is-lambda-strict (cons (car term) subterms))
(IS-LAMBDA (CONS (CAR TERM) SUBTERMS)))
:in-theory (e/d () (get-lambda-free-vars))))))||#
(defthm rp-termp-cons-car-term-subterms
(implies (and (rp-termp term)
(consp term)
#|(or ;(atom (car term))
#|(and (equal (len subterms)
(len (cdr term)))
#|(lambda-exp-free-listp subterms)||#)||#)||#
(not (equal (car term) 'quote))
(force (or (not (equal (car term) 'rp))
(is-rp (cons (car term) subterms))))
(force (or (not (equal (car term) 'falist))
(falist-consistent (cons (car term) subterms))))
(rp-term-listp subterms))
(rp-termp (cons (car term) subterms)))
:hints (("Goal"
:in-theory (e/d (is-rp
falist-consistent) ())))
))
(defthm rp-term-listp-append
(implies (and (rp-term-listp lst1)
(rp-term-listp lst2))
(rp-term-listp (append lst1 lst2)))
:hints (("Goal" :in-theory (enable append rp-term-listp))))
#|(defthm ALL-FALIST-CONSISTENT-LST-append
(implies (and (ALL-FALIST-CONSISTENT-LST lst1)
(ALL-FALIST-CONSISTENT-LST lst2))
(ALL-FALIST-CONSISTENT-LST (append lst1 lst2)))
:hints (("Goal" :in-theory (enable append ALL-FALIST-CONSISTENT-LST))))||#
(encapsulate
nil
(local
(defthm is-falist-remove-return-last-subterms
(implies (consp term)
(equal (is-falist (cons (car term)
(remove-return-last-subterms (cdr term))))
(is-falist term)))
:hints (("Goal"
; :in-theory (disable is-falist)
:Expand ((REMOVE-RETURN-LAST-SUBTERMS (CDR TERM))
(REMOVE-RETURN-LAST-SUBTERMS (CDDDR TERM))
(REMOVE-RETURN-LAST-SUBTERMS (CDDR TERM)))))))
(local
(defthm not-is-falist-cons-quote-return-last
(not (is-falist (cons 'return-last x)))))
(local
(defthm lemma1
(implies (is-falist term)
(equal (car term) 'falist))))
#|
;; needed for the guards of rp-rw-aux
(defthm-remove-return-last
(defthm all-falist-consistent-remove-return-last
(implies (all-falist-consistent term)
(all-falist-consistent (remove-return-last term)))
:flag remove-return-last)
(defthm all-falist-consistent-remove-return-last-subterms
(implies (all-falist-consistent-lst subterms)
(all-falist-consistent-lst (remove-return-last-subterms subterms)))
:flag remove-return-last-subterms)
:hints (("Goal"
:expand
((ALL-FALIST-CONSISTENT TERM)
(ALL-FALIST-CONSISTENT (CONS (CAR TERM)
(REMOVE-RETURN-LAST-SUBTERMS (CDR TERM)))))
:in-theory (e/d () (is-falist falist-consistent-aux
falist-consistent)))))||#)
(defthm dont-rw-syntaxp-dont-rw-if-fix
(implies (and (dont-rw-syntaxp dont-rw))
(and (dont-rw-syntaxp (dont-rw-if-fix dont-rw))
(dont-rw-syntaxp (cadr (dont-rw-if-fix dont-rw)))
(dont-rw-syntaxp (caddr (dont-rw-if-fix dont-rw)))
(dont-rw-syntaxp (cadddr (dont-rw-if-fix dont-rw)))))
:hints (("Goal"
:in-theory (e/d (dont-rw-syntaxp
dont-rw-if-fix)
()))))
#|(encapsulate
nil
(local
(defthm lemma1
(implies (is-rp term)
(equal (REMOVE-RETURN-LAST (CADR TERM))
(cadr term)))
:hints (("Goal"
:in-theory (e/d (is-rp) ())))))
(local
(DEFTHM IS-RP-IMPLIES-lemma
(IMPLIES (IS-RP TERM)
(CASE-MATCH TERM
