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|
; Milawa - A Reflective Theorem Prover
; Copyright (C) 2005-2009 Kookamara LLC
;
; Contact:
;
; Kookamara LLC
; 11410 Windermere Meadows
; Austin, TX 78759, USA
; http://www.kookamara.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: Jared Davis <jared@kookamara.com>
(in-package "MILAWA")
(include-book "tracep")
(include-book "../assms/hypbox-arities")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund rw.slow-flag-trace-arities (flag x)
(declare (xargs :guard (if (equal flag 'term)
(rw.tracep x)
(rw.trace-listp x))
:measure (two-nats-measure (rank x) (if (equal flag 'term) 1 0))))
(if (equal flag 'term)
(let* ((res (rw.slow-hypbox-arities (rw.trace->hypbox x)))
(res (app (logic.slow-term-arities (rw.trace->lhs x)) res))
(res (app (logic.slow-term-arities (rw.trace->rhs x)) res))
(res (app (rw.slow-flag-trace-arities 'list (rw.trace->subtraces x)) res)))
res)
(if (consp x)
(app (rw.slow-flag-trace-arities 'term (car x))
(rw.slow-flag-trace-arities 'list (cdr x)))
nil)))
(definlined rw.slow-trace-arities (x)
(declare (xargs :guard (rw.tracep x)))
(rw.slow-flag-trace-arities 'term x))
(definlined rw.slow-trace-list-arities (x)
(declare (xargs :guard (rw.trace-listp x)))
(rw.slow-flag-trace-arities 'list x))
(defthmd definition-of-rw.slow-trace-arities
(equal (rw.slow-trace-arities x)
(let* ((res (rw.slow-hypbox-arities (rw.trace->hypbox x)))
(res (app (logic.slow-term-arities (rw.trace->lhs x)) res))
(res (app (logic.slow-term-arities (rw.trace->rhs x)) res))
(res (app (rw.slow-trace-list-arities (rw.trace->subtraces x)) res)))
res))
:rule-classes :definition
:hints(("Goal"
:expand ((rw.slow-flag-trace-arities 'term x))
:in-theory (enable rw.slow-trace-list-arities rw.slow-trace-arities))))
(defthmd definition-of-rw.slow-trace-list-arities
(equal (rw.slow-trace-list-arities x)
(if (consp x)
(app (rw.slow-trace-arities (car x))
(rw.slow-trace-list-arities (cdr x)))
nil))
:rule-classes :definition
:hints(("Goal"
:expand ((rw.slow-flag-trace-arities 'list x))
:in-theory (enable rw.slow-trace-list-arities rw.slow-trace-arities))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition rw.slow-trace-arities))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition rw.slow-trace-arities-list))))
(defthm rw.slow-trace-list-arities-when-not-consp
(implies (not (consp x))
(equal (rw.slow-trace-list-arities x)
nil))
:hints(("Goal" :in-theory (enable definition-of-rw.slow-trace-list-arities))))
(defthm rw.slow-trace-list-arities-of-cons
(equal (rw.slow-trace-list-arities (cons a x))
(app (rw.slow-trace-arities a)
(rw.slow-trace-list-arities x)))
:hints(("Goal" :in-theory (enable definition-of-rw.slow-trace-list-arities))))
(defund rw.flag-trace-arities (flag x acc)
(declare (xargs :guard (and (if (equal flag 'term)
(rw.tracep x)
(rw.trace-listp x))
(true-listp acc))
:measure (two-nats-measure (rank x) (if (equal flag 'term) 1 0))
:verify-guards nil))
(if (equal flag 'term)
(let* ((acc (rw.hypbox-arities (rw.trace->hypbox x) acc))
(acc (logic.term-arities (rw.trace->lhs x) acc))
(acc (logic.term-arities (rw.trace->rhs x) acc)))
(rw.flag-trace-arities 'list (rw.trace->subtraces x) acc))
(if (consp x)
(rw.flag-trace-arities 'term (car x)
