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|
; Centaur Meta-reasoning Library
; Copyright (C) 2019 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>
(in-package "CMR")
(include-book "reconstruct")
(local (include-book "clause-processors/join-thms" :dir :system))
(defxdoc resolve-flag-cp
:parents (mutual-recursion make-flag)
:short "Clause processor to quickly remove flag junk from the clauses generated after a flag-function induction.")
(local (xdoc::set-default-parents resolve-flag-cp))
(defevaluator flag-ev flag-ev-list
((if a b c)
(not a)
(equal a b)
(eql a b)
(eq a b)
(acl2::flag-is x))
:namedp t)
(acl2::def-ev-pseudo-term-fty-support flag-ev flag-ev-list)
(local (acl2::def-join-thms flag-ev))
(local (defthm assoc-of-nonnil
(implies v
(equal (assoc v x)
(hons-assoc-equal v x)))))
(define match-flag-equal ((x pseudo-termp)
(flag-var pseudo-var-p))
:returns (mv matchedp obj)
(pseudo-term-case x
:fncall (if (member-eq x.fn '(equal eql eq))
(b* (((list arg1 arg2) x.args))
(pseudo-term-case arg1
:var (if (eq arg1.name (pseudo-var-fix flag-var))
(pseudo-term-case arg2
:quote (mv t arg2.val)
:otherwise (mv nil nil))
(mv nil nil))
:quote (pseudo-term-case arg2
:var (if (eq arg2.name (pseudo-var-fix flag-var))
(mv t arg1.val)
(mv nil nil))
:otherwise (mv nil nil))
:otherwise (mv nil nil)))
(mv nil nil))
:otherwise (mv nil nil))
///
(defret match-flag-equal-implies-eval
(implies matchedp
(equal (flag-ev x a)
(equal (cdr (hons-assoc-equal (pseudo-var-fix flag-var) a)) obj)))))
(define match-flag-not-equal ((x pseudo-termp)
(flag-var pseudo-var-p))
:returns (mv matchedp obj)
(pseudo-term-case x
:fncall (if (eq x.fn 'not)
(match-flag-equal (car x.args) flag-var)
(mv nil nil))
:otherwise (mv nil nil))
///
(defret match-flag-not-equal-implies-eval
(implies matchedp
(equal (flag-ev x a)
(not (equal (cdr (hons-assoc-equal (pseudo-var-fix flag-var) a)) obj))))))
(local (Defthm not-member-of-remove
(not (member a (remove a x)))))
(local (defthm member-of-remove-split
(iff (member a (remove b x))
(and (not (equal a b))
(member a x)))))
(local (defthm flag-ev-of-disjoin-pseudo-term-list-fix
(iff (flag-ev (disjoin (pseudo-term-list-fix x)) a)
(flag-ev (disjoin x) a))
:hints(("Goal"
:induct (len x)
:expand ((pseudo-term-list-fix x))))))
(define scan-clause-for-flag-facts ((x pseudo-term-listp)
(flag-var pseudo-var-p))
:returns (mv (new-clause pseudo-term-listp)
(known-value-p booleanp)
(known-value)
(eliminated-values true-listp :rule-classes :type-prescription))
(b* (((when (atom x))
(mv nil nil nil nil))
((mv matched val) (match-flag-not-equal (car x) flag-var))
((when matched)
(mv (cdr (pseudo-term-list-fix x))
t
val
nil))
((mv matched val) (match-flag-equal (car x) flag-var))
((mv rest known-value-p known-value eliminated-values)
(scan-clause-for-flag-facts (cdr x) flag-var))
((unless matched)
(mv (cons-with-hint (pseudo-term-fix (car x)) rest x)
known-value-p known-value eliminated-values))
((when known-value-p)
(mv rest known-value-p known-value nil)))
(mv rest nil nil (cons val eliminated-values)))
///
(defret scan-clause-for-flag-facts-known-value-correct
(implies (and known-value-p
(not (flag-ev (disjoin x) a)))
