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|
; Centaur AIG Library
; Copyright (C) 2008-2011 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 "ACL2")
(include-book "aig-base")
(include-book "centaur/misc/equal-sets" :dir :system)
(include-book "tools/mv-nth" :dir :system)
(include-book "misc/gentle" :dir :system)
(include-book "misc/hons-help" :dir :system)
(local (include-book "std/alists/alistp" :dir :system))
; (local (include-book "eval-restrict"))
;; (local (in-theory (disable append-of-nil)))
;; BOZO misplaced
(local (defthm true-listp-of-make-fal
(implies (true-listp name)
(true-listp (make-fal al name)))))
(defthm make-fal-is-append
(implies (alistp x)
(equal (make-fal x y) (append x y))))
(defthm aig-eval-alist-append
(equal (aig-eval-alist (append a b) env)
(append (aig-eval-alist a env)
(aig-eval-alist b env))))
;; (defun faig-vars-pat (pat aigs)
;; (if pat
;; (if (atom pat)
;; (list :signal pat
;; (aig-vars (car aigs))
;; (aig-vars (cdr aigs)))
;; (cons (faig-vars-pat (car pat) (car aigs))
;; (faig-vars-pat (cdr pat) (cdr aigs))))
;; nil))
;; Extracts necessary variable assignments from an AIG by breaking down its
;; top-level AND structure to the negations/variables. Any such leaf it
;; reaches which is a variable or negation implies an assignment.
(defun aig-extract-assigns (x)
(declare (xargs :guard t
:verify-guards nil))
(aig-cases
x
:true (mv nil nil)
:false (mv nil nil)
:var (mv (mbe :logic (set::insert x nil)
:exec (list x))
nil)
:inv (if (aig-var-p (car x))
(mv nil (mbe :logic (set::insert (car x) nil)
:exec (list (car x))))
(mv nil nil))
:and (mv-let (trues1 falses1)
(aig-extract-assigns (car x))
(mv-let (trues2 falses2)
(aig-extract-assigns (cdr x))
(mv (set::union trues1 trues2)
(set::union falses1 falses2))))))
(defthm aig-var-listp-aig-extract-assigns
(mv-let (trues falses)
(aig-extract-assigns x)
(and (aig-var-listp trues)
(aig-var-listp falses))))
(defthm setp-of-aig-extract-assigns
(b* (((mv trues falses) (aig-extract-assigns x)))
(and (set::setp trues)
(set::setp falses))))
(verify-guards aig-extract-assigns
:hints(("Goal" :in-theory (enable set::insert))))
(memoize 'aig-extract-assigns
:condition '(and (not (aig-atom-p x)) (cdr x))
:forget t)
(defthm aig-extract-assigns-member-impl
(mv-let (trues falses)
(aig-extract-assigns x)
(and (implies (and (member-equal v trues)
(aig-eval x env))
(aig-eval v env))
(implies (and (member-equal v falses)
(aig-eval x env))
(not (aig-eval v env)))))
:rule-classes nil)
(defthm var-eval-extend-env
(equal (aig-eval x (cons (cons v (aig-eval v env)) env))
(aig-eval x env))
:hints(("Goal" :in-theory (enable aig-env-lookup))))
(defthm aig-extract-assigns-extend-alist
(mv-let (trues falses)
(aig-extract-assigns x)
(and (implies (and (member-equal v trues)
(aig-eval x env))
(equal (aig-eval y (cons (cons v t) env))
(aig-eval y env)))
(implies (and (member-equal v falses)
(aig-eval x env))
(equal (aig-eval y (cons (cons v nil) env))
(aig-eval y env)))))
:hints (("goal" :do-not-induct t
:use (aig-extract-assigns-member-impl
(:instance var-eval-extend-env
(x y)))
:in-theory (disable var-eval-extend-env))))
(define boolean-val-alistp (x)
(if (atom x)
(eq x nil)
(and (consp (car x)) (booleanp (cdar x))
(boolean-val-alistp (cdr x))))
///
(defthmd aig-eval-alist-of-boolean-val-alistp
(implies (boolean-val-alistp x)
(equal (aig-eval-alist x env) x)))
(defthm lookup-in-boolean-val-alist
