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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.
; 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 "../rp-rewriter")
(include-book "local-lemmas")
(include-book "aux-function-lemmas")
(include-book "proof-function-lemmas")
(encapsulate
nil
(local
(defthm consp-extract-from-rp
(implies (consp (ex-from-rp term))
(consp term))))
(local
(defthm extract-from-rp-acl2-count
(implies (consp term)
(< (acl2-count (cdr (ex-from-rp term)))
(acl2-count term)))))
(local
(defthm consp-ex-from-rp-loose
(implies (consp (ex-from-rp-loose term))
(consp term))
:hints (("Goal"
:in-theory (e/d (ex-from-rp-loose
is-rp-loose) ())))))
(local
(defthm ex-from-rp-loose-acl2-count
(implies (consp term)
(< (acl2-count (cdr (ex-from-rp-loose term)))
(acl2-count term)))
:hints (("Goal"
:in-theory (e/d (ex-from-rp-loose
is-rp-loose) ())))))
(make-flag rp-equal-cnt :defthm-macro-name defthm-rp-equal-cnt)
(make-flag rp-equal :defthm-macro-name defthm-rp-equal)
(make-flag rp-equal-loose :defthm-macro-name defthm-rp-equal-loose))
(local (in-theory (disable rp-lhs rp-rhs rp-hyp)))
(local
(in-theory (disable is-synp extract-from-synp
should-term-be-in-cons put-term-in-cons)))
(local
(defthm consp-extract-from-rp
(implies (consp (ex-from-rp term))
(consp term))
:hints (("Goal" :in-theory (enable ex-from-rp)))))
(local
(defthm consp-extract-from-synp
(implies (consp (ex-from-synp term))
(consp term))
:hints (("Goal" :in-theory (enable is-synp extract-from-synp)))))
(defthm-rp-equal
(defthm rp-equal-reflexive
(implies (equal term1 term2)
(rp-equal term1 term2))
:flag rp-equal)
(defthm rp-equal-subterms-reflexive
(implies (equal subterm1 subterm2)
(rp-equal-subterms subterm1 subterm2))
:flag rp-equal-subterms))
(defthm evl-of-extract-from-rp
(equal (rp-evl (ex-from-rp term) a)
(rp-evl term a))
:hints (("Goal"
:in-theory (enable is-rp ex-from-rp))))
(defthm evl-of-extract-from-rp-loose
(equal (rp-evl (ex-from-rp-loose term) a)
(rp-evl term a))
:hints (("Goal"
:in-theory (enable is-rp-loose ex-from-rp-loose))))
(defthmd evl-of-extract-from-rp-loose-reverse
(implies (syntaxp (atom term))
(equal (rp-evl term a)
(rp-evl (ex-from-rp-loose term) a)))
:hints (("Goal"
:use ((:instance evl-of-extract-from-rp-loose))
:in-theory (disable evl-of-extract-from-rp-loose ))))
(defthm evl-of-extract-from-synp
(equal (rp-evl (ex-from-synp term) a)
(rp-evl term a))
:hints (("Goal"
:in-theory (enable is-synp extract-from-synp))))
(local
(defthm extract-from-rp-equal-to-evl
(implies (equal (ex-from-rp term1)
(ex-from-rp term2))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:hints (("goal"
:induct (ex-from-rp term2)
:in-theory (enable is-rp ex-from-rp)))))
(local
(defthm extract-from-rp-equal-to-evl-loose
(implies (equal (ex-from-rp-loose term1)
(ex-from-rp-loose term2))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:hints (("goal"
:induct (ex-from-rp-loose term2)
:in-theory (enable is-rp-loose ex-from-rp-loose)))))
(local
(defthm extract-from-rp-equal-to-evl-2
(implies (EQUAL (rp-evl (EX-FROM-RP TERM1) a)
(rp-evl (EX-FROM-RP TERM2) a))
(equal (EQUAL (RP-EVL TERM1 A)
(RP-EVL TERM2 A))
t))
:hints (("Goal"
:in-theory (e/d (is-rp ex-from-rp)
(NOT-INCLUDE-RP))))))
(local
(defthm extract-from-rp-equal-to-evl-2-loose
(implies (EQUAL (rp-evl (ex-from-rp-loose TERM1) a)
(rp-evl (ex-from-rp-loose TERM2) a))
(equal (EQUAL (RP-EVL TERM1 A)
(RP-EVL TERM2 A))
t))
:hints (("Goal"
:in-theory (e/d (is-rp-loose ex-from-rp-loose)
(NOT-INCLUDE-RP))))))
(local
(defthm extract-from-synp-equal-to-evl-1
(implies (EQUAL (EXTRACT-FROM-SYNP TERM1)
(EXTRACT-FROM-SYNP TERM2))
(equal (EQUAL (RP-EVL TERM1 A)
(RP-EVL TERM2 A))
t))
:hints (("Goal"
:in-theory (enable is-synp extract-from-synp)))))
(local
(defthm evl-of-is-synp