(rw.flag-trace-arities 'list (cdr x) acc))
acc)))
(definlined rw.trace-arities (x acc)
(declare (xargs :guard (and (rw.tracep x)
(true-listp acc))
:verify-guards nil))
(rw.flag-trace-arities 'term x acc))
(definlined rw.trace-list-arities (x acc)
(declare (xargs :guard (and (rw.trace-listp x)
(true-listp acc))
:verify-guards nil))
(rw.flag-trace-arities 'list x acc))
(defthmd definition-of-rw.trace-arities
(equal (rw.trace-arities x acc)
(let* ((acc (rw.hypbox-arities (rw.trace->hypbox x) acc))
(acc (logic.term-arities (rw.trace->lhs x) acc))
(acc (logic.term-arities (rw.trace->rhs x) acc)))
(rw.trace-list-arities (rw.trace->subtraces x) acc)))
:rule-classes :definition
:hints(("Goal"
:in-theory (e/d (rw.trace-arities
rw.trace-list-arities)
((:executable-counterpart acl2::force)))
:expand (rw.flag-trace-arities 'term x acc))))
(defthmd definition-of-rw.trace-list-arities
(equal (rw.trace-list-arities x acc)
(if (consp x)
(rw.trace-arities (car x)
(rw.trace-list-arities (cdr x) acc))
acc))
:rule-classes :definition
:hints(("Goal"
:in-theory (e/d (rw.trace-arities
rw.trace-list-arities)
((:executable-counterpart acl2::force)))
:expand (rw.flag-trace-arities 'list x acc))))
(defthm rw.flag-trace-arities-of-term
(equal (rw.flag-trace-arities 'term x acc)
(rw.trace-arities x acc))
:hints(("Goal" :in-theory (enable rw.trace-arities))))
(defthm rw.flag-trace-arities-of-list
(equal (rw.flag-trace-arities 'list x acc)
(rw.trace-list-arities x acc))
:hints(("Goal" :in-theory (enable rw.trace-list-arities))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition rw.trace-arities))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition rw.trace-list-arities))))
(defthm rw.trace-list-arities-when-not-consp
(implies (not (consp x))
(equal (rw.trace-list-arities x acc)
acc))
:hints(("Goal" :in-theory (enable definition-of-rw.trace-list-arities))))
(defthm rw.trace-list-arities-of-cons
(equal (rw.trace-list-arities (cons a x) acc)
(rw.trace-arities a
(rw.trace-list-arities x acc)))
:hints(("Goal" :in-theory (enable definition-of-rw.trace-list-arities))))
(defthms-flag
:shared-hyp (force (true-listp acc))
:thms ((term true-listp-of-rw.trace-arities
(equal (true-listp (rw.trace-arities x acc))
t))
(t true-listp-of-rw.trace-list-arities
(equal (true-listp (rw.trace-list-arities x acc))
t)))
:hints(("Goal"
:induct (rw.flag-trace-arities flag x acc)
:in-theory (enable (:induction rw.flag-trace-arities))
:expand ((rw.trace-arities x acc)))))
(verify-guards rw.flag-trace-arities)
(verify-guards rw.trace-arities)
(verify-guards rw.trace-list-arities)
(defthms-flag
:shared-hyp (force (true-listp acc))
:thms ((term rw.trace-arities-removal
(equal (rw.trace-arities x acc)
(app (rw.slow-trace-arities x)
acc)))
(t rw.trace-list-arities-removal
(equal (rw.trace-list-arities x acc)
(app (rw.slow-trace-list-arities x)
acc))))
:hints(("Goal"
:induct (rw.flag-trace-arities flag x acc)
:in-theory (enable (:induction rw.flag-trace-arities))
:expand ((rw.trace-arities x acc)
(rw.slow-trace-arities x)))))
(defthms-flag
:thms ((term rw.slow-trace-arities-correct
(implies (force (rw.tracep x))
(equal (logic.arities-okp (rw.slow-trace-arities x) atbl)
(rw.trace-atblp x atbl))))
(t rw.slow-trace-list-arities-correct