(('RP ('QUOTE TYPE) &)
(AND (SYMBOLP TYPE)
(NOT (EQUAL TYPE 'QUOTE))))
(& NIL)))
:hints (("Goal"
:in-theory (e/d (is-rp) ())))
:rule-classes :forward-chaining))
||#
;; (defthm RP-SYNTAXP-EX-FROM-RP-TERM
;; (implies (rp-syntaxp term)
;; (rp-syntaxp (ex-from-rp term)))
;; :hints (("Goal"
;; :induct (ex-from-rp term)
;; :in-theory (e/d (is-rp
;; ex-from-rp) ()))))
;; (defthm-rp-syntaxp
;; (defthm not-include-rp-means-rp-syntaxp
;; (implies (not (include-fnc term 'rp))
;; (rp-syntaxp term))
;; :flag rp-syntaxp)
;; (defthm not-include-rp-means-rp-syntaxp-lst
;; (implies (not (include-fnc-subterms lst 'rp))
;; (rp-syntaxp-lst lst))
;; :flag rp-syntaxp-lst))
#|(defthm-remove-return-last
(defthm not-include-rp-of-remove-return-last
(implies (not (include-fnc term 'rp))
(not (include-fnc (remove-return-last term) 'rp)))
:flag remove-return-last)
(defthm not-include-rp-of-remove-return-last-subterms
(implies (not (include-fnc-subterms subterms 'rp))
(Not (include-fnc-subterms (remove-return-last-subterms subterms) 'rp)))
:flag remove-return-last-subterms))||#
#|(defthm rp-syntaxp-ex-from-rp
(implies (rp-syntaxp term)
(rp-syntaxp (ex-from-rp term)))
:hints (("Goal"
:in-theory (e/d (ex-from-rp
is-rp) ()))))||#
#|
(defthm rp-syntaxp-ex-from-rp-lemma
(implies (and (rp-syntaxp term)
(not (equal (car (ex-from-rp term))
'quote)))
(rp-syntaxp-lst (cdr (ex-from-rp term))))
:hints (("Goal"
:in-theory (e/d (ex-from-rp
is-rp) ()))))
(defthm rp-syntaxp-lst-context-from-rp
(implies (and (rp-syntaxp term)
(rp-syntaxp-lst context))
(rp-syntaxp-lst (context-from-rp term context)))
:hints (("Goal"
:in-theory (e/d (context-from-rp
is-rp) ()))))
(defthm rp-syntaxp-put-term-in-cons
(implies
(should-term-be-in-cons rule-lhs term)
(and (rp-syntaxp (put-term-in-cons term))
(RP-SYNTAXP-LST (CDR (PUT-TERM-IN-CONS term)))))
:hints (("Goal"
:in-theory (e/d (put-term-in-cons
should-term-be-in-cons) ()))))
(encapsulate
nil
(local
(defthm lemma1
(IMPLIES
(AND
(CONSP TERM)
(NOT (EQUAL (CAR TERM) 'QUOTE))
(NOT (EQUAL (CAR TERM) 'RP))
(RP-SYNTAXP-LST
(REMOVE-RETURN-LAST-SUBTERMS (CDR TERM)))
(RP-SYNTAXP-LST (CDR TERM)))
(RP-SYNTAXP (REMOVE-RETURN-LAST TERM)))
:hints (("Goal"
:cases ((is-return-last term))
:in-theory (e/d () ())))))
#|(defthm-rp-syntaxp
(defthm rp-syntaxp-remove-return-last
(implies (rp-syntaxp term)
(rp-syntaxp (remove-return-last term)))
:flag rp-syntaxp)
(defthm rp-syntaxp-remove-return-last-subterms
(implies
(rp-syntaxp-lst lst)
(rp-syntaxp-lst (remove-return-last-subterms lst)))
:flag rp-syntaxp-lst)
:hints (("Goal"
:in-theory (e/d (is-rp) ()))))||#)
(defthmd context-syntaxp-implies
(implies (context-syntaxp context)
(AND (RP-TERM-LISTP CONTEXT)
(RP-SYNTAXP-LST CONTEXT)
(ALL-FALIST-CONSISTENT-LST CONTEXT)))
:hints (("Goal"
:in-theory (e/d (context-syntaxp) ()))))
(defthm rp-syntaxp-assoc-equal
(IMPLIES
(AND
(RP-SYNTAXP-LST (STRIP-CDRS BINDINGS))
(CONSP (ASSOC-EQUAL TERM BINDINGS)))