(IMPLIES (IS-SYNP TERM1)
(EQUAL (RP-EVL TERM1 A) T))
:hints (("Goal" :in-theory (enable is-synp)))))
(local
(defthm evl-of-is-synp-and-is-rp
(IMPLIES (and (or (is-rp term1)
(is-rp-loose term1))
(IS-SYNP (caddr term1)))
(EQUAL (RP-EVL TERM1 A) T))
:hints (("Goal" :in-theory (enable is-synp
is-rp
IS-RP-LOOSE)))))
(local
(defthm extract-from-synp-and-rp-equal-to-evl-1-lemma1
(IMPLIES (AND (or (IS-RP TERM1)
(is-rp-loose TERM1))
(IS-SYNP (CADDR TERM1))
(IS-RP TERM2)
(EQUAL ''T (CADDR TERM2)))
(equal (EQUAL T (RP-EVL TERM2 A))
t))
:hints (("Goal" :in-theory (enable is-rp
is-rp-loose
is-synp)))))
(local
(defthm extract-from-synp-and-rp-equal-to-evl-1
(implies (EQUAL (EX-FROM-SYNP (EX-FROM-RP TERM1))
(EX-FROM-SYNP (EX-FROM-RP TERM2)))
(equal (EQUAL (RP-EVL TERM1 A)
(RP-EVL TERM2 A))
t))
:hints (("Goal"
:cases (;(is-synp (EX-FROM-RP TERM1))
;(is-synp (EX-FROM-RP TERM2))
(is-rp term1)
(is-rp term2)
)
:in-theory (disable is-rp is-synp)))))
(local
(defthm extract-from-synp-equal-to-evl-2
(implies (EQUAL (rp-evl (ex-from-synp TERM1) a)
(rp-evl (ex-from-synp TERM2) a))
(equal (EQUAL (RP-EVL TERM1 A)
(RP-EVL TERM2 A))
t))
:hints (("Goal"
:in-theory (enable extract-from-synp)))))
(defthm ex-from-rp-lemma1
(implies (or (is-rp term)
(is-rp-loose term))
(equal (rp-evl (caddr term) a)
(rp-evl term a)))
:hints (("Goal" :in-theory (enable is-rp
is-rp-loose))))
(defthm evl-of-extract-from-rp-2
(implies (and (or (is-rp term)
(is-rp-loose term))
(rp-evl (caddr term) a))
(rp-evl term a))
:hints (("Goal"
:use (ex-from-rp-lemma1)
:in-theory '())))
(defthm ex-from-synp-lemma1
(implies (is-synp term)
(equal (rp-evl term a)
t))
:hints (("Goal" :in-theory (enable is-synp))))
(defthm is-rp-pseudo-termp
(implies (and (rp-termp term)
(or (is-rp term)
(is-rp-loose term)))
(rp-termp (caddr term)))
:hints (("Goal" :in-theory (enable is-rp
is-rp-loose))))
(defthm rp-termp-should-term-be-in-cons-lhs
(implies (and (should-term-be-in-cons lhs term)
(rp-termp lhs))
(and (rp-termp (cadr lhs))
(rp-termp (car lhs))
(rp-termp (caddr lhs))))
:hints (("Goal" :in-theory (enable should-term-be-in-cons))))
(defthm rp-termp-should-term-be-in-cons-term
(implies (and (rp-termp term))
(and (rp-termp (cadr (put-term-in-cons term)))
(rp-termp (car (put-term-in-cons term)))
(rp-termp (caddr (put-term-in-cons term)))))
:hints (("Goal" :in-theory (enable put-term-in-cons))))
(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) ()))))
(encapsulate
nil
(local
(defthm pseudo-termp-and-rp-evl-list
(implies (and (rp-termp term1)
(rp-termp term2)
(consp term1)
(consp term2)
(not (quotep term1))
(equal (car term1) (car term2)) ;;same function symbols
(equal (rp-evl-lst (cdr term1) a) ;;params evaluate to the same
(rp-evl-lst (cdr term2) a)))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:hints (("Goal" :in-theory (enable rp-evl-of-fncall-args)))))
(local
(defthm lemma1
(implies (and (equal (rp-evl-lst (cdr term1) a)
(rp-evl-lst (cdr term2) a))
(equal (car term1) (car term2))
(consp term1)
(not (equal (car term1) 'quote))
(not (equal (car term2) 'quote))
(syntaxp (lexorder term1 term2))
(consp term2))
(equal (rp-evl term1 a)
(rp-evl term2 a)))
:hints (("goal" :in-theory (enable rp-evl-of-fncall-args)))))
(local
(defthmd lemma2
(implies (quotep term)
(equal (unquote term)
(rp-evl term a)))))
#|(local
(defthm lemma3
(implies (and (not (equal (caddr term2) term2))
(not (is-rp-loose (caddr term2)))
(is-rp-loose term2)
(consp (caddr term2))
(equal (car (caddr term2)) 'quote)
(consp (cdr (caddr term2)))
(not (cddr (caddr term2)))
(rp-termp term2))
(equal (cadr (caddr term2))
(rp-evl term2 a)))
:instructions (:promote (:dive 1)
(:rewrite lemma2)
:top
:bash :s)))||#
(local
(in-theory (disable rp-evl-of-variable)))
(defthm-rp-equal
(defthm rp-evl-of-rp-equal
