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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 "terms-2")
(%interactive)
(%autoadmit logic.functionp)
(%autoadmit logic.function)
(%autoadmit logic.function-name)
(%autoadmit logic.function-args)
(%noexec logic.function)
(%autoprove booleanp-of-logic.functionp
(%enable default logic.functionp))
(%autoprove consp-when-logic.functionp-cheap
(%enable default logic.functionp))
(%autoprove logic.variablep-when-logic.functionp
(%enable default logic.functionp))
(%autoprove logic.constantp-when-logic.functionp
(%enable default logic.functionp))
(%autoprove consp-of-logic.function
(%enable default logic.function))
(%autoprove logic.function-under-iff
(%enable default logic.function))
(%autoprove forcing-logic.constantp-of-logic.function
(%enable default logic.function))
(%autoprove forcing-logic.variablep-of-logic.function
(%enable default logic.function))
(%autoprove forcing-logic.termp-of-logic.function
(%enable default logic.function)
(%restrict default definition-of-logic.termp (equal x '(cons name args)))
(%auto :strategy (cleanup split crewrite)))
(%autoprove forcing-logic.functionp-of-logic.function
(%enable default logic.functionp logic.function))
(%autoprove forcing-logic.function-namep-of-logic.function-name
(%enable default logic.functionp logic.function-name))
(%autoprove logic.function-name-of-logic.function
(%enable default logic.function-name logic.function))
(%autoprove forcing-true-listp-of-logic.function-args
(%enable default logic.functionp logic.function-args)
(%restrict default definition-of-logic.termp (equal x 'x))
(%auto :strategy (cleanup split crewrite)))
(%autoprove forcing-logic.term-listp-of-logic.function-args
(%enable default logic.functionp logic.function-args)
(%restrict default definition-of-logic.termp (equal x 'x))
(%auto :strategy (cleanup split crewrite)))
(%autoprove logic.function-args-of-logic.function
(%enable default logic.function-args logic.function))
(%autoprove forcing-logic.function-of-logic.function-name-and-logic.function-args
(%enable default logic.functionp logic.function logic.function-name logic.function-args))
(%autoprove logic.function-of-logic.function-name-and-nil-when-nil-logic.function-args
(%enable default logic.functionp logic.function-name logic.function logic.function-args))
(%autoprove forcing-logic.function-of-logic.function-name-and-logic.function-args-free)
(%autoprove rank-of-logic.function-args
(%enable default logic.function-args))
(%autoprove rank-of-first-of-logic.function-args
(%enable default logic.function-args))
(%autoprove rank-of-second-of-logic.function-args
(%enable default logic.function-args))
(%autoprove rank-of-third-of-logic.function-args
(%enable default logic.function-args))
(%autoprove equal-of-logic.function-rewrite
(%enable default logic.function logic.functionp logic.function-name logic.function-args))
(defthm equal-of-logic.function-rewrite-alt
;; bozo add this to acl2
(implies (force (logic.function-namep name))
(equal (equal x (logic.function name args))
(and (logic.functionp x)
(equal (logic.function-name x) name)
(equal (logic.function-args x) args))))
:hints(("goal" :use ((:instance equal-of-logic.function-rewrite)))))
(%autoprove equal-of-logic.function-rewrite-alt
(%use (%instance (%thm equal-of-logic.function-rewrite))))
(%autoprove equal-of-logic.function-and-logic.function
(%enable default logic.function))
(%autoprove logic.function-args-under-iff-with-len-free)
(%autoprove forcing-equal-of-logic.function-with-two-args)
(defthm forcing-equal-of-logic.function-with-two-args-alt
(implies (and (equal (len (logic.function-args x)) 2)
(force (logic.termp x))
(force (logic.functionp x)))
(equal (equal x (logic.function name (list a b)))
(and (equal name (logic.function-name x))
(equal a (first (logic.function-args x)))
(equal b (second (logic.function-args x)))))))
(%autoprove forcing-equal-of-logic.function-with-two-args-alt
(%use (%thm forcing-equal-of-logic.function-with-two-args)))
(%autoprove forcing-equal-of-logic.function-with-three-args)
(defthm forcing-equal-of-logic.function-with-three-args-alt
(implies (and (equal 3 (len (logic.function-args x)))
(force (logic.termp x))
(force (logic.functionp x)))
(equal (equal x (logic.function name (list a b c)))
(and (equal name (logic.function-name x))
(equal a (first (logic.function-args x)))
(equal b (second (logic.function-args x)))
(equal c (third (logic.function-args x)))))))
(%autoprove forcing-equal-of-logic.function-with-three-args-alt
(%use (%instance (%thm forcing-equal-of-logic.function-with-three-args))))
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