(and
(RP-SYNTAXP (CDR (ASSOC-EQUAL TERM BINDINGS)))
(RP-SYNTAXP (CDR (hons-ASSOC-EQUAL TERM BINDINGS))))))
(defthm rp-syntaxp-lst-append
(equal (rp-syntaxp-lst (append x y))
(and (rp-syntaxp-lst x)
(rp-syntaxp-lst y)))
:hints (("Goal"
:in-theory (e/d (rp-syntaxp-lst
append)
(rp-syntaxp)))))||#
(defthm is-if-implies
(implies (is-if term)
(CASE-MATCH TERM (('IF & & &) T)
(& NIL)))
:hints (("Goal"
:in-theory (e/d (is-if) ())))
:rule-classes :forward-chaining)
(defthmd is-rp-implies-fc
(implies (is-rp term)
(CASE-MATCH TERM
(('RP ('QUOTE TYPE) &)
(AND (SYMBOLP TYPE)
(NOT (BOOLEANP TYPE))
(NOT (EQUAL TYPE 'QUOTE))
(NOT (EQUAL TYPE 'RP))
(NOT (EQUAL TYPE 'LIST))
(NOT (EQUAL TYPE 'FALIST))))
(& NIL)))
:rule-classes :forward-chaining
:hints (("Goal"
:in-theory (e/d (is-rp) ()))))
(defthm is-rp-of-rp
(implies (AND (SYMBOLP TYPE)
(NOT (BOOLEANP TYPE))
(NOT (EQUAL TYPE 'QUOTE))
(NOT (EQUAL TYPE 'RP))
(NOT (EQUAL TYPE 'LIST))
(NOT (EQUAL TYPE 'FALIST)))
(is-rp `(rp ',type ,x)))
:hints (("Goal"
:in-theory (e/d (is-rp) ()))))
(defthmd rule-syntaxp-implies
(implies (and (rule-syntaxp rule :warning warning)
(not (rp-rule-metap rule)))
(and
(weak-custom-rewrite-rule-p rule)
(rp-term-listp (rp-hyp rule))
(rp-termp (rp-lhs rule))
(rp-termp (rp-rhs rule))
;; (rp-syntaxp (rp-lhs rule))
(not (include-fnc (rp-lhs rule) 'rp))
(not (include-fnc-subterms (rp-hyp rule) 'rp))
;;(rp-syntaxp (rp-rhs rule))
(not (include-fnc (rp-rhs rule) 'falist))
(not (include-fnc-subterms (rp-hyp rule) 'falist))
;;(not (include-fnc (rp-lhs rule) 'if))
(not (include-fnc (rp-lhs rule) 'synp))
#|(no-free-variablep rule)|#
(not (include-fnc (rp-lhs rule) 'list))
(not (include-fnc-subterms (rp-hyp rule) 'list))
(not (include-fnc (rp-rhs rule) 'list))
(not (include-fnc (rp-lhs rule) 'equals))
(not (include-fnc-subterms (rp-hyp rule) 'equals))
(not (include-fnc (rp-rhs rule) 'equals))))
:rule-classes (:rewrite :forward-chaining)
:hints (("Goal" :in-theory (enable rule-syntaxp))))
(defthmd rule-syntaxp-implies-2
(implies (and (rule-syntaxp rule :warning warning)
(rp-rule-metap rule))
(AND (SYMBOLP (RP-RULE-TRIG-FNC RULE))
(RP-RULE-TRIG-FNC RULE)
(SYMBOLP (RP-RULE-META-FNC RULE))
(RP-RULE-META-FNC RULE)))
:rule-classes (:rewrite :forward-chaining)
:hints (("Goal" :in-theory (enable rule-syntaxp))))
(defthm ex-from-rp-loose-of-ex-from-rp-loose
(equal (ex-from-rp-loose (ex-from-rp-loose term))
(ex-from-rp-loose term))
:hints (("Goal"
:in-theory (e/d (ex-from-rp-loose
is-rp-loose) ()))))
;; (defthm all-falist-consistent-of-ex-from-rp-loose
;; (implies (all-falist-consistent term)
;; (all-falist-consistent (ex-from-rp-loose term)))
;; :hints (("Goal"
;; :in-theory (e/d (ex-from-rp-loose
;; is-rp-loose) ()))))
;; (defthm rp-termp-ex-from-rp-loose
;; (implies (rp-termp term)
;; (rp-termp (ex-from-rp-loose term)))
;; :hints (("Goal"
;; :in-theory (e/d (rp-termp
;; ex-from-rp-loose
;; is-rp-loose) ()))))