(implies (and (rp-equal term1 term2))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:flag rp-equal)
(defthm rp-evl-of-rp-equal-subterms
(implies (and (rp-equal-subterms subterm1 subterm2))
(equal (equal (rp-evl-lst subterm1 a)
(rp-evl-lst subterm2 a))
t))
:flag rp-equal-subterms))
(defthm-rp-equal-loose
(defthm rp-evl-of-rp-equal-loose
(implies (and (rp-termp term1)
(rp-termp term2)
(rp-equal-loose term1 term2))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:flag rp-equal-loose)
(defthm rp-evl-of-rp-equal-loosesubterms
(implies (and (rp-equal-loose-subterms subterm1 subterm2)
(rp-term-listp subterm1)
(rp-term-listp subterm2))
(equal (equal (rp-evl-lst subterm1 a)
(rp-evl-lst subterm2 a))
t))
:flag rp-equal-loose-subterms)))
(encapsulate
nil
;; (local
;; (defthm lemma1
;; (IMPLIES (AND (CONSP (EX-FROM-RP TERM1))
;; ;(CONSP (EX-FROM-RP TERM2))
;; )
;; (O< 1
;; (CONS-COUNT TERM1)))
;; :hints (("Goal"
;; :in-theory (e/d (cons-count
;; ex-from-rp) ())))))
;; (local
;; (defthm lemma2
;; (IMPLIES (AND (consp term2)
;; (<= (cons-count term2)
;; (cons-count term1)))
;; (O< (CONS-COUNT (CADDR term2))
;; (CONS-COUNT TERM1)))
;; :hints (("Goal"
;; :in-theory (e/d (cons-count) ())))))
#|(local
(mutual-recursion
;; check if two terms are equivalent by discarding rp terms
(defun rp-equal-induct (term1 term2)
(declare (xargs :measure (+ (cons-count term1)
;(cons-count term2) ;
)
:hints (("Goal"
:in-theory (e/d (measure-lemmas)
((:DEFINITION INCLUDE-FNC)
ex-from-rp
(:LINEAR
ACL2::APPLY$-BADGEP-PROPERTIES . 1)
(:DEFINITION
ACL2::APPLY$-BADGEP)
))))))
"Check syntactic equivalance of two terms by ignoring all the rp terms"
(let* ((term1 (ex-from-rp term1))
(term2 (ex-from-rp term2)))
(cond
((or (atom term1)
(atom term2)
(acl2::fquotep term1)
(acl2::fquotep term2))
(mv (equal term1 term2) term1 term2))
((or (is-falist term1)
(is-falist term2))
(b* (((mv rest-equal t1 t2)
(rp-equal-induct (caddr term1) (caddr term2))))
(mv (and (equal (car term1) (car term2))
(equal (cadr term1) (cadr term2))
rest-equal)
t1 t2)))
((or (and (equal (car term1) 'list)
(consp (cdr term1)))
(and (equal (car term2) 'list)
(consp (cdr term2))))
(b* (((mv rest-equal t1 t2)
(rp-equal-induct-subterms (cdr term1) (cdr term2)))
(t1 (trans-list t1))
(t2 (trans-list t2)))
(mv (and (and (equal (car term1) 'list)
(consp (cdr term1)))
(and (equal (car term2) 'list)
(consp (cdr term2)))
rest-equal)
t1 t2)))
(t (b* (((mv rest-equal t1 t2)
(rp-equal-induct-subterms (cdr term1) (cdr term2))))
(mv (and (equal (car term1) (car term2))
rest-equal)
(cons (car term1) t1)
(cons (car term2) t2)))))))
(defun rp-equal-induct-subterms (subterm1 subterm2)
(declare (xargs :mode :logic
:measure (+ (cons-count subterm1)
;(cons-count subterm2) ;
)))
(if (or (atom subterm1)
(atom subterm2))
(equal subterm1 subterm2)
(and (rp-equal-induct (car subterm1) (car subterm2))
(rp-equal-induct-subterms (cdr subterm1) (cdr subterm2)))))))||#
#|(mutual-recursion
(defun rp-trans-induct (term)
(let* ((term (ex-from-rp term)))
(cond ((atom term) term)
((quotep term) term)
((and (equal (car term) 'list)
(consp (cdr term)))
(trans-list (rp-trans-induct-lst (cdr term))))
((and (is-falist term))
(rp-trans-induct (caddr term)))
(t (cons (car term)
(rp-trans-lst (cdr term)))))))
(defun rp-trans-induct-lst (lst)
(if (atom lst)
lst
(cons (rp-trans-induct (car lst))
(rp-trans-induct-lst (cdr lst))))))||#
#|(make-flag rp-trans-induct :defthm-macro-name defthm-rp-trans-induct )||#
#|(local
(make-flag rp-equal-induct :defthm-macro-name defthm-rp-equal-induct
:hints (("Goal"
:in-theory (e/d (measure-lemmas)
((:definition include-fnc)
ex-from-rp
(:linear acl2::apply$-badgep-properties . 1)
(:definition acl2::apply$-badgep)))))))||#
(mutual-recursion
(defun remove-rp (term)
(let* ((term (ex-from-rp term)))
