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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-2-strip-conclusions")
(include-book "proofp-2-induction")
(%interactive)
(%autoadmit logic.axiom-okp)
(%autoprove booleanp-of-logic.axiom-okp
(%enable default logic.axiom-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.axiom-okp
(%enable default logic.axiom-okp))
(%autoadmit logic.theorem-okp)
(%autoprove booleanp-of-logic.theorem-okp
(%enable default logic.theorem-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.theorem-okp
(%enable default logic.theorem-okp))
(%autoadmit logic.propositional-schema-okp)
(%autoprove booleanp-of-logic.propositional-schema-okp
(%enable default logic.propositional-schema-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.propositional-schema-okp
(%enable default
logic.propositional-schema-okp
backtracking-logic.formula-atblp-rules)
(%disable default
forcing-logic.formula-atblp-rules))
(%autoadmit logic.check-functional-axiom)
(%autoprove booleanp-of-logic.check-functional-axiom
(%induct (rank x)
((equal (logic.fmtype x) 'pequal*)
nil)
((equal (logic.fmtype x) 'por*)
(((x (logic.vrhs x))
(ti (cons (logic.=lhs (logic.~arg (logic.vlhs x))) ti))
(si (cons (logic.=rhs (logic.~arg (logic.vlhs x))) si)))))
((and (not (equal (logic.fmtype x) 'pequal*))
(not (equal (logic.fmtype x) 'por*)))
nil))
(%restrict default logic.check-functional-axiom (equal x 'x)))
(%autoadmit logic.functional-equality-okp)
(%autoprove booleanp-of-logic.functional-equality-okp
(%enable default logic.functional-equality-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.functional-equality-okp
(%enable default logic.functional-equality-okp))
(%autoadmit logic.expansion-okp)
(%autoprove booleanp-of-logic.expansion-okp
(%enable default logic.expansion-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.expansion-okp
(%enable default
logic.expansion-okp
backtracking-logic.formula-atblp-rules
logic.formula-list-atblp-of-logic.strip-conclusions-when-len-1)
(%disable default
forcing-logic.formula-atblp-rules
forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.contraction-okp)
(%autoprove booleanp-of-logic.contraction-okp
(%enable default logic.contraction-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.contraction-okp
(%enable default
logic.contraction-okp
backtracking-logic.formula-atblp-rules
logic.formula-list-atblp-of-logic.strip-conclusions-when-len-1)
(%disable default
forcing-logic.formula-atblp-rules
forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.associativity-okp)
(%autoprove booleanp-of-logic.associativity-okp
(%enable default logic.associativity-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.associativity-okp
(%enable default
logic.associativity-okp
backtracking-logic.formula-atblp-rules
logic.formula-list-atblp-of-logic.strip-conclusions-when-len-1)
(%disable default
forcing-logic.formula-atblp-rules
forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.cut-okp)
(%autoprove booleanp-of-logic.cut-okp
(%enable default logic.cut-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.cut-okp
(%enable default
logic.cut-okp
backtracking-logic.formula-atblp-rules
logic.formula-list-atblp-of-logic.strip-conclusions-when-len-2)
(%disable default
forcing-logic.formula-atblp-rules
forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.instantiation-okp)
(%autoprove booleanp-of-logic.instantiation-okp
(%enable default logic.instantiation-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.instantiation-okp
(%enable default
logic.instantiation-okp
backtracking-logic.formula-atblp-rules
logic.formula-list-atblp-of-logic.strip-conclusions-when-len-1)
(%disable default
forcing-logic.formula-atblp-rules
forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.beta-reduction-okp)
(%autoprove booleanp-of-logic.beta-reduction-okp
(%enable default logic.beta-reduction-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.beta-reduction-okp
(%enable default logic.beta-reduction-okp))
(%autoadmit logic.base-eval-okp)
(%autoprove booleanp-of-logic.base-eval-okp
(%enable default logic.base-eval-okp))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.base-eval-okp
(%enable default
logic.base-eval-okp
backtracking-logic.formula-atblp-rules)
(%disable default
forcing-logic.formula-atblp-rules
forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.induction-okp)
(%autoprove booleanp-of-logic.induction-okp
(%enable default logic.induction-okp))
(%autoprove lemma-for-logic.formula-atblp-of-logic.conclusion-when-logic.induction-okp
(%enable default logic.make-basis-step))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.induction-okp
(%enable default
logic.induction-okp
lemma-for-logic.formula-atblp-of-logic.conclusion-when-logic.induction-okp)
(%disable default
logic.formula-atblp-when-memberp-of-logic.formula-list-atblp
logic.formula-atblp-when-memberp-of-logic.formula-list-atblp-alt)
(%auto)
(%use (%instance (%thm logic.formula-atblp-when-memberp-of-logic.formula-list-atblp)
(a (logic.make-basis-step (logic.conclusion x) (second (logic.extras x))))
(x (logic.strip-conclusions (logic.subproofs x))))))
(%autoadmit logic.appeal-step-okp)
;; (defsection logic.appeal-step-okp
;; ;; Bleh skip okp thing. We need autoadmit to respect :export.