;; (defthm rp-syntaxp-ex-from-rp-loose
;; (implies (rp-syntaxp term)
;; (rp-syntaxp (ex-from-rp-loose term)))
;; :hints (("Goal"
;; :in-theory (e/d (rp-syntaxp
;; ex-from-rp-loose
;; is-rp-loose) ()))))
;; (defthm all-falist-consistent-of-ex-from-rp
;; (implies (all-falist-consistent term)
;; (all-falist-consistent (ex-from-rp term)))
;; :hints (("Goal"
;; :in-theory (e/d (ex-from-rp
;; is-rp ) ()))))
(defthm
rp-termp-ex-from-rp
(implies (rp-termp term)
(and (rp-termp (ex-from-rp term))
(rp-termp (ex-from-rp-loose term))))
:hints
(("goal" :in-theory
(e/d (ex-from-rp-loose ex-from-rp is-rp-loose is-rp)
nil))))
;; (defthm all-falist-consistent-ex-from-rp-loose
;; (implies (all-falist-consistent term)
;; (all-falist-consistent (ex-from-rp-loose term)))
;; :hints (("Goal"
;; :in-theory (e/d (all-falist-consistent
;; is-falist
;; ex-from-rp-loose
;; is-rp-loose) ()))))
(defthm rp-termp-cadr
(implies (and (rp-termp term)
(consp term)
(not (quotep term))
(consp (cdr term)))
(rp-termp (cadr term)))
:hints (("Goal"
:in-theory (e/d (rp-termp
is-rp
ex-from-rp-loose
is-rp-loose) ()))))
#|(defthm rp-syntaxp-cadr
(implies (and (rp-syntaxp term)
(consp term)
(not (quotep term))
(not (equal (car term) 'rp))
(consp (cdr term)))
(rp-syntaxp (cadr term)))
:hints (("Goal"
:in-theory (e/d (rp-termp
ex-from-rp-loose
is-rp-loose) ()))))||#
#|(defthm all-falist-consistent-cadr
(implies (and (all-falist-consistent term)
(consp term)
(not (quotep term))
(consp (cdr term)))
(all-falist-consistent (cadr term)))
:hints (("Goal"
:in-theory (e/d (all-falist-consistent
ex-from-rp-loose
is-rp-loose) ()))))||#
#|(defthm all-falist-consistent-caddr
(implies (and (all-falist-consistent term)
(consp term)
(not (quotep term))
(consp (cdr term))
(consp (cddr term)))
(all-falist-consistent (caddr term)))
:hints (("Goal"
:in-theory (e/d (all-falist-consistent
ex-from-rp-loose
is-rp-loose) ()))))||#
#|(defthm all-falist-consistent-cadddr
(implies (and (all-falist-consistent term)
(consp term)
(not (quotep term))
(consp (cdr term))
(consp (cddr term))
(consp (cdddr term)))
(all-falist-consistent (cadddr term)))
:hints (("Goal"
:in-theory (e/d (all-falist-consistent
ex-from-rp-loose
is-rp-loose) ()))))||#
(defthm rp-termp-caddr
(implies (and (rp-termp term)
(consp term)
(not (quotep term))
(consp (cdr term))
(consp (cddr term)))
(rp-termp (caddr term)))
:hints (("Goal"
:in-theory (e/d (rp-termp
is-rp
ex-from-rp-loose
is-rp-loose) ()))))
(defthm rp-termp-cadddr
(implies (and (rp-termp term)
(consp term)
(not (quotep term))
(consp (cdr term))
(consp (cddr term))
(consp (cdddr term)))
(rp-termp (cadddr term)))
:hints (("Goal"
:in-theory (e/d (rp-termp
is-rp
ex-from-rp-loose
is-rp-loose) ()))))
(defthm rp-termp-caddddr
(implies (and (rp-termp term)
(consp term)
(not (quotep term))
(consp (cdr term))
(consp (cddr term))
(consp (cdddr term))
(consp (cddddr term)))
(rp-termp (car (cddddr term))))