(cond ((or (atom term)
(acl2::fquotep term))
term)
(t (cons (car term)
(remove-rp-lst (cdr term)))))))
(defun remove-rp-lst (lst)
(if (atom lst)
lst
(cons (remove-rp (car lst))
(remove-rp-lst (cdr lst))))))
(defthm-rp-equal
(defthmd rp-equal-of-remove-rp
(implies (and (rp-equal term1 term2))
(equal (remove-rp term1)
(remove-rp term2)))
:flag rp-equal)
(defthmd rp-equal-subterms-of-remove-rp-lst
(implies (and (rp-equal-subterms subterm1 subterm2))
(equal (remove-rp-lst subterm1)
(remove-rp-lst subterm2)))
:flag rp-equal-subterms))
(local
(mutual-recursion
(defun rp-trans-induct (term)
(let* ((term (ex-from-rp term)))
(cond ((atom term) term)
((quotep term) term)
((and (equal (car term) 'list)
(consp (cdr term)))
(trans-list (rp-trans-induct-lst (cdr term))))
((and (is-falist term))
(rp-trans-induct (caddr term)))
(t (cons (car term)
(rp-trans-induct-lst (cdr term)))))))
(defun rp-trans-induct-lst (lst)
(if (atom lst)
lst
(cons (rp-trans-induct (car lst))
(rp-trans-induct-lst (cdr lst)))))))
(local
(make-flag rp-trans-induct
:defthm-macro-name defthm-rp-trans-induct))
(local
(defthm lemma10
(equal (ex-from-rp (cons 'falist x))
(cons 'falist x))
:hints (("Goal"
:in-theory (e/d (ex-from-rp
is-rp) ())))))
(Local
(defthmd insert-ex-from-rp-rp-trans
(implies (syntaxp (or (atom term)))
(equal (rp-evlt term a)
(rp-evlt (ex-from-rp term) a)))))
(local
(defthm-rp-trans-induct
(defthmd rp-evlt-of-remove-rp
(implies (syntaxp (or (atom term)
(not (equal (car term) 'remove-rp))))
(equal (rp-evlt term a)
(rp-evlt (remove-rp term) a)))
:flag rp-trans-induct)
(defthmd rp-evlt-lst-of-remove-rp-lst
(implies (syntaxp (or (atom lst)
(not (equal (car lst) 'remove-rp-lst))))
(equal (rp-evlt-lst lst a)
(rp-evlt-lst (remove-rp-lst lst) a)))
:flag rp-trans-induct-lst)
:hints (("Goal"
:do-not-induct t
:in-theory (e/d (rp-evl-of-fncall-args
insert-ex-from-rp-rp-trans)
(ex-from-rp
trans-list
RP-EVLT-OF-EX-FROM-RP))))))
(defthm rp-evlt-of-rp-equal
(implies (and (rp-equal term1 term2))
(equal (equal (rp-evlt term1 a)
(rp-evlt term2 a))
t))
:hints (("Goal"
:in-theory (e/d (rp-evlt-of-remove-rp
rp-equal-of-remove-rp)
(rp-trans
rp-equal)))))
(defthm rp-evlt-lst-of-rp-equal-lst
(implies (and (rp-equal-subterms subterm1 subterm2))
(equal (equal (rp-evlt-lst subterm1 a)
(rp-evlt-lst subterm2 a))
t))
:hints (("Goal"
:in-theory (e/d (rp-evlt-lst-of-remove-rp-lst
rp-equal-subterms-of-remove-rp-lst)
(rp-trans-lst
rp-equal-subterms)))))
#|(defthm-rp-trans-induct
(defthm rp-evlt-of-rp-equal
(implies (and (rp-equal term term2))
(equal (equal (rp-evlt term a)
(rp-evlt term2 a))
t))
:flag rp-trans-induct)
(defthm rp-evlt-of-rp-equal-subterms
(implies (and (rp-equal-subterms lst subterm2))
(equal (equal (rp-evlt-lst lst a)
(rp-evlt-lst subterm2 a))
t))
:flag rp-trans-induct-lst)
:hints (("Goal"
:do-not-induct t
:in-theory (e/d (;;ex-from-rp
is-rp
is-falist
rp-equal-subterms
rp-equal)
(cons-equal)))))||#)
(defthm-rp-equal
(defthm rp-equal-is-symmetric
(equal (rp-equal term2 term1)
(rp-equal term1 term2))
:flag rp-equal)
(defthm rp-equal-subterms-is-symmetric
(equal (rp-equal-subterms subterm2 subterm1)
(rp-equal-subterms subterm1 subterm2))
:flag rp-equal-subterms))
(encapsulate
nil
(local
(in-theory (disable ex-from-rp ex-from-synp )))
(local
(defthm lemma1
(implies (rp-equal2 term term2)
(iff (consp (ex-from-synp (ex-from-rp term)))
(consp (ex-from-synp (ex-from-rp term2)))))
:hints (("goal"
:in-theory (enable ex-from-rp ex-from-synp)))))
(local
(defthm lemma1-2
(implies (rp-equal term1 term2)
(and #|(iff (consp (ex-from-rp-loose term1))
(consp (ex-from-rp-loose term2)))||#
(iff (consp (ex-from-rp term1))
(consp (ex-from-rp term2)))
(iff (consp (ex-from-synp (ex-from-rp term1)))
(consp (ex-from-synp (ex-from-rp term2))))))
:rule-classes :forward-chaining
