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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 "proofp")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund logic.functional-axiom (fn ti si)
;; Create the functional axiom instance for fn, ti, and si.
(declare (xargs :guard (and (logic.function-namep fn)
(logic.term-listp ti)
(logic.term-listp si)
(equal (len ti) (len si)))))
(logic.disjoin-formulas (fast-app (logic.negate-formulas (logic.pequal-list ti si))
(list (logic.pequal (logic.function fn (list-fix ti))
(logic.function fn (list-fix si)))))))
(defthm forcing-logic.formulap-of-logic.functional-axiom
(implies (force (and (logic.function-namep fn)
(equal (len ti) (len si))
(logic.term-listp ti)
(logic.term-listp si)))
(equal (logic.formulap (logic.functional-axiom fn ti si))
t))
:hints(("Goal" :in-theory (enable logic.functional-axiom))))
(defthm forcing-logic.formula-atblp-of-logic.functional-axiom
(implies (force (and (logic.function-namep fn)
(logic.term-list-atblp ti atbl)
(logic.term-list-atblp si atbl)
(equal (cdr (lookup fn atbl)) (len ti))
(equal (len ti) (len si))))
(equal (logic.formula-atblp (logic.functional-axiom fn ti si) atbl)
t))
:hints(("Goal" :in-theory (enable logic.functional-axiom))))
;; We introduce two intermediate functions to bridge the gap between our axiom
;; generator and the checker in proofp.
(defund logic.functional-axiom-alt1 (fn ti si tacc sacc)
(declare (xargs :verify-guards nil))
(if (and (consp ti)
(consp si))
(logic.por (logic.pnot (logic.pequal (car ti) (car si)))
(logic.functional-axiom-alt1 fn (cdr ti) (cdr si) (cons (car ti) tacc) (cons (car si) sacc)))
(logic.pequal (logic.function fn (rev tacc))
(logic.function fn (rev sacc)))))
(defthm logic.check-functional-axiom-of-logic.functional-axiom-alt1
(implies (and (logic.function-namep fn)
(equal (len ti) (len si)))
(equal (logic.check-functional-axiom (logic.functional-axiom-alt1 fn ti si tacc sacc) tacc sacc)
t))
:hints(("Goal"
:in-theory (enable logic.check-functional-axiom
logic.functional-axiom-alt1)
:induct (logic.functional-axiom-alt1 fn ti si tacc sacc))))
(defund logic.functional-axiom-alt2 (fn ti si tacc sacc)
(declare (xargs :verify-guards nil))
(logic.disjoin-formulas
(app (logic.negate-formulas (logic.pequal-list ti si))
(list (logic.pequal (logic.function fn (rev (revappend ti tacc)))
(logic.function fn (rev (revappend si sacc))))))))
(encapsulate
()
(local (ACL2::allow-fertilize t))
(defthm logic.functional-axiom-alt1/alt2-equivalence
(implies (and (logic.function-namep fn)
(equal (len ti) (len si))
(true-listp tacc)
(true-listp sacc))
(equal (logic.functional-axiom-alt1 fn ti si tacc sacc)
(logic.functional-axiom-alt2 fn ti si tacc sacc)))
:hints(("Goal"
:in-theory (e/d (logic.functional-axiom-alt2
logic.functional-axiom-alt1)
(forcing-logic.formulap-of-logic.pequal
forcing-logic.formulap-of-logic.pnot
forcing-equal-of-logic.por-rewrite-two
forcing-equal-of-logic.por-rewrite))
:induct (logic.functional-axiom-alt1 fn ti si tacc sacc)))))
(defthm logic.functional-axiom-alt2/main-equivalence
(implies (and (logic.function-namep fn)
(equal (len ti) (len si)))
(equal (logic.functional-axiom-alt2 fn ti si nil nil)
(logic.functional-axiom fn ti si)))
:hints(("Goal" :in-theory (enable logic.functional-axiom-alt2
logic.functional-axiom))))
(defthm forcing-logic.check-functional-axiom-of-logic.functional-axiom
(implies (force (and (logic.function-namep fn)
(equal (len ti) (len si))))
(equal (logic.check-functional-axiom (logic.functional-axiom fn ti si) nil nil)
t))
:hints(("Goal"
:use ((:instance logic.check-functional-axiom-of-logic.functional-axiom-alt1
(tacc nil)
(sacc nil))))))
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