:hints (("Goal"
:in-theory (e/d (rp-termp
is-rp
ex-from-rp-loose
is-rp-loose) ()))))
#|(defthm rp-syntaxp-caddr
(implies (and (rp-syntaxp term)
(consp term)
(not (quotep term))
;(not (equal (car term) 'rp)) ;
(consp (cdr term))
(consp (cddr term)))
(rp-syntaxp (caddr term)))
:hints (("Goal"
:in-theory (e/d (rp-termp
ex-from-rp-loose
is-rp-loose) ()))))||#
#|(defthm rp-syntaxp-cadddr
(implies (and (rp-syntaxp term)
(consp term)
(not (quotep term))
(consp (cdr term))
(consp (cddr term))
(consp (cdddr term)))
(rp-syntaxp (cadddr term)))
:hints (("Goal"
:expand ((rp-syntaxp term))
:in-theory (e/d (rp-termp
ex-from-rp-loose
rp-syntaxp
is-rp
is-rp-loose) ()))))||#
(defthmd ex-from-rp-loose-is-ex-from-rp
(implies (rp-termp term)
(equal (ex-from-rp-loose term)
(ex-from-rp term)))
:hints (("Goal"
:in-theory (e/d (is-rp-loose
is-rp
ex-from-rp
ex-from-rp-loose) ()))))
(defthm car-of-ex-from-rp-is-not-rp
(implies (rp-termp term)
(not (equal (car (ex-from-rp term))
'rp)))
:hints (("Goal"
:in-theory (e/d (ex-from-rp
is-rp) ()))))
(defthm dont-rw-syntaxp-dont-rw-syntax-fix
(dont-rw-syntaxp (dont-rw-syntax-fix dont-rw))
:hints (("Goal"
:in-theory (e/d (dont-rw-syntax-fix)
(DONT-RW-SYNTAXP)))))
(defthm rp-termp-implies-dont-rw-syntaxp
(implies (rp-termp term)
(dont-rw-syntaxp term)))
(defthm rp-termp-ex-from-falist
(implies (rp-termp x)
(rp-termp (ex-from-falist x)))
:rule-classes (:type-prescription :rewrite)
:hints (("Goal"
:expand (ex-from-falist x)
:in-theory (e/d () ()))))
(defthm is-falist-strict-to-is-falist
(implies (rp-termp term)
(equal (is-falist-strict term)
(is-falist term))))
(defthm rp-termp-trans*-list
(implies (and (rp-term-listp lst)
(consp lst))
(rp-termp (trans-list lst))))
(defthm consp-rp-trans-lst
(equal (consp (rp-trans-lst lst))
(consp lst))
:hints (("Goal"
:induct (len lst)
:in-theory (e/d () ()))))
(defthm is-rp-rp-trans-lst
(IMPLIES (AND (RP-TERMP TERM)
(is-rp term))
(IS-RP (CONS 'RP (RP-TRANS-LST (CDR TERM)))))
:hints (("Goal"
:in-theory (e/d (is-rp) ()))))
(defthm-rp-trans
(defthm rp-termp-of-rp-trans
(implies (rp-termp term)
(rp-termp (rp-trans term)))
:flag rp-trans)
(defthm rp-term-listp-of-rp-trans-lst
(implies (rp-term-listp lst)
(rp-term-listp (rp-trans-lst lst)))
:flag rp-trans-lst)
:otf-flg t
:hints (("Goal"
:expand ((:free (x y)
(rp-termp (cons x y)))
(RP-TERMP TERM))
:in-theory (e/d ()
(FALIST-CONSISTENT
RP-TERMP-CONS-CAR-TERM-SUBTERMS)))))
(defthm-rp-trans
(defthm rp-trans-not-include-fnc-list
(not (include-fnc (rp-trans term) 'list))
:flag rp-trans)
(defthm rp-trans-lst-not-include-fnc-subterms-list
(not (include-fnc-subterms (rp-trans-lst lst) 'list))
:flag rp-trans-lst)
:otf-flg t
:hints (("Goal"
:in-theory (e/d ()
()))))
(defthm rp-trans-of-trans-list
(equal (rp-trans (trans-list lst))
(trans-list (rp-trans-lst lst))))
(defthm-rp-trans
(defthm rp-trans-of-rp-trans
(equal (rp-trans (rp-trans term))
(rp-trans term))