:hints (("goal" :in-theory (enable ex-from-rp
ex-from-rp-loose
is-rp
is-rp-loose
ex-from-synp)))))
(local
(defthm lemma3 (implies (and (acl2::flag-is 'rp-equal2)
(not (consp (ex-from-synp (ex-from-rp term2))))
(rp-equal term1 term2))
(equal (equal (ex-from-synp (ex-from-rp term1))
(ex-from-synp (ex-from-rp term2)))
t))
:hints (("goal" :expand (rp-equal term1 term2)))))
(local
(defthm lemma4
(implies (and (not (consp (ex-from-synp (ex-from-rp term1))))
(rp-equal term1 term2))
(equal (ex-from-synp (ex-from-rp term1))
(ex-from-synp (ex-from-rp term2))))
:hints (("goal"
:use (:instance lemma1-2)
:expand (rp-equal term1 term2)
:in-theory (disable lemma1-2)))))
(local
(defthm lemma5
(implies
(and (consp (ex-from-synp (ex-from-rp term1)))
(not (should-term-be-in-cons (ex-from-synp (ex-from-rp term2))
(ex-from-synp (ex-from-rp term1))))
(not (equal (car (ex-from-synp (ex-from-rp term1)))
'quote))
(not (equal (car (ex-from-synp (ex-from-rp term2)))
'quote))
(not (equal (car (ex-from-synp (ex-from-rp term1)))
(car (ex-from-synp (ex-from-rp term2))))))
(not (rp-equal term1 term2)))
:hints (("goal" :expand (rp-equal term1 term2)
:in-theory (enable ex-from-synp)))))
(local
(defthm lemma6
(implies (not (iff (is-synp (ex-from-rp term1))
(is-synp (ex-from-rp term2))))
(not (rp-equal term1 term2)))
:hints (("goal" :in-theory (enable is-synp)
:expand ((rp-equal term1 term2)
(rp-equal-subterms (cdr (ex-from-rp term1))
(cdr (ex-from-rp term2)))
(rp-equal-subterms (cddr (ex-from-rp term1))
(cddr (ex-from-rp term2)))
(rp-equal-subterms (cdddr (ex-from-rp term1))
(cdddr (ex-from-rp term2))))))))
(local
(defthm lemma7
(implies (rp-equal term1 term2)
(rp-equal-subterms (cdr (ex-from-synp (ex-from-rp term1)))
(cdr (ex-from-synp (ex-from-rp term2)))))
:hints (("goal" :in-theory (enable ex-from-synp)))))
(local
(defthm lemma8
(implies (not (equal (car (ex-from-synp (ex-from-rp term1)))
(car (ex-from-synp (ex-from-rp term2)))))
(not (rp-equal term1 term2)))
:hints (("goal" :in-theory (enable ex-from-synp)
:expand ((rp-equal term1 term2)
(rp-equal-subterms (cdr (ex-from-rp term1))
(cdr (ex-from-rp term2))))))))
(local
(defthm lemma9-lemma1
(implies (and (equal (car a) (car b))
(consp b)
(equal (cdr a) (cdr b))
(consp a))
(equal a b))
:rule-classes :forward-chaining))
(local
(defthm lemma9-lemma2
(implies (and (equal a b)
(is-synp a))
(is-synp b))))
(local
(defthm lemma9-lemma
(implies (and (consp b)
(equal (car a) (car b))
(equal (cdr a) (cdr b))
(is-synp a))
(is-synp b))
; Removed by Matt K. 7/2021 (is-synp-implies removed in aux-function-lemmas.lisp)
#||
:hints (("goal" :in-theory (disable is-synp-implies)
:use ((:instance is-synp-implies (term a)))))
||#
))
(local
(defthm lemma9-lemma3
(implies (and (consp (ex-from-rp term2))
(not (equal (car (ex-from-rp term1)) 'quote))
(equal (car (ex-from-rp term1))
(car (ex-from-rp term2)))
(consp (cdr (ex-from-rp term1)))
(consp (cdr (ex-from-rp term2)))
(rp-equal (cadr (ex-from-rp term1))
(cadr (ex-from-rp term2)))
(rp-equal-subterms (cddr (ex-from-rp term1))
(cddr (ex-from-rp term2)))
(is-synp (ex-from-rp term1)))
(is-synp (ex-from-rp term2)))
:hints (("goal" :in-theory (enable is-synp)
:expand
((rp-equal-subterms (cddr (ex-from-rp term1))
(cddr (ex-from-rp term2)))
(rp-equal-subterms (cdddr (ex-from-rp term1))
(cdddr (ex-from-rp term2))))))))
(local
(defthm lemma9
(implies (and (rp-equal term1 term2)
(consp (ex-from-synp (ex-from-rp term1)))
(equal (car (ex-from-synp (ex-from-rp term1)))
'quote))
(equal (equal (ex-from-synp (ex-from-rp term1))
(ex-from-synp (ex-from-rp term2)))
t))
:hints (("goal"
:in-theory (enable ex-from-synp)
:expand ((rp-equal term1 term2)
(rp-equal-subterms (cdr (ex-from-rp term1))
(cdr (ex-from-rp term2))))))))
(local
(defthm lemma10
