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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 "subst")
(include-book "term-vars")
(local (include-book "std/alists/alist-keys" :dir :system))
(local (include-book "std/lists/sets" :dir :system))
(defines term-subst
:flag-local nil
(define term-subst ((x pseudo-termp)
(a pseudo-term-subst-p))
:returns (new-x pseudo-termp)
:measure (pseudo-term-count x)
:verify-guards nil
(pseudo-term-case x
:const (pseudo-term-fix x)
:var (let ((look (assoc-eq x.name (pseudo-term-subst-fix a))))
(if look (cdr look) (pseudo-term-fix x)))
:call (pseudo-term-call x.fn (termlist-subst x.args a))))
(define termlist-subst ((x pseudo-term-listp)
(a pseudo-term-subst-p))
:returns (new-x pseudo-term-listp)
:measure (pseudo-term-list-count x)
(if (Atom x)
nil
(cons (term-subst (car x) a)
(termlist-subst (cdr x) a))))
///
(defthm len-of-termlist-subst
(equal (len (termlist-subst x a))
(len x)))
(verify-guards term-subst)
(local (defthm assoc-of-append
(implies k
(equal (assoc k (append a b))
(or (assoc k a) (assoc k b))))))
(defret-mutual base-ev-of-term-subst
(defret base-ev-of-term-subst
(equal (base-ev (term-subst x a) env)
(base-ev x (append (base-ev-alist a env) env)))
:hints ('(:expand (<call>)
:in-theory (enable acl2::base-ev-when-pseudo-term-call
acl2::base-ev-of-pseudo-term-call)))
:fn term-subst)
(defret base-ev-list-of-termlist-subst
(equal (base-ev-list (termlist-subst x a) env)
(base-ev-list x (append (base-ev-alist a env) env)))
:hints ('(:expand (<call>)))
:fn termlist-subst))
(defret-mutual acons-non-var-preserves-<fn>
(defret acons-non-var-preserves-<fn>
(implies (not (member k (term-vars x)))
(equal (term-subst x (cons (cons k v) a))
new-x))
:hints ('(:expand ((term-vars x)
(:free (a) <call>))))
:fn term-subst)
(defret acons-non-var-preserves-<fn>
(implies (not (member k (termlist-vars x)))
(equal (termlist-subst x (cons (cons k v) a))
new-x))
:hints ('(:expand ((termlist-vars x)
(:free (a) <call>))))
:fn termlist-subst))
(fty::deffixequiv-mutual term-subst))
(defines term-subst-strict
:flag-local nil
(define term-subst-strict ((x pseudo-termp)
(a pseudo-term-subst-p))
:returns (new-x pseudo-termp)
:measure (pseudo-term-count x)
:verify-guards nil
(pseudo-term-case x
:const (pseudo-term-fix x)
:var (cdr (assoc-eq x.name (pseudo-term-subst-fix a)))
:call (pseudo-term-call x.fn (termlist-subst-strict x.args a))))
(define termlist-subst-strict ((x pseudo-term-listp)
(a pseudo-term-subst-p))
:returns (new-x pseudo-term-listp)
:measure (pseudo-term-list-count x)
(if (Atom x)
nil
(cons (term-subst-strict (car x) a)
(termlist-subst-strict (cdr x) a))))
///
(defthm len-of-termlist-subst-strict
(equal (len (termlist-subst-strict x a))
(len x)))
(verify-guards term-subst-strict)
(defret-mutual base-ev-of-term-subst-strict
(defret base-ev-of-term-subst-strict
(equal (base-ev (term-subst-strict x a) env)
(base-ev x (base-ev-alist a env)))
:hints ('(:expand (<call>)
:in-theory (enable acl2::base-ev-when-pseudo-term-call
acl2::base-ev-of-pseudo-term-call)))
:fn term-subst-strict)
(defret base-ev-list-of-termlist-subst-strict
(equal (base-ev-list (termlist-subst-strict x a) env)
(base-ev-list x (base-ev-alist a env)))
:hints ('(:expand (<call>)))
:fn termlist-subst-strict))
(defret-mutual acons-non-var-preserves-<fn>
(defret acons-non-var-preserves-<fn>
(implies (not (member k (term-vars x)))
(equal (term-subst-strict x (cons (cons k v) a))
new-x))
:hints ('(:expand ((term-vars x)
(:free (a) <call>))))
:fn term-subst-strict)
(defret acons-non-var-preserves-<fn>
(implies (not (member k (termlist-vars x)))
(equal (termlist-subst-strict x (cons (cons k v) a))
new-x))
:hints ('(:expand ((termlist-vars x)
(:free (a) <call>))))
:fn termlist-subst-strict))
(fty::deffixequiv-mutual term-subst-strict))
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