:flag rp-trans)
(defthm rp-trans-lst-of-rp-trans-lst
(equal (rp-trans-lst (rp-trans-lst lst))
(rp-trans-lst lst))
:flag rp-trans-lst)
:otf-flg t
:hints (("goal"
:expand ((is-falist (list (car term)))
(rp-trans-lst (cdr term))
(rp-trans-lst (cddr term))
(rp-trans-lst (cdddr term))
(rp-trans (cons (car term)
(rp-trans-lst (cdr term)))))
:in-theory (e/d ()
()))))
#|(defthm-rp-trans
(defthm rp-trans-is-term-when-list-is-absent
(implies (not (include-fnc term 'list))
(equal (rp-trans term) term))
:flag rp-trans)
(defthm rp-trans-lst-is-lst-when-list-is-absent
(implies (not (include-fnc-subterms lst 'list))
(equal (rp-trans-lst lst) lst))
:flag rp-trans-lst))||#
(defthm rp-state-new-run-returns-rp-statep
(implies (rp-statep rp-state)
(rp-statep (rp-state-new-run rp-state)))
:hints (("Goal"
:in-theory (e/d (rp-state-new-run
rp-statep)
()))))
(defthm RP-TERM-LISTP-of-append
(implies (and (rp-term-listp lst1)
(rp-term-listp lst2))
(rp-term-listp (append lst1 lst2))))
(defthm rp-state-preservedp-of-the-same
(implies (rp-statep rp-state)
(rp-state-preservedp rp-state rp-state))
:hints (("Goal"
:in-theory (e/d (rp-state-preservedp) ()))))
(defthm rp-state-preservedp-implies-rp-statep
(implies (and (rp-statep rp-state)
(rp-state-preservedp rp-state new-rp-state))
(rp-statep new-rp-state))
:hints (("Goal"
:in-theory (e/d (rp-state-preservedp) ()))))
(defthm rp-state-preservedp-implies-valid-rp-state-syntaxp
(implies (and (valid-rp-state-syntaxp rp-state)
(rp-state-preservedp rp-state new-rp-state))
(valid-rp-state-syntaxp new-rp-state))
:hints (("Goal"
:do-not-induct t
:use ((:instance RP-STATE-PRESERVEDP-SK-necc
(key (VALID-RP-STATE-SYNTAXP-AUX-WITNESS
NEW-RP-STATE))
(OLD-RP-STATE rp-state))
(:instance VALID-RP-STATE-SYNTAXP-AUX-necc
(key (VALID-RP-STATE-SYNTAXP-AUX-WITNESS NEW-RP-STATE))))
:expand (VALID-RP-STATE-SYNTAXP-AUX NEW-RP-STATE)
:in-theory (e/d (rp-state-preservedp
valid-rp-state-syntaxp)
(RP-STATE-PRESERVEDP-SK
VALID-RP-STATE-SYNTAXP-AUX
RP-STATEP)))))
#|(local
(defthmd rp-termp-ex-from-rp-all2-lemma
(implies (syntaxp (not (include-fnc term 'ex-from-rp)))
(equal (rp-termp term)
(and (hide (rp-termp term))
(rp-termp (ex-from-rp term)))))
:hints
(("goal"
:expand (hide (rp-termp term))
:in-theory
(e/d (ex-from-rp-loose ex-from-rp is-rp-loose is-rp)
nil)))))|#
(defthm-ex-from-rp-all2
(defthm rp-termp-ex-from-rp-all2
(implies (rp-termp term)
(rp-termp (ex-from-rp-all2 term)))
:flag ex-from-rp-all2)
(defthm rp-term-listp-ex-from-rp-all2-lst
(implies (rp-term-listp lst)
(rp-term-listp (ex-from-rp-all2-lst lst)))
:flag ex-from-rp-all2-lst)
:hints (("Goal"
:do-not-induct t
:expand (RP-TERMP (EX-FROM-RP TERM))
:in-theory (e/d (
EX-FROM-RP-ALL2
IS-RP-LOOSE
is-rp
;;rp-termp-ex-from-rp-all2-lemma
ex-from-rp-all2-lst
)
(ex-from-rp
;;FALIST-CONSISTENT
RP-TERMP-EX-FROM-RP
RP-TERMP-CONS-CAR-TERM-SUBTERMS
)))))
(defthm-ex-from-rp-all2
(defthm ex-from-rp-all2-not-include-rp