(implies (should-term-be-in-cons (ex-from-synp (ex-from-rp term2))
(ex-from-synp (ex-from-rp term1)))
(not (rp-equal term1 term2)))
:hints (("goal" :in-theory (enable should-term-be-in-cons
ex-from-synp)))))
(local
(defthm lemma11
(implies (should-term-be-in-cons (ex-from-synp (ex-from-rp term1))
(ex-from-synp (ex-from-rp term2)))
(not (rp-equal term1 term2)))
:hints
(("goal" :in-theory (enable is-synp should-term-be-in-cons)
:expand (;(ex-from-synp (ex-from-rp term1))
(rp-equal term1 term2))))))
#|(defthm lemma4
(implies (or (and (not (is-synp (ex-from-rp term1)))
(is-synp (ex-from-rp term2)))
(and (is-synp (ex-from-rp term1))
(not (is-synp (ex-from-rp term2)))))
(not (rp-equal term1 term2)))
:hints (("goal" :in-theory (enable )
:expand (rp-equal term1 term2))))||#
(defthm-rp-equal2
(defthm rp-equal-implies-rp-equal2
(implies (rp-equal term1 term2)
(rp-equal2 term1 term2))
:flag rp-equal2)
(defthm rp-equal-subterms-implies-rp-equal2-subterms
(implies (rp-equal-subterms subterm1 subterm2)
(rp-equal2-subterms subterm1 subterm2))
:flag rp-equal2-subterms)))
(encapsulate
nil
(local
(in-theory (disable ex-from-synp ex-from-rp)))
(local
(in-theory (disable should-term-be-in-cons-lemma4
should-term-be-in-cons-lemma2)))
(local
(defthm lemma1
(implies (rp-equal2 term1 term2)
(iff (consp (ex-from-synp (ex-from-rp term1)))
(consp (ex-from-synp (ex-from-rp term2)))))
:hints (("Goal" :in-theory (enable ex-from-rp ex-from-synp)))))
(local
(defthm lemma2
(implies (and (EQUAL (RP-EVL-LST (CDR (EX-FROM-SYNP (EX-FROM-RP TERM1)))
A)
(RP-EVL-LST (CDR (EX-FROM-SYNP (EX-FROM-RP TERM2)))
A))
(CONSP (EX-FROM-SYNP (EX-FROM-RP TERM1)))
(CONSP (EX-FROM-SYNP (EX-FROM-RP TERM2)))
(NOT (EQUAL (CAR (EX-FROM-SYNP (EX-FROM-RP TERM2)))
'QUOTE))
(NOT (EQUAL (CAR (EX-FROM-SYNP (EX-FROM-RP TERM1)))
'QUOTE))
(syntaxp (and (equal term1 'term1)
(equal term2 'term2)))
(EQUAL (CAR (EX-FROM-SYNP (EX-FROM-RP TERM1)))
(CAR (EX-FROM-SYNP (EX-FROM-RP TERM2)))))
(equal (rp-evl (EX-FROM-SYNP (EX-FROM-RP TERM1)) a)
(rp-evl (EX-FROM-SYNP (EX-FROM-RP TERM2)) a)))
:rule-classes :rewrite
:hints (("Goal" :in-theory (e/d (rp-evl-of-fncall-args)
(EVL-OF-EXTRACT-FROM-RP
EVL-OF-EXTRACT-FROM-SYNP))))))
; Matt K. mod 7/2021: The following lemma is no longer accepted due to a
; strengthening of remove-guard-holders.
#||
(local
(defthm lemma4
(implies (SHOULD-TERM-BE-IN-CONS rule-lhs term)
(AND (QUOTEP TERM)
(CONSP (UNQUOTE TERM))
(CASE-MATCH RULE-LHS (('CONS & &) T)
(& NIL))
(equal (car (put-term-in-cons term))
(car rule-lhs))))
:hints (("Goal" :in-theory (enable put-term-in-cons should-term-be-in-cons)))))
||#
(local
(defthm lemma5
(implies (and (rp-termp term1)
(syntaxp (and (equal term1 'term1)
(equal term2 'term2)))
(rp-termp term2))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
(equal (rp-evl (EX-FROM-SYNP (EX-FROM-RP TERM1)) a)
(rp-evl (EX-FROM-SYNP (EX-FROM-RP TERM2)) a))))))
(local
(defthm lemma6
(implies (and (quotep term)
(consp (unquote term)))
(and (equal (rp-evl (put-term-in-cons term) a)
(rp-evl term a))))
:hints (("Goal" :in-theory (enable put-term-in-cons)))))
(local
(defthm lemma7
(implies (and (rp-termp term)
(quotep term)
(consp (unquote term)))
(rp-term-listp (cdr (put-term-in-cons term))))
:hints (("Goal" :in-theory (enable put-term-in-cons)))))
(local
(in-theory (disable EVL-OF-EXTRACT-FROM-RP
EVL-OF-EXTRACT-FROM-SYNP)))
(local
(defthm lemma8-lemma0
(equal (equal (list a b)
(list c d))
(and (equal a c)
(equal b d)))))
(local
(defthm lemma8-lemma1
(equal (equal (list a b)
(list c d))
(equal (cons a b)
(cons c d)))))
(local
(defthm lemma8
(implies (and (should-term-be-in-cons lhs term)
(equal (rp-evl-lst (cdr (put-term-in-cons term)) a)
(rp-evl-lst (cdr lhs) a))
(syntaxp (or
(and (equal term '(EX-FROM-SYNP (EX-FROM-RP TERM1)))
(equal lhs '(EX-FROM-SYNP (EX-FROM-RP
