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|
; Centaur AIG Library
; Copyright (C) 2008-2013 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 authors: Jared Davis <jared@centtech.com>
; Sol Swords <sswords@centtech.com>
(in-package "ACL2")
(include-book "aig-sat")
(include-book "faig-base")
(local (in-theory (disable faig-eval)))
(defsection faig-purebool-p
:parents (faig)
:short "Does a FAIG always evaluate to a purely Boolean value, i.e., is it
never X or Z?"
:long "<p>When an FAIG is known to be purely Boolean, then there is not much
reason to represent it as an FAIG—we might as well throw its offset away
and just work with its onset as an AIG.</p>
<p>When you are dealing with nice, well-behaved, RTL-level circuits that don't
use any fancy low-level, four-valued sorts of things like tri-state buffers,
this can be a useful optimization. For instance, it may reduce the complexity
of SAT queries, or carry out other kinds of analysis where you don't have to
think about four-valuedness.</p>
<p>@(call faig-purebool-p) is a logically nice, but non-executable way to
express pure Boolean-ness. See also @(see faig-purebool-check), which can be
executed; it uses a SAT solver to answer the question.</p>
@(def faig-purebool-p)"
(defun-sk faig-purebool-p (x)
(forall (env)
(or (equal (faig-eval x env) (faig-t))
(equal (faig-eval x env) (faig-f)))))
(verify-guards faig-purebool-p))
(define faig-purebool-aig ((x "A single FAIG."))
:parents (faig-purebool-p)
:short "An AIG that captures exactly when the FAIG X is Boolean valued."
:long "<p>This is useful mainly to implement @(see faig-purebool-check).</p>"
:returns aig
(b* ((x (faig-fix x))
(onset (car x))
(offset (cdr x)))
(aig-or (aig-and onset (aig-not offset))
(aig-and offset (aig-not onset))))
///
(local (defthm l0
(implies (not (aig-eval (faig-purebool-aig x) env))
(not (faig-purebool-p x)))
:hints(("Goal"
:in-theory (e/d (faig-eval)
(faig-purebool-p
faig-purebool-p-necc))
:use ((:instance faig-purebool-p-necc
(env env)))))))
(local (defthm l1
(implies (not (faig-purebool-p x))
(not (aig-eval (faig-purebool-aig x)
(faig-purebool-p-witness x))))
:hints(("Goal"
:in-theory (e/d (faig-eval)
(faig-purebool-p))
:use ((:instance faig-purebool-p))))))
(local (in-theory (disable faig-purebool-aig)))
(local (defthm l2
(implies (faig-purebool-p x)
(aig-eval (faig-purebool-aig x) env))))
(defthmd faig-purebool-p-as-aig-eval
(equal (faig-purebool-p x)
(aig-eval (faig-purebool-aig x)
(faig-purebool-p-witness x))))
(defthm faig-purebool-p-monotonicity
(implies (not (aig-eval (faig-purebool-aig x) env))
(not (aig-eval (faig-purebool-aig x)
(faig-purebool-p-witness x))))))
(define faig-purebool-check
:parents (faig-purebool-p)
:short "An executable version of @(see faig-purebool-p) using SAT."
((x "The FAIG to check.")
&key
((config satlink::config-p) 'satlink::*default-config*))
:returns (mv (fail booleanp :rule-classes :type-prescription
"If true, calling the SAT solver failed and the other
answers are meaningless.")
(purebool booleanp :rule-classes :type-prescription
"Does this FAIG always evaluate to purely Boolean?")
(alist "When this FAIG is not purely Boolean: an example
environment for @(see faig-eval) that drives it to
X or Z."))
(b* ((aig (faig-purebool-aig x))
((mv status alist) (aig-sat (aig-not aig) :config config))
((when (eq status :sat))
(mv nil nil alist))
((when (eq status :unsat))
(mv nil t nil)))
(mv t nil nil))
///
(local (defthm l0
(b* (((mv fail purebool ?alist)
(faig-purebool-check x :config config)))
(implies (and (not fail)
(not purebool))
(not (faig-purebool-p x))))
:hints(("Goal"
:in-theory (e/d (faig-purebool-p-as-aig-eval)
(aig-sat-when-sat))
:use ((:instance aig-sat-when-sat
(aig (aig-not (faig-purebool-aig x)))
(gatesimp (aignet::default-gatesimp))
(transform-config nil)))))))
(local (defthm l1
(b* (((mv fail purebool ?alist)
(faig-purebool-check x :config config)))
(implies (and (not fail)
purebool)
(faig-purebool-p x)))
:hints(("Goal"
:in-theory (e/d (faig-purebool-p-as-aig-eval)
(aig-sat-when-unsat))
:use ((:instance aig-sat-when-unsat
(aig (aig-not (faig-purebool-aig x)))
(gatesimp (aignet::default-gatesimp))
(env (faig-purebool-p-witness x))
(transform-config nil)))))))
(defthm faig-purebool-check-correct
(b* (((mv fail purebool ?alist)
(faig-purebool-check x :config config)))
(implies (not fail)
(equal purebool
(faig-purebool-p x))))
:hints(("Goal"
:use ((:instance l0)
(:instance l1)))))
(local (defthm l2
(b* (((mv fail purebool alist)
(faig-purebool-check x :config config)))
(implies (and (not fail)
(not purebool))
(and (not (equal (faig-eval x alist) (faig-f)))
(not (equal (faig-eval x alist) (faig-t))))))
:hints(("Goal"
:in-theory (e/d (faig-purebool-p-as-aig-eval
faig-purebool-aig
faig-eval)
(aig-sat-when-sat))
:use ((:instance aig-sat-when-sat
(aig (aig-not (faig-purebool-aig x)))
(gatesimp (aignet::default-gatesimp))
(transform-config nil)))))))
(defthm faig-purebool-counterexample-correct
(b* (((mv fail ?purebool alist)
(faig-purebool-check x :config config)))
(implies (and (not fail)
(not (faig-purebool-p x)))
(and (not (equal (faig-eval x alist) (faig-f)))
(not (equal (faig-eval x alist) (faig-t))))))
:hints(("Goal"
:in-theory (disable faig-purebool-check-correct
faig-purebool-check)
:use ((:instance l1))))))
(std::deflist faig-purebool-list-p (x)
(faig-purebool-p x)
:guard t
:parents (faig-purebool-p)
:short "Do a list of FAIGs always evaluate to purely Boolean values, i.e.,
are they never X or Z?"