(equal known-value
(cdr (hons-assoc-equal (pseudo-var-fix flag-var) a)))))
(defret scan-clause-for-flag-facts-eliminated-values-correct
(implies (not (flag-ev (disjoin x) a))
(not (member-equal (cdr (hons-assoc-equal (pseudo-var-fix flag-var) a))
eliminated-values))))
(defret scan-clause-for-flag-facts-new-clause-correct
(implies (not (flag-ev (disjoin x) a))
(not (flag-ev (disjoin new-clause) a)))))
(local (defthm true-list-fix-when-true-listp
(implies (true-listp x)
(equal (true-list-fix x) x))))
(local (defthm member-of-true-list-fix
(iff (member x (true-list-fix y))
(member x y))))
(define flag-facts-p (x)
(and (consp x)
(booleanp (car x))
(or (car x) (true-listp (cdr x))))
///
(define flag-facts-fix ((x flag-facts-p))
:returns (new-x flag-facts-p)
(mbe :logic (if (car x)
(cons t (cdr x))
(cons (car x) (true-list-fix (cdr x))))
:exec x)
///
(defthm flag-facts-fix-when-flag-facts-p
(implies (flag-facts-p x)
(equal (flag-facts-fix x) x)))
(fty::deffixtype flag-facts :pred flag-facts-p :fix flag-facts-fix :equiv flag-facts-equiv
:define t)
(defthm consp-of-flag-facts-fix
(consp (flag-facts-fix x))
:rule-classes :type-prescription)))
(define make-flag-facts (known-value-p
known-val
(eliminated-vals true-listp))
:returns (facts flag-facts-p
:hints(("Goal" :in-theory (enable flag-facts-p))))
(if known-value-p
(cons t known-val)
(cons nil (mbe :logic (true-list-fix eliminated-vals) :exec eliminated-vals)))
///
(defcong iff equal (make-flag-facts known-value-p known-val eliminated-vals) 1))
(define flag-possible-value-p ((x flag-facts-p)
(val))
:guard-hints (("goal" :in-theory (enable flag-facts-p)))
(b* ((x (flag-facts-fix x)))
(if (car x)
(equal val (cdr x))
(not (member-equal val (cdr x)))))
///
(defthmd flag-possible-value-p-of-make-flag-facts-split
(equal (flag-possible-value-p (make-flag-facts known-value-p known-val eliminated-vals) val)
(if known-value-p
(equal val known-val)
(not (member val eliminated-vals))))
:hints ((and stable-under-simplificationp
'(:in-theory (enable make-flag-facts)))))
(defthm flag-possible-value-p-of-make-flag-facts-when-known-value
(equal (flag-possible-value-p (make-flag-facts t known-val eliminated-vals) val)
(equal val known-val))
:hints(("Goal" :in-theory (e/d (flag-possible-value-p-of-make-flag-facts-split)
(flag-possible-value-p)))))
(defthm flag-possible-value-p-of-make-flag-facts-when-eliminated-vals
(equal (flag-possible-value-p (make-flag-facts nil known-val eliminated-vals) val)
(not (member val eliminated-vals)))
:hints(("Goal" :in-theory (e/d (flag-possible-value-p-of-make-flag-facts-split)
(flag-possible-value-p))))))
(define flag-only-value-p ((x flag-facts-p)
(val))
:guard-hints (("goal" :in-theory (enable flag-facts-p)))
(b* ((x (flag-facts-fix x)))
(and (car x)
(equal val (cdr x))))
///
(defthmd flag-only-value-p-of-make-flag-facts-split
(equal (flag-only-value-p (make-flag-facts known-value-p known-val eliminated-vals) val)
(if known-value-p
(equal val known-val)
nil))
:hints ((and stable-under-simplificationp
'(:in-theory (enable make-flag-facts)))))
(defthm flag-only-value-p-of-make-flag-facts-when-known-value
(equal (flag-only-value-p (make-flag-facts t known-val eliminated-vals) val)