TERM2))))
(and (equal term '(EX-FROM-SYNP (EX-FROM-RP TERM2)))
(equal lhs '(EX-FROM-SYNP (EX-FROM-RP TERM1)))))))
(and (equal (car (put-term-in-cons term))
(car lhs))
(equal (rp-evl term a)
(rp-evl lhs a))))
:hints (("Goal" :in-theory (enable
rp-evl-of-fncall-args
should-term-be-in-cons
put-term-in-cons)))))
(local
(defthm lemma9
(implies (and (should-term-be-in-cons lhs term)
(rp-termp lhs))
(rp-term-listp (cdr lhs)))
:hints (("Goal" :in-theory (enable should-term-be-in-cons)))))
(local
(defthm lemma10
(implies (and (consp term)
(not (EQUAL (CAR TERM) 'QUOTE))
(rp-termp term))
(rp-term-listp (cdr term)))))
(local
(defthm lemma11
(implies (and (should-term-be-in-cons term1 term2)
(equal (rp-evl (cadr term1) a)
(rp-evl (cadr (put-term-in-cons term2)) a))
(equal (rp-evl (caddr term1) a)
(rp-evl (caddr (put-term-in-cons term2)) a)))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:hints (("Goal" :in-theory (enable put-term-in-cons
should-term-be-in-cons)))))
(local
(defthm lemma11-2
(implies (and (should-term-be-in-cons term1 term2)
(equal (rp-evl (cadr term1) a)
(rp-evl (cadr (put-term-in-cons term2)) a))
(equal (rp-evl (caddr term1) a)
(rp-evl (caddr (put-term-in-cons term2)) a)))
(equal (equal (rp-evl term2 a)
(rp-evl term1 a))
t))
:hints (("Goal" :in-theory (enable put-term-in-cons
should-term-be-in-cons)))))
(local
(in-theory (disable is-cons)))
(local
(defthm lemma12-1
(implies (and
(RP-TERMP term1)
(is-cons term1))
(RP-TERMP (CADDR term1)))
:hints (("Goal" :in-theory (enable is-cons )))))
(local
(defthm lemma12-2
(implies (and
(RP-TERMP term)
(QUOTEP TERM)
(CONSP (UNQUOTE TERM)))
(RP-TERMP (CADDR (PUT-TERM-IN-CONS term))))
:hints (("Goal" :in-theory (enable PUT-TERM-IN-CONS )))))
(local
(defthm lemma13
(implies (and (SHOULD-TERM-BE-IN-CONS rule-lhs term)
t)
(AND (QUOTEP TERM)
(CONSP (UNQUOTE TERM))
(is-cons rule-lhs)))
:hints (("Goal" :in-theory (enable is-cons should-term-be-in-cons)))))
(defthm-rp-equal2
(defthm rp-evl-of-rp-equal2
(implies (and (rp-termp term1)
(rp-termp term2)
(rp-equal2 term1 term2))
(equal (equal (rp-evl term1 a)
(rp-evl term2 a))
t))
:flag rp-equal2)
(defthm rp-evl-of-rp-equal2-subterms
(implies (and (rp-equal2-subterms subterm1 subterm2)
(rp-term-listp subterm1)
(rp-term-listp subterm2))
(equal (equal (rp-evl-lst subterm1 a)
(rp-evl-lst subterm2 a))
t))
:flag rp-equal2-subterms)))
(defthm rp-equal2-of-ex-from-rp
(implies (rp-termp term)
(equal (rp-equal2 term1 (ex-from-rp term2))
(rp-equal2 term1 term2)))
:hints (("Goal" :in-theory (disable ex-from-synp)
:do-not-induct t
:expand ((rp-equal2 term1 (ex-from-rp term2))
(rp-equal2 term1 term2)))))
(defthm-rp-equal2
(defthm rp-equal2-reflexive
(implies (equal term1 term2)
(rp-equal2 term1 term2))
:flag rp-equal2)
(defthm rp-equal2-subterms-reflexive
(implies (equal subterm1 subterm2)
(rp-equal2-subterms subterm1 subterm2))
:flag rp-equal2-subterms))
(defthm-rp-equal2
(defthm rp-equal2-booleanp
(booleanp (rp-equal2 term1 term2))
:flag rp-equal2)
(defthm rp-equal2-subterms-booleanp
(booleanp (rp-equal2-subterms subterm1 subterm2))
:flag rp-equal2-subterms))
#|(encapsulate
nil
(local
(include-book "measure-lemmas"))
(defun
flag2-rp-equal2
(flag term1 term2 subterm1 subterm2)
(declare (xargs :non-executable t :mode :logic))
(declare
(xargs :verify-guards nil
:normalize nil
:measure (case flag (rp-equal2 (cons-count term2))
(otherwise (cons-count subterm2)))
:hints nil
:well-founded-relation o<
:mode :logic)
(ignorable term1 term2 subterm1 subterm2))
(prog2$
(acl2::throw-nonexec-error
'flag2-rp-equal2
(list flag term1 term2 subterm1 subterm2))
(cond
((equal flag 'rp-equal2)
((lambda
(term1 term2)
((lambda
(term1 term2)
((lambda
(term2 term1)
((lambda
(term2 term1)
(if
(consp term1)
(if
(consp term2)
(if
(should-term-be-in-cons term2 term1)
