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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 "lifted-termp")
(include-book "complementary")
(%interactive)
;; BOZO move this to arithmetic
(defthm |(zp (+ 1 a))|
;; Why have this silly rule? It's useful when the more expensive arithmetic
;; rules are disabled. For example, (= 0 (+ a b)) introduces case-splits.
;; Yet we often need a fact like this in inductive proofs where some count is
;; being decremented.
(equal (zp (+ 1 a))
nil))
(%autoprove |(zp (+ 1 a))|)
(%autoadmit clause.split-count)
(%autoprove natp-of-clause.split-count
(%restrict default clause.split-count (equal x 'x)))
(%autoprove |(< 0 (clause.split-count x))|
(%restrict default clause.split-count (equal x 'x)))
(%autoprove clause.split-count-when-clause.negative-termp
(%restrict default clause.split-count (equal x 'x)))
(%autoprove clause.split-count-when-if
(%restrict default clause.split-count (equal x 'x)))
(%autoadmit clause.split-count-list)
(%autoprove clause.split-count-list-when-not-consp
(%restrict default clause.split-count-list (equal x 'x)))
(%autoprove clause.split-count-list-of-cons
(%restrict default clause.split-count-list (equal x '(cons a x))))
(%autoprove natp-of-clause.split-count-list
(%restrict default clause.split-count-list (equal x 'x)))
;; BOZO consider moving this to a lower level, particularly for the builder.
(%autoadmit clause.aux-split-trivial-branchp)
(%autoprove booleanp-of-clause.aux-split-trivial-branchp
(%enable default clause.aux-split-trivial-branchp))
(defsection clause.aux-split-trivial-branch-bldr
(%autoadmit clause.aux-split-trivial-branch-bldr)
(local (%enable default
clause.aux-split-trivial-branchp
clause.aux-split-trivial-branch-bldr
clause.aux-split-goal))
(%autoprove logic.appealp-of-clause.aux-split-trivial-branch-bldr)
(%autoprove logic.conclusion-of-clause.aux-split-trivial-branch-bldr)
(%autoprove logic.proofp-of-clause.aux-split-trivial-branch-bldr))
(local (%disable default
expensive-arithmetic-rules
expensive-arithmetic-rules-two
type-set-like-rules
formula-decomposition
expensive-term/formula-inference
expensive-subsetp-rules
unusual-consp-rules))
(%autoadmit clause.aux-split)
;; (defmacro %clause.aux-split-induction (todo done)
;; `(%induct (clause.split-count-list ,todo)
;; ((not (consp ,todo))
;; nil)
;; ((and (consp ,todo)
;; (clause.negative-termp (car ,todo))
;; (clause.negative-termp (clause.negative-term-guts (car ,todo))))
;; (((,todo (cons (clause.negative-term-guts (clause.negative-term-guts (car ,todo)))
;; (cdr ,todo))))))
;; ((and (consp ,todo)
;; (clause.negative-termp (car ,todo))
;; (not (clause.negative-termp (clause.negative-term-guts (car ,todo))))
;; (logic.functionp (clause.negative-term-guts (car ,todo)))
;; (equal (logic.function-name (clause.negative-term-guts (car ,todo))) 'if)
;; (equal (len (logic.function-args (clause.negative-term-guts (car ,todo)))) 3))
;; (((,todo (cons (logic.function 'not (list (first (logic.function-args (clause.negative-term-guts (car ,todo))))))
;; (cons (logic.function 'not (list (second (logic.function-args (clause.negative-term-guts (car ,todo))))))
;; (cdr ,todo)))))
;; ((,todo (cons (first (logic.function-args (clause.negative-term-guts (car ,todo))))
;; (cons (logic.function 'not (list (third (logic.function-args (clause.negative-term-guts (car ,todo))))))
;; (cdr ,todo)))))))
;; ((and (consp ,todo)
;; (not (clause.negative-termp (car ,todo)))
;; (logic.functionp (car ,todo))
;; (equal (logic.function-name (car ,todo)) 'if)
;; (equal (len (logic.function-args (car ,todo))) 3))
;; (((,todo (cons (logic.function 'not (list (first (logic.function-args (car ,todo)))))
;; (cons (second (logic.function-args (car ,todo)))
;; (cdr ,todo)))))
;; ((,todo (cons (first (logic.function-args (car ,todo)))
;; (cons (third (logic.function-args (car ,todo)))