(implies (force (rw.trace-listp x))
(equal (logic.arities-okp (rw.slow-trace-list-arities x) atbl)
(rw.trace-list-atblp x atbl)))))
:hints(("Goal"
:induct (rw.trace-induction flag x)
:expand ((rw.trace-atblp x atbl)
(rw.slow-trace-arities x))
:in-theory (disable (:executable-counterpart acl2::force)))))
(definlined rw.fast-trace-atblp (x atbl)
(declare (xargs :guard (and (rw.tracep x)
(logic.arity-tablep atbl))))
(logic.fast-arities-okp (rw.trace-arities x nil) atbl))
(defthm rw.fast-trace-atblp-removal
(implies (and (force (rw.tracep x))
(force (mapp atbl)))
(equal (rw.fast-trace-atblp x atbl)
(rw.trace-atblp x atbl)))
:hints(("Goal" :in-theory (enable rw.fast-trace-atblp))))
(defund rw.fast-trace-list-atblp (x atbl)
(declare (xargs :guard (and (rw.trace-listp x)
(logic.arity-tablep atbl))))
(logic.fast-arities-okp (rw.trace-list-arities x nil) atbl))
(defthm rw.fast-trace-list-atblp-removal
(implies (force (and (rw.trace-listp x)
(mapp atbl)))
(equal (rw.fast-trace-list-atblp x atbl)
(rw.trace-list-atblp x atbl)))
:hints(("Goal" :in-theory (enable rw.fast-trace-list-atblp))))
; Now we want to do develop a similar arity table check that avoids redundantly gathering
; arities from equal hypboxes.
(defund rw.slow-faster-flag-trace-arities (flag x ext-hypbox)
(declare (xargs :guard (and (if (equal flag 'term)
(rw.tracep x)
(rw.trace-listp x))
(rw.hypboxp ext-hypbox))
:measure (two-nats-measure (rank x) (if (equal flag 'term) 1 0))))
(if (equal flag 'term)
(let* ((hypbox (rw.trace->hypbox x))
(res (if (equal hypbox ext-hypbox)
nil
(rw.slow-hypbox-arities hypbox)))
(res (app (logic.slow-term-arities (rw.trace->lhs x)) res))
(res (app (logic.slow-term-arities (rw.trace->rhs x)) res))
(res (app (rw.slow-faster-flag-trace-arities 'list (rw.trace->subtraces x) hypbox) res)))
res)
(if (consp x)
(app (rw.slow-faster-flag-trace-arities 'term (car x) ext-hypbox)
(rw.slow-faster-flag-trace-arities 'list (cdr x) ext-hypbox))
nil)))
(defund rw.slow-faster-trace-arities (x ext-hypbox)
(declare (xargs :guard (and (rw.tracep x)
(rw.hypboxp ext-hypbox))))
(rw.slow-faster-flag-trace-arities 'term x ext-hypbox))
(defund rw.slow-faster-trace-list-arities (x ext-hypbox)
(declare (xargs :guard (and (rw.trace-listp x)
(rw.hypboxp ext-hypbox))))
(rw.slow-faster-flag-trace-arities 'list x ext-hypbox))
(defthmd definition-of-rw.slow-faster-trace-arities
(equal (rw.slow-faster-trace-arities x ext-hypbox)
(let* ((hypbox (rw.trace->hypbox x))
(res (if (equal hypbox ext-hypbox)
nil
(rw.slow-hypbox-arities hypbox)))
(res (app (logic.slow-term-arities (rw.trace->lhs x)) res))
(res (app (logic.slow-term-arities (rw.trace->rhs x)) res))
(res (app (rw.slow-faster-trace-list-arities (rw.trace->subtraces x) hypbox) res)))
res))
:rule-classes :definition
:hints(("Goal"
:expand ((rw.slow-faster-flag-trace-arities 'term x ext-hypbox))
:in-theory (enable rw.slow-faster-trace-arities
rw.slow-faster-trace-list-arities ))))
(defthmd definition-of-rw.slow-faster-trace-list-arities
(equal (rw.slow-faster-trace-list-arities x ext-hypbox)
(if (consp x)
(app (rw.slow-faster-trace-arities (car x) ext-hypbox)
(rw.slow-faster-trace-list-arities (cdr x) ext-hypbox))
nil))
:rule-classes :definition
:hints(("Goal"