((lambda
(nterm term2)
(if (flag2-rp-equal2 'rp-equal2
(car (cdr nterm))
(car (cdr term2))
nil nil)
(flag2-rp-equal2 'rp-equal2
(car (cdr (cdr nterm)))
(car (cdr (cdr term2)))
nil nil)
'nil))
(put-term-in-cons term1)
term2)
(if
(should-term-be-in-cons term1 term2)
((lambda
(nterm term1)
(if (flag2-rp-equal2 'rp-equal2
(car (cdr term1))
(car (cdr nterm))
nil nil)
(flag2-rp-equal2 'rp-equal2
(car (cdr (cdr term1)))
(car (cdr (cdr nterm)))
nil nil)
'nil))
(put-term-in-cons term2)
term1)
(if
(quotep term1)
(equal term1 term2)
(if (quotep term2)
(equal term1 term2)
(if (equal (car term1) (car term2))
(flag2-rp-equal2 'rp-equal2-subterms
nil nil (cdr term1)
(cdr term2))
'nil)))))
'nil)
(equal term1 term2)))
(extract-from-synp term2)
term1))
(ex-from-rp term2)
term1))
(extract-from-synp term1)
term2))
(ex-from-rp term1)
term2))
(t (if (consp subterm1)
(if (consp subterm2)
(if (flag2-rp-equal2 'rp-equal2
(car subterm1)
(car subterm2)
nil nil)
(flag2-rp-equal2 'rp-equal2-subterms
nil nil (cdr subterm1)
(cdr subterm2))
'nil)
'nil)
(equal subterm1 subterm2)))))))||#
(encapsulate
nil
(local
(in-theory (disable ex-from-synp)))
(local
(defthm rp-equal2-lemma1
(implies (should-term-be-in-cons term1 term2)
(not (should-term-be-in-cons term2 term1)))
:hints (("Goal" :in-theory (enable should-term-be-in-cons)))))
(defthm-rp-equal2
(defthm rp-equal2-is-symmetric
(equal (rp-equal2 term2 term1)
(rp-equal2 term1 term2))
:flag rp-equal2)
(defthm rp-equal2-subterms-is-symmetric
(equal (rp-equal2-subterms subterm2 subterm1)
(rp-equal2-subterms subterm1 subterm2))
:flag rp-equal2-subterms)
:hints (("Goal" :expand ((rp-equal2 term2 term1)
(rp-equal2-subterms subterm2 subterm1)))))
#|(skip-proofs
;; necessary for def-equiv
(defthm-rp-equal2
(defthm rp-equal2-transitive
(implies (and (rp-equal2 term0 term1)
(rp-equal2 term1 term2))
(rp-equal2 term0 term2))
:flag rp-equal2)
(defthm rp-equal2-subterms2-transitive
(implies (and (rp-equal2-subterms subterm0 subterm1)
(rp-equal2-subterms subterm1 subterm2))
(rp-equal2-subterms subterm0 subterm2))
:flag rp-equal2-subterms)
;:hints (("Goal" :induct (flag2-rp-equal2 flag term0 term1 term2 subterm0 ; ; ; ; ; ; ; ; ; ; ; ; ; ;
; subterm1 subterm2))) ; ; ; ; ; ; ; ; ; ; ; ; ; ;
))||#
)
#|(local
(defequiv rp-equal2))||#
#|(local
(defequiv rp-equal2-subterms))||#
(defthm-rp-equal-cnt
(defthm rp-equal-cnt-is-rp-equal
(equal (rp-equal-cnt term1 term2 cnt)
(rp-equal term1 term2 ))
:flag rp-equal-cnt)
(defthm rp-equal-cnt-subterms-is-rp-equal-subterms
(equal (rp-equal-cnt-subterms subterm1 subterm2 cnt)
(rp-equal-subterms subterm1 subterm2 ))
:flag rp-equal-cnt-subterms))
(defthm-rp-equal
(defthmd rp-equal-alt-def
(equal (rp-equal term1 term2)
(equal (ex-from-rp-all term1)
(ex-from-rp-all term2)))
:flag rp-equal)
(defthmd rp-equal-subterms-alt-def
(equal (rp-equal-subterms subterm1 subterm2)
(equal (ex-from-rp-all-lst subterm1)
(ex-from-rp-all-lst subterm2)))
:flag rp-equal-subterms)
:hints (("Goal"
:expand ((EX-FROM-RP-ALL TERM1)
(EX-FROM-RP-ALL-LST SUBTERM1)
(EX-FROM-RP-ALL-LST SUBTERM2)
(EX-FROM-RP-ALL TERM2))
:in-theory (e/d (;is-rp
ex-from-rp-all
)
(ex-from-rp)))))
(defequiv rp-equal
:hints (("Goal"
:in-theory (e/d (rp-equal-alt-def) ()))))
(defequiv rp-equal-subterms
:hints (("Goal"
:in-theory (e/d (rp-equal-subterms-alt-def) ()))))
(defcong rp-equal equal (rp-evlt term a) 1)
(defcong rp-equal equal (rp-evl term a) 1)
(defcong rp-equal-subterms equal (rp-evlt-lst lst a) 1)
(defthm rp-equal-of-rp
(implies (is-rp (cons 'rp x))
(and (equal (rp-equal y (cons 'rp x))
(rp-equal y (cadr x)))
(equal (rp-equal (cons 'rp x) y)
(rp-equal (cadr x) y))))
:hints (("Goal"
:Expand ((EX-FROM-RP-ALL (CONS 'RP X))
(EX-FROM-RP (CONS 'RP X)))
:in-theory (e/d (rp-equal-alt-def
ex-from-rp-all)
()))))
|