;; (cdr ,todo)))))))
;; ((and (consp ,todo)
;; (clause.negative-termp (car ,todo))
;; (not (clause.negative-termp (clause.negative-term-guts (car ,todo))))
;; (not (and (logic.functionp (clause.negative-term-guts (car ,todo)))
;; (equal (logic.function-name (clause.negative-term-guts (car ,todo))) 'if)
;; (equal (len (logic.function-args (clause.negative-term-guts (car ,todo)))) 3))))
;; (((,todo (cdr ,todo))
;; (,done (cons (logic.function 'not (list (clause.negative-term-guts (car ,todo)))) ,done)))))
;; ((and (consp ,todo)
;; (not (clause.negative-termp (car ,todo)))
;; (not (and (logic.functionp (car ,todo))
;; (equal (logic.function-name (car ,todo)) 'if)
;; (equal (len (logic.function-args (car ,todo))) 3))))
;; (((,todo (cdr ,todo))
;; (,done (cons (car ,todo) ,done)))))))
(%autoprove true-listp-of-clause.aux-split
(%autoinduct clause.aux-split todo done)
;(%clause.aux-split-induction todo done)
(%restrict default clause.aux-split (equal todo 'todo)))
;; (%autoprove consp-of-clause.aux-split
;; (%clause.aux-split-induction todo done)
;; (%restrict default clause.aux-split (equal todo 'todo)))
;; (%autoprove clause.aux-split-under-iff
;; (%use (%instance (%thm consp-of-clause.aux-split)))
;; (%disable default consp-of-clause.aux-split [outside]consp-of-clause.aux-split))
(%autoprove forcing-term-list-listp-of-clause.aux-split
(%autoinduct clause.aux-split todo done)
;(%clause.aux-split-induction todo done)
(%restrict default clause.aux-split (equal todo 'todo)))
(%autoprove forcing-term-list-list-atblp-of-clause.aux-split
(%autoinduct clause.aux-split todo done)
;(%clause.aux-split-induction todo done)
(%restrict default clause.aux-split (equal todo 'todo)))
(%autoprove forcing-cons-listp-of-clause.aux-split
(%autoinduct clause.aux-split todo done)
;(%clause.aux-split-induction todo done)
(%restrict default clause.aux-split (equal todo 'todo)))
;; BOZO we don't bother to show that splitting is complete in the sense of the
;; lifted-guts terms. Maybe we eventually want to do that, but I don't think
;; we will need it for now.
;; (local (%enable default logic.term-formula))
;; (local (%disable default
;; equal-of-cons-rewrite
;; forcing-equal-of-logic.pequal-rewrite-two
;; forcing-equal-of-logic.pnot-rewrite-two
;; forcing-equal-of-logic.por-rewrite-two
;; forcing-equal-of-logic.pequal-rewrite
;; forcing-equal-of-logic.pnot-rewrite
;; forcing-equal-of-logic.por-rewrite))
;; (%autoprove clause.aux-split-when-double-negative
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-negative-1
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-negative-2
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-negative-3
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-negative-4
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-positive-1
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-positive-2
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-positive-3
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-positive-4
;; (%restrict default clause.aux-split (equal todo '(cons a x))))
;; (%autoprove clause.aux-split-when-not-consp
;; (%restrict default clause.aux-split (equal todo 'todo)))
;; (%create-theory clause.aux-split-openers)
;; (%enable clause.aux-split-openers
;; clause.aux-split-when-double-negative
;; clause.aux-split-when-negative-1
;; clause.aux-split-when-negative-1
;; clause.aux-split-when-negative-2
;; clause.aux-split-when-negative-3
;; clause.aux-split-when-negative-4
;; clause.aux-split-when-positive-1
;; clause.aux-split-when-positive-2
;; clause.aux-split-when-positive-3
;; clause.aux-split-when-positive-4
;; clause.aux-split-when-not-consp)
;; BOZO this does NOT belong here. It's in aux-split-bldr.lisp but it really belongs
;; in utilities/utilities.
(%autoprove len-when-not-consp-of-cdr-cheap)
|
