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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 "translate")
(include-book "substitute-term")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund logic.translate-sigma (x)
;; We should be given a true-list of (var term) 2-tuples, where each var is a
;; variable symbol and each term is an untranslated term. We translate each
;; term and call the resulting (var . translated term) pairs the answer.
;;
;; We return (t . answer) if all the terms are successfully translated, or
;; nil otherwise. If we return nil, a message will be printed indicating
;; where the error occurs.
(declare (xargs :guard t))
(if (consp x)
(and (tuplep 2 (car x))
(let* ((var (first (car x)))
(term (second (car x)))
(trans-term (logic.translate term)))
(and (logic.variablep var)
trans-term
(let ((others (logic.translate-sigma (cdr x))))
(and others
(let* ((others-answer (cdr others))
(answer (cons (cons var trans-term) others-answer)))
(cons t answer)))))))
(if (equal x nil)
(cons t nil)
nil)))
(defthm logic.sigmap-of-cdr-of-logic.translate-sigma
(equal (logic.sigmap (cdr (logic.translate-sigma x)))
t)
:hints(("Goal" :in-theory (enable logic.translate-sigma))))
(defund logic.translate-sigma-list (x)
;; We should be given a true-list of translatable sigmas. We translate them
;; all, producing answer = (sigma1 ... sigmaN), and return (t . answer) upon
;; success. If any sigma is not translatable, we return nil.
(if (consp x)
(let ((part1 (logic.translate-sigma (car x))))
(and part1
(let ((part2 (logic.translate-sigma-list (cdr x))))
(and part2
(let ((answer (cons (cdr part1) (cdr part2))))
(cons t answer))))))
(if (equal x nil)
(cons t nil)
nil)))
(defthm logic.sigma-listp-of-cdr-of-logic.translate-sigma-list
(equal (logic.sigma-listp (cdr (logic.translate-sigma-list x)))
t)
:hints(("Goal" :in-theory (enable logic.translate-sigma-list))))
(defund logic.translate-sigma-list-list (x)
;; We should be given a true-list of translatable sigma lists. We translate
;; them all, producing answer = (sigmas1 ... sigmasN), and return (t
;; . answer) upon success. If any sigma is not translatable, we return nil.
(if (consp x)
(let ((part1 (logic.translate-sigma-list (car x))))
(and part1
(let ((part2 (logic.translate-sigma-list-list (cdr x))))
(and part2
(let ((answer (cons (cdr part1) (cdr part2))))
(cons t answer))))))
(if (equal x nil)
(cons t nil)
nil)))
(defthm logic.sigma-list-listp-of-cdr-of-logic.translate-sigma-list-list
(equal (logic.sigma-list-listp (cdr (logic.translate-sigma-list-list x)))
t)
:hints(("Goal" :in-theory (enable logic.translate-sigma-list-list))))
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