(implies (rp-termp term)
(not (include-fnc (ex-from-rp-all2 term) 'rp)))
:flag ex-from-rp-all2)
(defthm ex-from-rp-all2-lst-not-include-rp
(implies (rp-term-listp lst)
(not (include-fnc-subterms (ex-from-rp-all2-lst lst) 'rp)))
:flag ex-from-rp-all2-lst)
:hints (("Goal"
:do-not-induct t
:expand (RP-TERMP (EX-FROM-RP TERM))
:in-theory (e/d (
EX-FROM-RP-ALL2
IS-RP-LOOSE
is-rp
;;rp-termp-ex-from-rp-all2-lemma
ex-from-rp-all2-lst
)
(ex-from-rp
;;FALIST-CONSISTENT
RP-TERMP-EX-FROM-RP
RP-TERMP-CONS-CAR-TERM-SUBTERMS
)))))
(defthmd equal-of-len-with-constant
(implies (and (syntaxp (quotep x))
(posp x))
(equal (equal (len lst) x)
(and (consp lst)
(equal (len (cdr lst)) (1- x)))))
:hints (("Goal"
:in-theory (e/d (len) ()))))
(defthm equal-of-len-with-0
(equal (equal (len lst) 0)
(atom lst))
:hints (("Goal"
:in-theory (e/d (len) ()))))
(defthm len-of-ex-from-rp-all2-lst
(equal (len (ex-from-rp-all2-lst lst))
(len lst))
:hints (("Goal"
:induct (len lst)
:in-theory (e/d (ex-from-rp-all2-lst len) ()))))
(defthm-ex-from-rp-all2
(defthm ex-from-rp-all2-not-include-equals
(implies (rp-termp term)
(not (include-fnc (ex-from-rp-all2 term) 'equals 2)))
:flag ex-from-rp-all2)
(defthm ex-from-rp-all2-lst-not-include-equals
(implies (rp-term-listp lst)
(not (include-fnc-subterms (ex-from-rp-all2-lst lst) 'equals 2)))
:flag ex-from-rp-all2-lst)
:hints (("Goal"
:do-not-induct t
:expand (RP-TERMP (EX-FROM-RP TERM))
:in-theory (e/d (equal-of-len-with-constant
is-equals
EX-FROM-RP-ALL2
IS-RP-LOOSE
is-rp
;;rp-termp-ex-from-rp-all2-lemma
ex-from-rp-all2-lst
)
(ex-from-rp
;;FALIST-CONSISTENT
RP-TERMP-EX-FROM-RP
RP-TERMP-CONS-CAR-TERM-SUBTERMS
)))))
(defthmd rp-termp-single-step
(implies (is-rp term)
(and (equal (rp-termp (list (car term)
(cadr term)
rest))
(rp-termp rest))
(equal (rp-termp term)
(rp-termp (caddr term)))))
:hints (("Goal"
:in-theory (e/d (is-rp) ()))))
(defthm rp-termp-single-step-2
(implies (is-rp term)
(equal (rp-termp (list (car term)
(cadr term)
rest))
(rp-termp rest)))
:hints (("Goal"
:in-theory (e/d (is-rp) ()))))
(defthm rp-termp-single-step-3
(implies (and (is-rp term)
(rp-termp term))
(rp-termp (caddr term)))
:hints (("Goal"
:in-theory (e/d (is-rp
rp-termp-single-step) ()))))
(defthm rp-term-listp-of-rev
(implies (rp-term-listp x)
(rp-term-listp (rev x)))
:hints (("Goal"
:in-theory (e/d (rev) ()))))
(progn
(define binary-or**/and**-guard-meta-aux (term)
(cond
((atom term)
term)
((atom (cdr term))
term)
((atom (cddr term))
(case-match term
(('hide x)
(binary-or**/and**-guard-meta-aux x))
(& term)))
((atom (cdddr term))
(case-match term
(('acl2::binary-or* x y)
`(binary-or** ,(binary-or**/and**-guard-meta-aux x)
,(binary-or**/and**-guard-meta-aux y)))
(('acl2::binary-and* x y)
`(binary-and** ,(binary-or**/and**-guard-meta-aux x)
,(binary-or**/and**-guard-meta-aux y)))
(('binary-or** x y)
`(binary-or** ,(binary-or**/and**-guard-meta-aux x)
