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; Copyright (C) 2008 Centaur Technology
;
; Contact:
; Centaur Technology Formal Verification Group
; 7600-C N. Capital of Texas Highway, Suite 300, Austin, TX 78731, USA.
; http://www.centtech.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: Sol Swords <sswords@centtech.com>
;; join-thms.lisp
;; by Sol Swords
;; Provides a macro which, when invoked, proves several useful theorems about
;; an evaluator, involving that evaluator's actions on conjoin, disjoin, etc.
;; The evaluator should recognize IF for this to work.
;; Example (from null-fail-hints.lisp:)
;; (defevaluator null-fail-hint-ev null-fail-hint-evl ((if a b c)))
;; (def-join-thms null-fail-hint-ev)
(in-package "ACL2")
(include-book "ev-find-rules")
(defthm conjoin-clauses-of-one
(equal (conjoin-clauses (list x))
(disjoin x)))
(in-theory (disable conjoin-clauses conjoin disjoin))
(defthm pseudo-termp-disjoin
(implies (pseudo-term-listp x)
(pseudo-termp (disjoin x)))
:hints(("Goal" :in-theory (enable pseudo-termp pseudo-term-listp disjoin)
:induct (disjoin x))))
(defthm pseudo-termp-conjoin
(implies (pseudo-term-listp x)
(pseudo-termp (conjoin x)))
:hints(("Goal" :in-theory (enable conjoin pseudo-termp pseudo-term-listp))))
(defthm pseudo-term-listp-disjoin-lst
(implies (pseudo-term-list-listp x)
(pseudo-term-listp (disjoin-lst x))))
(defthm pseudo-termp-conjoin-clauses
(implies (pseudo-term-list-listp clauses)
(pseudo-termp (conjoin-clauses clauses)))
:hints(("Goal" :in-theory (e/d (conjoin-clauses) (disjoin-lst)))))
(defconst *def-join-thms-body*
'(encapsulate
nil
(local (in-theory nil))
(local (in-theory (e/d (append
conjoin disjoin car-cons cdr-cons
disjoin2 conjoin2 iff if-rule quote-rule
endp atom car-cdr-elim)
(default-car default-cdr))))
(defthm disjoin-cons
(iff (ev (disjoin (cons x y)) a)
(or (ev x a)
(ev (disjoin y) a))))
(defthmd disjoin-when-consp
(implies (consp x)
(iff (ev (disjoin x) a)
(or (ev (car x) a)
(ev (disjoin (cdr x)) a)))))
(defthm disjoin-atom
(implies (not (consp x))
(equal (ev (disjoin x) a)
nil))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm disjoin-append
(iff (ev (disjoin (append x y)) a)
(or (ev (disjoin x) a)
(ev (disjoin y) a)))
:hints (("goal" :induct (append x y)
:in-theory (e/d (disjoin-when-consp)
(disjoin)))))
(defthm conjoin-cons
(iff (ev (conjoin (cons x y)) a)
(and (ev x a)
(ev (conjoin y) a))))
(defthmd conjoin-when-consp
(implies (consp x)
(iff (ev (conjoin x) a)
(and (ev (car x) a)
(ev (conjoin (cdr x)) a)))))
(defthm conjoin-atom
(implies (not (consp x))
(equal (ev (conjoin x) a)
t))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm conjoin-append
(iff (ev (conjoin (append x y)) a)
(and (ev (conjoin x) a)
(ev (conjoin y) a)))
:hints (("goal" :induct (append x y)
:in-theory (e/d (conjoin-when-consp)
(conjoin)))))
(defthm conjoin-clauses-cons
(iff (ev (conjoin-clauses (cons x y)) a)
(and (ev (disjoin x) a)
(ev (conjoin-clauses y) a)))
:hints(("Goal" :in-theory (enable conjoin-clauses disjoin-lst))))
(defthmd conjoin-clauses-when-consp
(implies (consp x)
(iff (ev (conjoin-clauses x) a)
(and (ev (disjoin (car x)) a)
(ev (conjoin-clauses (cdr x)) a)))))
(defthm conjoin-clauses-atom
(implies (not (consp x))
(equal (ev (conjoin-clauses x) a)
t))
:hints(("Goal" :in-theory (enable conjoin-clauses disjoin-lst)))
:rule-classes ((:rewrite :backchain-limit-lst 0)))
(defthm conjoin-clauses-append
(iff (ev (conjoin-clauses (append x y)) a)
(and (ev (conjoin-clauses x) a)
(ev (conjoin-clauses y) a)))
:hints (("goal" :induct (append x y))))))
(defun ev-mk-rulename (ev name)
(intern-in-package-of-symbol
(concatenate 'string (symbol-name ev) "-"
(symbol-name name))
ev))
(defun ev-pair-rulenames (ev names)
(if (atom names)
nil
(cons (cons (car names) (ev-mk-rulename ev (car names)))
(ev-pair-rulenames ev (cdr names)))))
(defmacro def-join-thms (ev)
(let ((alist `((ev . ,ev)
. ,(ev-pair-rulenames ev '(disjoin-cons
disjoin-when-consp
disjoin-atom
disjoin-append
conjoin-cons
conjoin-when-consp
conjoin-atom
conjoin-append
conjoin-clauses-cons
conjoin-clauses-when-consp
conjoin-clauses-atom
conjoin-clauses-append)))))
`(make-event
(let* ((if-rule (ev-find-fncall-rule ',ev 'if (w state)))
(quote-rule (ev-find-quote-rule ',ev (w state)))
(alist (list* (cons 'if-rule if-rule)
(cons 'quote-rule quote-rule)
',alist)))
(cond ((not if-rule)
(er soft 'def-join-thms
"Unable to find a rewrite rule for (~x0 X A) when ~
(CAR X) is IF~%" ',ev))
((not quote-rule)
(er soft 'def-join-thms
"Unable to find a rewrite rule for (~x0 X A) when ~
(CAR X) is QUOTE~%" ',ev))
(t (value (sublis alist *def-join-thms-body*))))))))
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