(implies (boolean-val-alistp x)
(booleanp (cdr (hons-assoc-equal k x)))))
(defthm alistp-when-boolean-val-alistp
(implies (boolean-val-alistp x)
(alistp x))
:rule-classes :forward-chaining)
(defthm boolean-val-alistp-of-append
(implies (and (boolean-val-alistp x)
(boolean-val-alistp y))
(boolean-val-alistp (append x y)))))
(local (in-theory (enable aig-eval-alist-of-boolean-val-alistp)))
(defun assign-var-list (vars val)
(declare (xargs :guard t))
(if (atom vars)
nil
(cons (cons (car vars) val)
(assign-var-list (cdr vars) val))))
(defthm boolean-val-alistp-of-assign-var-list
(implies (booleanp val)
(boolean-val-alistp (assign-var-list vars val)))
:hints(("Goal" :in-theory (enable boolean-val-alistp))))
(local
(defthm aig-extract-assigns-assign-var-list1
(mv-let (trues falses)
(aig-extract-assigns x)
(implies (aig-eval x env)
(and (implies
(subsetp-equal vars trues)
(aig-eval x (append (assign-var-list vars t)
env)))
(implies
(subsetp-equal vars falses)
(aig-eval x (append (assign-var-list vars nil)
env))))))
:hints ((and stable-under-simplificationp
'(:induct (len vars) :in-theory (enable subsetp-equal))))
:otf-flg t))
(defthm aig-extract-assigns-assign-var-list
(mv-let (trues falses)
(aig-extract-assigns x)
(implies (aig-eval x env)
(and (implies
(subsetp-equal vars trues)
(equal (aig-eval y (append (assign-var-list vars t)
env))
(aig-eval y env)))
(implies
(subsetp-equal vars falses)
(equal (aig-eval y (append (assign-var-list vars nil)
env))
(aig-eval y env))))))
:hints ((and stable-under-simplificationp
(not (cdr (car id))) ;; not under induction
'(:induct (len vars) :in-theory (enable subsetp-equal)
:do-not-induct t)))
:otf-flg t)
(defthm aig-extract-assigns-var-list-rw
(mv-let (trues falses)
(aig-extract-assigns x)
(implies (aig-eval x env)
(and (equal (aig-eval y (append (assign-var-list trues t)
env))
(aig-eval y env))
(equal (aig-eval y (append (assign-var-list falses nil)
env))
(aig-eval y env))))))
(defthm alistp-assign-var-list
(alistp (assign-var-list vars val)))
(defthm aig-eval-alist-assign-var-list
(equal (aig-eval-alist (assign-var-list vars val) env)
(assign-var-list vars (aig-eval val env))))
(in-theory (disable assign-var-list))
(defun aig-extract-assigns-alist (x)
(declare (xargs :guard t))
(mv-let (trues falses)
(aig-extract-assigns x)
(make-fal (assign-var-list trues t)
(make-fal (assign-var-list falses nil)
nil))))
(defthm boolean-val-alistp-of-aig-extract-assigns-alist
(boolean-val-alistp (aig-extract-assigns-alist x)))
(local (defthm true-listp-of-aig-extract-assigns-alist
(true-listp (aig-extract-assigns-alist x))))
(defthm alistp-aig-extract-assigns-alist
(alistp (aig-extract-assigns-alist x)))
(defthm aig-eval-alist-aig-extract-assigns-alist
(equal (aig-eval-alist (aig-extract-assigns-alist x) env)
(aig-extract-assigns-alist x)))
(defthm assign-var-list-lookup
(equal (hons-assoc-equal k (assign-var-list x v))
(and (member k x)
(cons k v)))
:hints(("Goal" :in-theory (enable assign-var-list hons-assoc-equal member))))
(local (defthm hons-assoc-equal-of-append
(equal (hons-assoc-equal k (append x y))
(or (hons-assoc-equal k x)
(hons-assoc-equal k y)))))
(defthmd aig-extract-assigns-alist-lookup-boolean
(booleanp (cdr (hons-assoc-equal k (aig-extract-assigns-alist x))))
:hints(("Goal" :in-theory (enable aig-extract-assigns-alist)))
:rule-classes :type-prescription)
(defthm aig-extract-assigns-restrict
;; (implies (aig-eval x env)