(equal val known-val))
:hints(("Goal" :in-theory (e/d (flag-only-value-p-of-make-flag-facts-split)
(flag-only-value-p)))))
(defthm flag-only-value-p-of-make-flag-facts-when-eliminated-vals
(equal (flag-only-value-p (make-flag-facts nil known-val eliminated-vals) val)
nil)
:hints(("Goal" :in-theory (e/d (flag-only-value-p-of-make-flag-facts-split)
(flag-only-value-p)))))
(defthm flag-possible-value-p-when-only-value-p
(implies (flag-only-value-p x val)
(equal (flag-possible-value-p x val2)
(equal val2 val)))
:hints(("Goal" :in-theory (enable flag-possible-value-p)))))
(define clause-get-flag-facts ((x pseudo-term-listp)
(flag-var pseudo-var-p))
:returns (mv (new-clause pseudo-term-listp)
(flag-facts flag-facts-p))
(b* (((mv new-clause known-value-p known-val eliminated-vals)
(scan-clause-for-flag-facts x flag-var)))
(mv new-clause (make-flag-facts known-value-p known-val eliminated-vals)))
///
(defret clause-get-flag-facts-possible-values-correct
(implies (not (flag-ev (disjoin x) a))
(flag-possible-value-p flag-facts
(cdr (hons-assoc-equal (pseudo-var-fix flag-var) a))))
:hints(("Goal" :in-theory (enable flag-possible-value-p-of-make-flag-facts-split))))
(defret clause-get-flag-facts-only-value-correct
(implies (and (not (flag-ev (disjoin x) a))
(not (equal (cdr (hons-assoc-equal (pseudo-var-fix flag-var) a)) val)))
(not (flag-only-value-p flag-facts val)))
:hints(("Goal" :in-theory (enable flag-only-value-p-of-make-flag-facts-split))))
(defret clause-get-flag-facts-new-clause-correct
(implies (not (flag-ev (disjoin x) a))
(not (flag-ev (disjoin new-clause) a)))))
(define match-not ((x pseudo-termp))
:returns (mv matchedp
(arg pseudo-termp))
(pseudo-term-case x
:fncall (case x.fn
(not (mv t (car x.args)))
(equal (cond ((equal (car x.args) ''nil)
(mv t (cadr x.args)))
((equal (cadr x.args) ''nil)
(mv t (car x.args)))
(t (mv nil nil))))
(if (cond ((and (equal (cadr x.args) ''nil)
(equal (caddr x.args) ''t))
(mv t (car x.args)))
(t (mv nil nil))))
(otherwise (mv nil nil)))
:otherwise (mv nil nil))
///
(defret match-not-correct
(implies matchedp
(equal (flag-ev x a)
(not (flag-ev arg a)))))
(defret match-not-pseudo-term-count
(implies matchedp
(< (pseudo-term-count arg) (pseudo-term-count x)))
:rule-classes :linear))
(define simplify-not ((x pseudo-termp) (iff-p))
:returns (not-x pseudo-termp)
(pseudo-term-case x
:const (pseudo-term-quote (not x.val))
:var (pseudo-term-fncall 'not (list x))
:fncall (if iff-p
(b* (((mv matchedp arg) (match-not x))
((when matchedp) arg))
(pseudo-term-fncall 'not (list x)))
(pseudo-term-fncall 'not (list x)))
:otherwise (pseudo-term-fncall 'not (list x)))
///
(defthm simplify-not-correct-iff
(iff (flag-ev (simplify-not x iff-p) a)
(not (flag-ev x a))))
(defthm simplify-not-correct-equal
(equal (flag-ev (simplify-not x nil) a)
(not (flag-ev x a))))
(defthm simplify-not-when-iff-p
(implies (and (syntaxp (not (equal iff-p ''t)))
iff-p)
(equal (simplify-not x iff-p)
(simplify-not x t)))))
(define simplify-if ((test pseudo-termp)
(then pseudo-termp)
(else pseudo-termp)
(iff-p))
;; Assumes the test is not a quoted val. Just mainly looking to turn it into a NOT.