:expand ((rw.slow-faster-flag-trace-arities 'list x ext-hypbox))
:in-theory (enable rw.slow-faster-trace-arities
rw.slow-faster-trace-list-arities))))
(defthm rw.slow-faster-flag-trace-arities-of-term
(equal (rw.slow-faster-flag-trace-arities 'term x ext-hypbox)
(rw.slow-faster-trace-arities x ext-hypbox))
:hints(("Goal" :in-theory (enable rw.slow-faster-trace-arities))))
(defthm rw.slow-faster-flag-trace-arities-of-list
(equal (rw.slow-faster-flag-trace-arities 'list x ext-hypbox)
(rw.slow-faster-trace-list-arities x ext-hypbox))
:hints(("Goal" :in-theory (enable rw.slow-faster-trace-list-arities))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition rw.slow-faster-trace-arities))))
(ACL2::theory-invariant (not (ACL2::active-runep '(:definition rw.slow-faster-trace-list-arities))))
(defthm rw.slow-faster-trace-list-arities-when-not-consp
(implies (not (consp x))
(equal (rw.slow-faster-trace-list-arities x ext-hypbox)
nil))
:hints(("Goal" :expand (rw.slow-faster-trace-list-arities x ext-hypbox))))
(defthm rw.slow-faster-trace-list-arities-of-cons
(equal (rw.slow-faster-trace-list-arities (cons a x) ext-hypbox)
(app (rw.slow-faster-trace-arities a ext-hypbox)
(rw.slow-faster-trace-list-arities x ext-hypbox)))
:hints(("Goal" :expand (rw.slow-faster-trace-list-arities (cons a x) ext-hypbox))))
(defthms-flag
:shared-hyp (force (and (rw.hypboxp hypbox)
(rw.hypbox-atblp hypbox atbl)))
:thms ((term rw.slow-faster-trace-arities-correct
(implies (rw.tracep x)
(equal (logic.arities-okp (rw.slow-faster-trace-arities x hypbox) atbl)
(rw.trace-atblp x atbl))))
(t rw.slow-faster-trace-list-arities-correct
(implies (rw.trace-listp x)
(equal (logic.arities-okp (rw.slow-faster-trace-list-arities x hypbox) atbl)
(rw.trace-list-atblp x atbl)))))
:hints(("Goal"
:in-theory (e/d ((:induction rw.slow-faster-flag-trace-arities))
((:executable-counterpart acl2::force)))
:induct (rw.slow-faster-flag-trace-arities flag x hypbox)
:expand ((rw.slow-faster-trace-arities x hypbox)
(rw.trace-atblp x atbl)))))
(defund rw.faster-flag-trace-arities (flag x ext-hypbox acc)
(declare (xargs :guard (and (if (equal flag 'term)
(rw.tracep x)
(rw.trace-listp x))
(rw.hypboxp ext-hypbox)
(true-listp acc))
:measure (two-nats-measure (rank x) (if (equal flag 'term) 1 0))
:verify-guards nil))
(if (equal flag 'term)
(let* ((hypbox (rw.trace->hypbox x))
(acc (if (equal hypbox ext-hypbox)
acc
(rw.hypbox-arities (rw.trace->hypbox x) acc)))
(acc (logic.term-arities (rw.trace->lhs x) acc))
(acc (logic.term-arities (rw.trace->rhs x) acc)))
(rw.faster-flag-trace-arities 'list (rw.trace->subtraces x) hypbox acc))
(if (consp x)
(rw.faster-flag-trace-arities 'term (car x) ext-hypbox
(rw.faster-flag-trace-arities 'list (cdr x) ext-hypbox acc))
acc)))
(defund rw.faster-trace-arities (x ext-hypbox acc)
(declare (xargs :guard (and (rw.tracep x)
(rw.hypboxp ext-hypbox)
(true-listp acc))
:verify-guards nil))
(rw.faster-flag-trace-arities 'term x ext-hypbox acc))
(defund rw.faster-trace-list-arities (x ext-hypbox acc)
(declare (xargs :guard (and (rw.trace-listp x)
(rw.hypboxp ext-hypbox)
(true-listp acc))
:verify-guards nil))
(rw.faster-flag-trace-arities 'list x ext-hypbox acc))
(defthmd definition-of-rw.faster-trace-arities