;; (aig-eval (aig-restrict x (aig-extract-assigns-alist x)) env))
(implies (aig-eval x env)
(equal (aig-eval y (append (aig-extract-assigns-alist x) env))
(aig-eval y env)))
:hints (("goal" :do-not-induct t)))
(defun aig-extract-iterated-assigns-alist (x clk)
(declare (Xargs :measure (nfix clk)
:guard (natp clk)))
(let* ((al (aig-extract-assigns-alist x))
(newx (aig-restrict x al)))
(prog2$
(clear-memoize-table 'aig-restrict)
(if (or (hons-equal newx x) (zp clk))
al
(let* ((more (aig-extract-iterated-assigns-alist newx (1- clk))))
(make-fal (flush-hons-get-hash-table-link al) more))))))
(defthm boolean-val-alistp-of-aig-extract-iterated-assigns-alist
(boolean-val-alistp (aig-extract-iterated-assigns-alist x clk)))
(in-theory (disable aig-extract-assigns-alist))
(local (defthm true-listp-of-aig-extract-iterated-assigns-alist
(true-listp (aig-extract-iterated-assigns-alist x clk))))
(defthm alistp-aig-extract-iterated-assigns
(alistp (aig-extract-iterated-assigns-alist x clk)))
(defthm aig-eval-alist-extract-iterated-assigns
(equal (aig-eval-alist (aig-extract-iterated-assigns-alist x clk) env)
(aig-extract-iterated-assigns-alist x clk)))
(local
(defun aig-extract-iterated-assigns-restrict-ind (x y clk)
(declare (Xargs :measure (nfix clk)))
(let* ((al (aig-extract-assigns-alist x))
(newx (aig-restrict x al)))
(if (or (hons-equal newx x) (zp clk))
(list al y)
(list (aig-extract-iterated-assigns-restrict-ind newx y (1- clk))
(aig-extract-iterated-assigns-restrict-ind newx x (1- clk)))))))
(defthm aig-extract-iterated-assigns-restrict
;; (implies (aig-eval x env)
;; (aig-eval (aig-restrict x (aig-extract-iterated-assigns-alist
;; x clk))
;; env))
(implies (aig-eval x env)
(equal (aig-eval y (append (aig-extract-iterated-assigns-alist x clk)
env))
(aig-eval y env)))
:hints (("goal" :induct (aig-extract-iterated-assigns-restrict-ind x y clk))))
(defthm aig-extract-iterated-assigns-special-case
(implies (aig-eval x nil)
(equal (aig-eval y (aig-extract-iterated-assigns-alist x clk))
(aig-eval y nil)))
:hints (("goal" :use ((:instance aig-extract-iterated-assigns-restrict
(env nil))))))
(defthmd aig-extract-iterated-assigns-alist-lookup-boolean
(booleanp (cdr (hons-assoc-equal k (aig-extract-iterated-assigns-alist x clk))))
:rule-classes :type-prescription)
(memoize 'aig-extract-iterated-assigns-alist
:recursive nil)
(defthmd lookup-in-aig-extract-assigns
(b* (((mv trues falses) (aig-extract-assigns x)))
(and (implies (and (member v trues)
(aig-eval x env))
(aig-env-lookup v env))
(implies (and (member v falses)
(aig-eval x env))
(not (aig-env-lookup v env)))))
:hints(("Goal" :in-theory (enable aig-extract-assigns))))
(defthmd lookup-in-aig-extract-assigns-alist
(implies (and (hons-assoc-equal v (aig-extract-assigns-alist x))
(aig-eval x env))
(iff (aig-env-lookup v env)
(cdr (hons-assoc-equal v (aig-extract-assigns-alist x)))))
:hints(("Goal" :in-theory (e/d (aig-extract-assigns-alist)
(aig-env-lookup
lookup-in-aig-extract-assigns))
:use lookup-in-aig-extract-assigns)))
(defthmd lookup-in-aig-extract-iterated-assigns-alist
(implies (and (hons-assoc-equal v (aig-extract-iterated-assigns-alist x n))
(aig-eval x env))
(iff (aig-env-lookup v env)
(cdr (hons-assoc-equal v (aig-extract-iterated-assigns-alist x n)))))
:hints(("Goal" :in-theory (e/d (aig-extract-iterated-assigns-alist
lookup-in-aig-extract-assigns-alist)
(aig-env-lookup))
:induct (aig-extract-iterated-assigns-alist x n))))
|