:returns (if-term pseudo-termp)
(b* ((then (pseudo-term-fix then))
(else (pseudo-term-fix else))
((when (equal then else)) then)
((unless (and (pseudo-term-case then :quote)
(pseudo-term-case else :quote)))
(pseudo-term-fncall 'if (list test then else)))
(thenval (pseudo-term-quote->val then))
(elseval (pseudo-term-quote->val else))
((when iff-p)
(if thenval
(if elseval
''t
(pseudo-term-fix test))
(if elseval
(simplify-not test t)
''nil))))
(cond ((eq thenval t)
(cond ((eq elseval t) ''t)
(t (pseudo-term-fncall 'if (list test then else)))))
((eq thenval nil)
(cond ((eq elseval t) (simplify-not test nil))
((eq elseval nil) ''nil)
(t (pseudo-term-fncall 'if (list test then else)))))
(T (pseudo-term-fncall 'if (list test then else)))))
///
(defthm simplify-if-correct-iff
(iff (flag-ev (simplify-if test then else iff-p) a)
(if (flag-ev test a)
(flag-ev then a)
(flag-ev else a))))
(defthm simplify-if-correct-equal
(equal (flag-ev (simplify-if test then else nil) a)
(if (flag-ev test a)
(flag-ev then a)
(flag-ev else a))))
(defthm simplify-if-when-iff-p
(implies (and (syntaxp (not (equal iff-p ''t)))
iff-p)
(equal (simplify-if test then else iff-p)
(simplify-if test then else t)))))
(defines term-simplify-flag-conds
(define term-simplify-flag-conds ((x pseudo-termp)
(iff-p)
(flag-var pseudo-var-p)
(flag-facts flag-facts-p))
:returns (new-x pseudo-termp)
:measure (pseudo-term-count x)
:verify-guards nil
(pseudo-term-case x
:fncall
(b* (((mv matchedp val) (match-flag-equal x flag-var))
((when matchedp)
(cond ((flag-only-value-p flag-facts val) ''t)
((flag-possible-value-p flag-facts val) (pseudo-term-fix x))
(t ''nil)))
((mv matchedp arg) (match-not x))
((When matchedp)
(b* ((new-arg (term-simplify-flag-conds arg t flag-var flag-facts)))
(simplify-not new-arg iff-p)))
((when (eq x.fn 'if))
(b* ((test (term-simplify-flag-conds (car x.args) t flag-var flag-facts))
((when (pseudo-term-case test :quote))
(if (pseudo-term-quote->val test)
(term-simplify-flag-conds (cadr x.args) iff-p flag-var flag-facts)
(term-simplify-flag-conds (caddr x.args) iff-p flag-var flag-facts)))
(then (term-simplify-flag-conds (cadr x.args) iff-p flag-var flag-facts))
(else (term-simplify-flag-conds (caddr x.args) iff-p flag-var flag-facts)))
(simplify-if test then else iff-p)))
(args (termlist-simplify-flag-conds x.args flag-var flag-facts)))
(pseudo-term-fncall x.fn args))
:lambda
(b* ((args (termlist-simplify-flag-conds x.args flag-var flag-facts)))
(pseudo-term-lambda-with-hint
x.formals x.body args x))
:otherwise (pseudo-term-fix x)))
(define termlist-simplify-flag-conds ((x pseudo-term-listp)
(flag-var pseudo-var-p)
(flag-facts flag-facts-p))
:returns (new-x pseudo-term-listp)
:measure (pseudo-term-list-count x)
(if (atom x)
nil
(cons-with-hint (term-simplify-flag-conds (car x) nil flag-var flag-facts)
(termlist-simplify-flag-conds (cdr x) flag-var flag-facts)
x)))
///
(defret len-of-termlist-simplify-flag-conds
(equal (len new-x) (len x))
:hints (("Goal" :induct (len x)
:expand (<call>)))
:fn termlist-simplify-flag-conds)
(verify-guards term-simplify-flag-conds)
(local (in-theory (disable FLAG-EV-WHEN-PSEUDO-TERM-FNCALL)))
(defret-mutual term-simplify-flag-conds-correct
(defret term-simplify-flag-conds-correct-iff
(implies (flag-possible-value-p flag-facts
(cdr (hons-assoc-equal (pseudo-var-fix flag-var) a)))
(iff (flag-ev new-x a)
(flag-ev x a)))
:hints ('(:expand (<call>)
:in-theory (enable flag-ev-of-fncall-args))
(and stable-under-simplificationp
'(:in-theory (enable FLAG-EV-WHEN-PSEUDO-TERM-FNCALL
flag-ev-of-fncall-args))))
:fn term-simplify-flag-conds)
(defret term-simplify-flag-conds-correct-equal
(implies (and (not iff-p)
(flag-possible-value-p flag-facts