(equal (rw.faster-trace-arities x ext-hypbox acc)
(let* ((hypbox (rw.trace->hypbox x))
(acc (if (equal hypbox ext-hypbox)
acc
(rw.hypbox-arities (rw.trace->hypbox x) acc)))
(acc (logic.term-arities (rw.trace->lhs x) acc))
(acc (logic.term-arities (rw.trace->rhs x) acc)))
(rw.faster-trace-list-arities (rw.trace->subtraces x) hypbox acc)))
:rule-classes :definition
:hints(("Goal"
:expand (rw.faster-flag-trace-arities 'term x ext-hypbox acc)
:in-theory (enable rw.faster-trace-arities rw.faster-trace-list-arities))))
(defthmd definition-of-rw.faster-trace-list-arities
(equal (rw.faster-trace-list-arities x ext-hypbox acc)
(if (consp x)
(rw.faster-trace-arities (car x) ext-hypbox
(rw.faster-trace-list-arities (cdr x) ext-hypbox acc))
acc))
:rule-classes :definition
:hints(("Goal"
:expand (rw.faster-flag-trace-arities 'list x ext-hypbox acc)
:in-theory (enable rw.faster-trace-arities rw.faster-trace-list-arities))))
(defthm rw.faster-flag-trace-arities-of-term
(equal (rw.faster-flag-trace-arities 'term x ext-hypbox acc)
(rw.faster-trace-arities x ext-hypbox acc))
:hints(("Goal" :in-theory (enable rw.faster-trace-arities))))
(defthm rw.faster-flag-trace-arities-of-list
(equal (rw.faster-flag-trace-arities 'list x ext-hypbox acc)
(rw.faster-trace-list-arities x ext-hypbox acc))
:hints(("Goal" :in-theory (enable rw.faster-trace-list-arities))))
(defthm rw.faster-trace-list-arities-when-not-consp
(implies (not (consp x))
(equal (rw.faster-trace-list-arities x ext-hypbox acc)
acc))
:hints(("Goal" :expand (rw.faster-trace-list-arities x ext-hypbox acc))))
(defthm rw.faster-trace-list-arities-of-cons
(equal (rw.faster-trace-list-arities (cons a x) ext-hypbox acc)
(rw.faster-trace-arities a ext-hypbox
(rw.faster-trace-list-arities x ext-hypbox acc)))
:hints(("Goal"
:expand (rw.faster-trace-list-arities (cons a x) ext-hypbox acc)
:in-theory (disable (:executable-counterpart acl2::force))
)))
(defthms-flag
:shared-hyp (force (true-listp acc))
:thms ((term true-listp-of-rw.faster-trace-arities
(equal (true-listp (rw.faster-trace-arities x ext-hypbox acc))
t))
(t true-listp-of-rw.faster-trace-list-arities
(equal (true-listp (rw.faster-trace-list-arities x ext-hypbox acc))
t)))
:hints(("Goal"
:induct (rw.faster-flag-trace-arities flag x ext-hypbox acc)
:in-theory (e/d ((:induction rw.faster-flag-trace-arities)))
:expand ((rw.faster-trace-arities x ext-hypbox acc)
(rw.slow-faster-trace-arities x ext-hypbox)))))
(defthms-flag
:shared-hyp (force (true-listp acc))
:thms ((term rw.faster-trace-arities-removal
(equal (rw.faster-trace-arities x ext-hypbox acc)
(app (rw.slow-faster-trace-arities x ext-hypbox)
acc)))
(t rw.faster-trace-list-arities-removal
(equal (rw.faster-trace-list-arities x ext-hypbox acc)
(app (rw.slow-faster-trace-list-arities x ext-hypbox)
acc))))
:hints(("Goal"
:induct (rw.faster-flag-trace-arities flag x ext-hypbox acc)
:in-theory (e/d ((:induction rw.faster-flag-trace-arities))
;((:executable-counterpart acl2::force)))
)
:expand ((rw.faster-trace-arities x ext-hypbox acc)
(rw.slow-faster-trace-arities x ext-hypbox)))))
(verify-guards rw.faster-flag-trace-arities)
(verify-guards rw.faster-trace-arities)
(verify-guards rw.faster-trace-list-arities)
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