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; Def-functional-instance: automates defining functional instances of existing theorems
; Copyright (C) 2010 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 "std/util/bstar" :dir :system)
(defxdoc def-functional-instance
:parents (functional-instantiation)
:short "Functionally instantiate a pre-existing theorem to prove a new one."
:long "<p>Usage:</p>
@({
(def-functional-instance new-thm-name
orig-thm-name
((orig-fn substitute-fn) ...)
:hints (...) ;; optional
:rule-classes rule-classes) ;; optional
})
<p>Def-functional-instance attempts to define a new theorem based on
functionally instantiating an existing one with a user-provided function
substitution. It looks up the body of the theorem named ORIG-THM-NAME in the
ACL2 world and applies the functional substitution, replacing each ORIG-FN with
SUBSTITUTE-FN in the theorem body. It then submits this as a new theorem named
NEW-THM-NAME with a hint to prove it using a functional instance of the
original theorem. This theorem has either the given rule-classes or, if this
argument is omitted, the rule-classes of the original theorem.</p>
<p>Sometimes further hints are needed to show that the functional instantiation
is valid. These may be given by the :hints keyword. Note, however, that there
is already a hint provided at \"goal\", so that if one of the user-provided
hints uses this as its subgoal specifier, this hint will be ignored. The extra
hints given should either be computed hints or reference later subgoals.</p>")
(defun look-for-goal-hint (hints)
(if (atom hints)
nil
(or (and (consp (car hints))
(stringp (caar hints))
(standard-char-listp (coerce (caar hints) 'list))
(equal (string-upcase (caar hints)) "GOAL")
(car hints))
(look-for-goal-hint (cdr hints)))))
(defun def-functional-instance-fn
(newname oldname subst hints rule-classes rule-classesp
translate macro-subst by-hint-p state)
(declare (xargs :stobjs state :mode :program))
(b* ((world (w state))
(body (if translate
(fgetprop oldname 'theorem nil world)
(fgetprop oldname 'untranslated-theorem nil world)))
(rule-classes (if rule-classesp
rule-classes
(fgetprop oldname 'classes nil world)))
((unless body)
(er soft 'def-functional-instance-fn
"Theorem ~x0 not found in the ACL2 world" oldname))
(alist (append (pairlis$ (strip-cars subst)
(strip-cadrs subst))
(pairlis$ (strip-cars macro-subst)
(strip-cadrs macro-subst))))
(new-body (sublis alist body))
(untrans-body (if translate
(untranslate new-body nil world)
new-body))
(form `(defthm ,newname
,untrans-body
:hints (("goal"
,@(if by-hint-p
`(:by (:functional-instance ,oldname . ,subst))
`(:use ((:functional-instance ,oldname . ,subst))))
. ,(cdr (look-for-goal-hint hints)))
. ,hints)
:rule-classes ,rule-classes)))
;; (and (look-for-goal-hint hints)
;; (cw "WARNING: In DEF-FUNCTIONAL-INSTANCE, any user-provided hint ~
;; keyed on subgoal \"GOAL\" will be ignored. If your proof fails, please try ~
;; again with a computed hint or a subgoal specifier other than \"GOAL\". "))
(value form)))
(defmacro def-functional-instance
(newname oldname subst &key hints (rule-classes 'nil rule-classesp)
(translate 't)
(by-hint-p 'nil)
macro-subst)
`(make-event
(def-functional-instance-fn
',newname ',oldname ',subst ',hints ',rule-classes ',rule-classesp ',translate ',macro-subst ',by-hint-p state)))
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