,(binary-or**/and**-guard-meta-aux y)))
(('binary-and** x y)
`(binary-and** ,(binary-or**/and**-guard-meta-aux x)
,(binary-or**/and**-guard-meta-aux y)))
(('equal x y)
(b* ((x (binary-or**/and**-guard-meta-aux x))
(y (binary-or**/and**-guard-meta-aux y)))
(if (equal x y)
''t
`(equal ,x ,y))))
(& term)))
((atom (cddddr term))
(case-match term
(('RETURN-LAST & & x)
(binary-or**/and**-guard-meta-aux x))
(('if x x y)
`(binary-or** ,(binary-or**/and**-guard-meta-aux x)
,(binary-or**/and**-guard-meta-aux y)))
(('if x y ''nil)
`(binary-and** ,(binary-or**/and**-guard-meta-aux x)
,(binary-or**/and**-guard-meta-aux y)))
(& term)))
(t term)))
(define binary-or**/and**-guard-meta (term)
(case-match term
(('equal & ('hide &))
(binary-or**/and**-guard-meta-aux
(beta-search-reduce term *big-number*)))
(('equal ('hide &) &)
(binary-or**/and**-guard-meta-aux
(beta-search-reduce term *big-number*)))
(& term)))
(defevaluator binary-or**/and**-guard-meta-eval
binary-or**/and**-guard-meta-eval-lst
((acl2::binary-or* x y)
(binary-or** x y)
(acl2::binary-and* x y)
(binary-and** x y)
(hide x)
(equal x y)
(if x y z)
(RETURN-LAST x y z))
:namedp t)
(defthm binary-or**/and**-guard-meta-eval-beta-search-reduce
(implies
(pseudo-termp term)
(equal (binary-or**/and**-guard-meta-eval (beta-search-reduce term limit) a)
(binary-or**/and**-guard-meta-eval term a)))
:hints (("Goal"
:use ((:functional-instance
eval-of-beta-search-reduce
(acl2::beta-eval binary-or**/and**-guard-meta-eval)
(acl2::beta-eval-list binary-or**/and**-guard-meta-eval-lst)))
:in-theory (e/d (binary-or**/and**-guard-meta-eval-of-fncall-args) ()))))
(defthm binary-or**/and**-guard-meta-aux-correct
(implies t
(equal (binary-or**/and**-guard-meta-eval
(binary-or**/and**-guard-meta-aux term) a)
(binary-or**/and**-guard-meta-eval
term a)))
:hints (("Goal"
:do-not-induct t
:expand ((:free (x) (hide x)))
:induct (binary-or**/and**-guard-meta-aux term)
:in-theory (e/d (binary-or**/and**-guard-meta-aux
BINARY-AND**
acl2::BINARY-AND*
BINARY-or**
acl2::BINARY-or*)
()))))
(defthm binary-or**/and**-guard-meta-correct
(implies (pseudo-termp term)
(equal (binary-or**/and**-guard-meta-eval term a)
(binary-or**/and**-guard-meta-eval
(binary-or**/and**-guard-meta term) a)))
:rule-classes ((:meta :trigger-fns (equal)))
:hints (("Goal"
:do-not-induct t
:in-theory (e/d (binary-or**/and**-guard-meta)
())))))
#|(defthm binary-and**-of-nil/t
(and (equal (binary-and** nil a)
nil)
(equal (binary-and** t a)
a))
:hints (("Goal"
:in-theory (e/d (binary-and**) ()))))|#
(defthm-include-fnc
(defthmd include-fnc-without-size-implies-with-size
(implies (not (include-fnc term fnc nil))
(not (include-fnc term fnc arg-size)))
:flag include-fnc-fn)
(defthmd include-fnc-subterms-without-size-implies-with-size
(implies (not (include-fnc-subterms subterms fnc nil))
(not (include-fnc-subterms subterms fnc arg-size)))
:flag include-fnc-subterms-fn))
|