(cdr (hons-assoc-equal (pseudo-var-fix flag-var) a))))
(equal (flag-ev new-x a)
(flag-ev x a)))
:hints ('(:expand (<call>)))
:fn term-simplify-flag-conds)
(defret termlist-simplify-flag-conds-correct
(implies (flag-possible-value-p flag-facts
(cdr (hons-assoc-equal (pseudo-var-fix flag-var) a)))
(equal (flag-ev-list new-x a)
(flag-ev-list x a)))
:hints ('(:expand (<call>)))
:fn termlist-simplify-flag-conds)))
(define clause-simplify-flag-conds ((x pseudo-term-listp)
(flag-var pseudo-var-p)
(flag-facts flag-facts-p))
:returns (new-x pseudo-term-listp)
(b* (((when (atom x)) nil)
(lit1 (term-simplify-flag-conds (car x) t flag-var flag-facts))
((when (pseudo-term-case lit1 :quote))
(if (pseudo-term-quote->val lit1)
'('t)
(clause-simplify-flag-conds (cdr x) flag-var flag-facts)))
(rest (clause-simplify-flag-conds (cdr x) flag-var flag-facts))
((when (equal rest '('t))) rest))
(cons-with-hint lit1 rest x))
///
(defret clause-simplify-flag-conds-correct
(implies (and (not (flag-ev (disjoin x) a))
(flag-possible-value-p flag-facts
(cdr (hons-assoc-equal (pseudo-var-fix flag-var) a))))
(not (flag-ev (disjoin new-x) a)))
:hints (("goal" :induct <call> :expand (<call>))
(and stable-under-simplificationp
'(:use ((:instance term-simplify-flag-conds-correct-iff
(x (car x)) (iff-p t)))
:in-theory (disable term-simplify-flag-conds-correct-iff))))))
(define filter-possible-flag-values ((x true-listp)
(flag-facts flag-facts-p))
:returns (new-x true-listp :rule-classes :type-prescription)
(if (atom x)
nil
(if (flag-possible-value-p flag-facts (car x))
(cons (car x) (filter-possible-flag-values (cdr x) flag-facts))
(filter-possible-flag-values (cdr x) flag-facts))))
(define resolve-flags-cp ((clause pseudo-term-listp)
(var-and-possible-vals))
:returns (new-clauses)
(b* (((unless (and (consp var-and-possible-vals)
(pseudo-var-p (car var-and-possible-vals))
(true-listp (cdr var-and-possible-vals))))
(cw "Resolve-flags-cp: malformed hint object -- should be (cons flag-var possible-flag-vals)~%")
(list (pseudo-term-list-fix clause)))
((cons flag-var possible-flag-vals) var-and-possible-vals)
((mv reduced-clause flag-facts)
(clause-get-flag-facts clause flag-var))
(fully-reduced-clause (clause-simplify-flag-conds reduced-clause flag-var flag-facts))
((when (equal fully-reduced-clause '('t))) nil)
(possible-vals (filter-possible-flag-values possible-flag-vals flag-facts)))
(list (cons (pseudo-term-fncall
'not
(list (pseudo-term-fncall
'acl2::flag-is
(list (pseudo-term-quote
(cond ((atom possible-vals) :unknown!!)
((atom (cdr possible-vals)) (car possible-vals))
(t possible-vals)))))))
fully-reduced-clause)))
///
;; (local (defret clause-simplify-flag-conds-correct-converse
;; (implies (and (flag-ev (disjoin new-x) a)
;; (flag-possible-value-p flag-facts
;; (cdr (hons-assoc-equal (pseudo-var-fix flag-var) a))))
;; (flag-ev (disjoin x) a))
;; :fn clause-simplify-flag-conds))
;; (local (defret clause-get-flag-facts-new-clause-correct-converse
;; (implies (flag-ev (disjoin new-clause) a)
;; (flag-ev (disjoin x) a))
;; :fn clause-get-flag-facts))
(defthm resolve-flags-cp-correct
(implies (and (pseudo-term-listp clause)
(alistp a)
(flag-ev (conjoin-clauses (resolve-flags-cp clause var-and-possible-vals)) a))
(flag-ev (disjoin clause) a))
:hints (("goal" :do-not-induct t
:use ((:instance clause-simplify-flag-conds-correct
(x (mv-nth 0 (clause-get-flag-facts clause (car var-and-possible-vals))))
(flag-var (car var-and-possible-vals))
(flag-facts (mv-nth 1 (clause-get-flag-facts clause (car var-and-possible-vals))))))
:in-theory (disable clause-simplify-flag-conds-correct)))
:rule-classes :clause-processor))
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