:long "<p>This is a logically nice, but non-executable way to express pure
Boolean-ness. See also @(see faig-purebool-list-check), which can be executed;
it uses a SAT solver to answer the question.</p>")
(define faig-purebool-list-witness (x)
(cond ((atom x)
nil)
((faig-purebool-p (car x))
(faig-purebool-list-witness (cdr x)))
(t
(faig-purebool-p-witness (car x))))
///
(defthm faig-purebool-list-witness-when-atom
(implies (atom x)
(equal (faig-purebool-list-witness x)
nil)))
(defthm faig-purebool-list-witness-of-cons
(equal (faig-purebool-list-witness (cons a x))
(if (faig-purebool-p a)
(faig-purebool-list-witness x)
(faig-purebool-p-witness a)))))
(define faig-purebool-list-aig ((x "An FAIG List"))
:returns (aig)
:parents (faig-purebool-list-p)
:short "An AIG that captures exactly when a list of FAIGs always evaluate to
purely Boolean values."
:long "<p>This is useful mainly to implement @(see
faig-purebool-list-check).</p>"
(if (atom x)
t
(aig-and (faig-purebool-aig (car x))
(faig-purebool-list-aig (cdr x))))
///
(local (defthm l0
(implies (not (aig-eval (faig-purebool-list-aig x) env))
(not (faig-purebool-list-p x)))
:hints(("Goal"
:in-theory (enable faig-purebool-p-as-aig-eval)))))
(local (defthm l1
(implies (not (faig-purebool-list-p x))
(not (aig-eval (faig-purebool-list-aig x)
(faig-purebool-list-witness x))))
:hints(("Goal"
:induct (len x)
:in-theory (e/d (faig-purebool-list-witness
faig-purebool-p-as-aig-eval))))))
(local (in-theory (disable faig-purebool-list-aig)))
(local (defthm l2
(implies (faig-purebool-list-p x)
(aig-eval (faig-purebool-list-aig x) env))))
(defthmd faig-purebool-list-p-as-aig-eval
(equal (faig-purebool-list-p x)
(aig-eval (faig-purebool-list-aig x)
(faig-purebool-list-witness x)))
:hints(("Goal" :cases ((faig-purebool-list-p x)))))
(defthm faig-purebool-list-p-monotonicity
(implies (not (aig-eval (faig-purebool-list-aig x) env))
(not (aig-eval (faig-purebool-list-aig x)
(faig-purebool-list-witness x))))))
(define faig-purebool-list-check
:parents (faig-purebool-list-p)
:short "An executable version of @(see faig-purebool-list-p) using SAT."
((x "The FAIG List to check.")
&key
((config satlink::config-p) 'satlink::*default-config*))
:returns (mv (fail booleanp :rule-classes :type-prescription
"If true, calling the SAT solver failed and the other
answers are meaningless.")
(purebool-list booleanp :rule-classes :type-prescription
"Do these FAIGs always evaluate to purely Boolean?")
(alist "When these FAIGs are not purely Boolean: an example
environment for @(see faig-eval-list) that drives
some FAIG to X or Z."))
(b* ((aig (faig-purebool-list-aig x))
((mv status alist) (aig-sat (aig-not aig) :config config))
((when (eq status :sat))
(mv nil nil alist))
((when (eq status :unsat))
(mv nil t nil)))
(mv t nil nil))
///
(local (defthm l0
(b* (((mv fail purebool-list ?alist)
(faig-purebool-list-check x :config config)))
(implies (and (not fail)
(not purebool-list))
(not (faig-purebool-list-p x))))
:hints(("Goal"
:in-theory (e/d (faig-purebool-list-p-as-aig-eval)
(aig-sat-when-sat))
:use ((:instance aig-sat-when-sat
(gatesimp (aignet::default-gatesimp))
(aig (aig-not (faig-purebool-list-aig x)))
(transform-config nil)))))))
(local (defthm l1
(b* (((mv fail purebool-list ?alist)
(faig-purebool-list-check x :config config)))
(implies (and (not fail)
purebool-list)
(faig-purebool-list-p x)))
:hints(("Goal"
:in-theory (e/d (faig-purebool-list-p-as-aig-eval)
(aig-sat-when-unsat))
:use ((:instance aig-sat-when-unsat
(gatesimp (aignet::default-gatesimp))
(aig (aig-not (faig-purebool-list-aig x)))
(env (faig-purebool-list-witness x))
(transform-config nil)))))))
(defthm faig-purebool-list-check-correct
(b* (((mv fail purebool-list ?alist)
(faig-purebool-list-check x :config config)))
(implies (not fail)
(equal purebool-list
(faig-purebool-list-p x))))
:hints(("Goal"
:use ((:instance l0)
(:instance l1)))))
;; BOZO could eventually prove that the alist returned does indeed drive at
;; least some FAIG to X or Z.
)
|