;; (%defun logic.appeal-step-okp (x axioms thms atbl)
;; (LET ((HOW (LOGIC.METHOD X)))
;; (COND ((EQUAL HOW 'AXIOM)
;; (LOGIC.AXIOM-OKP X AXIOMS ATBL))
;; ((EQUAL HOW 'THEOREM)
;; (LOGIC.THEOREM-OKP X THMS ATBL))
;; ((EQUAL HOW 'PROPOSITIONAL-SCHEMA)
;; (LOGIC.PROPOSITIONAL-SCHEMA-OKP X ATBL))
;; ((EQUAL HOW 'FUNCTIONAL-EQUALITY)
;; (LOGIC.FUNCTIONAL-EQUALITY-OKP X ATBL))
;; ((EQUAL HOW 'BETA-REDUCTION)
;; (LOGIC.BETA-REDUCTION-OKP X ATBL))
;; ((EQUAL HOW 'EXPANSION)
;; (LOGIC.EXPANSION-OKP X ATBL))
;; ((EQUAL HOW 'CONTRACTION)
;; (LOGIC.CONTRACTION-OKP X))
;; ((EQUAL HOW 'ASSOCIATIVITY)
;; (LOGIC.ASSOCIATIVITY-OKP X))
;; ((EQUAL HOW 'CUT) (LOGIC.CUT-OKP X))
;; ((EQUAL HOW 'INSTANTIATION)
;; (LOGIC.INSTANTIATION-OKP X ATBL))
;; ((EQUAL HOW 'INDUCTION)
;; (LOGIC.INDUCTION-OKP X))
;; ((EQUAL HOW 'BASE-EVAL)
;; (LOGIC.BASE-EVAL-OKP X ATBL))
;; ;((EQUAL HOW 'SKIP)
;; ; (LOGIC.SKIP-OKP X ATBL))
;; (T NIL))))
;; (%admit))
(%autoprove booleanp-of-logic.appeal-step-okp
(%enable default logic.appeal-step-okp))
(%autoprove logic.appeal-step-okp-when-not-consp
(%enable default logic.appeal-step-okp logic.method))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.appeal-step-okp
(%enable default logic.appeal-step-okp))
(encapsulate
()
;; BOZO add hints facility to %autoadmit
(local (%disable default forcing-true-listp-of-logic.subproofs))
(%autoadmit logic.flag-proofp))
(%autoadmit logic.proofp)
(%autoadmit logic.proof-listp)
(%autoprove definition-of-logic.proofp
(%enable default logic.proofp logic.proof-listp)
(%restrict default logic.flag-proofp (equal x 'x)))
(%autoprove definition-of-logic.proof-listp
(%enable default logic.proofp logic.proof-listp)
(%restrict default logic.flag-proofp (equal x 'x)))
(%autoprove logic.proofp-when-not-consp
(%restrict default definition-of-logic.proofp (equal x 'x)))
(%autoprove logic.proof-listp-when-not-consp
(%restrict default definition-of-logic.proof-listp (equal x 'x)))
(%autoprove logic.proof-listp-of-cons
(%restrict default definition-of-logic.proof-listp (equal x '(cons a x))))
(%autoprove lemma-for-booleanp-of-logic.proofp
(%logic.appeal-induction flag x)
(%disable default forcing-true-listp-of-logic.subproofs)
(%restrict default definition-of-logic.proofp (equal x 'x)))
(%autoprove booleanp-of-logic.proofp
(%use (%instance (%thm lemma-for-booleanp-of-logic.proofp) (flag 'proof))))
(%autoprove booleanp-of-logic.proof-listp
(%use (%instance (%thm lemma-for-booleanp-of-logic.proofp) (flag 'list))))
(%deflist logic.proof-listp (x axioms thms atbl)
(logic.proofp x axioms thms atbl))
(%autoprove logic.proofp-of-nth-when-logic.proof-listp
(%autoinduct nth)
(%restrict default nth (equal n 'n)))
(%autoprove forcing-logic.proof-listp-of-firstn)
(%autoprove forcing-logic.proof-listp-of-restn)
(%autoprove lemma-for-logic.formula-atblp-of-logic.conclusion-when-logic.proofp
(%logic.appeal-induction flag x)
(%restrict default definition-of-logic.proofp (equal x 'x))
(%disable default forcing-true-listp-of-logic.subproofs))
(%autoprove logic.formula-atblp-of-logic.conclusion-when-logic.proofp
(%use (%instance (%thm lemma-for-logic.formula-atblp-of-logic.conclusion-when-logic.proofp)
(flag 'proof))))
(%autoprove logic.formula-list-atblp-of-logic.strip-conclusions-when-logic.proof-listp
(%use (%instance (%thm lemma-for-logic.formula-atblp-of-logic.conclusion-when-logic.proofp)
(flag 'list))))
(%autoprove logic.proof-listp-of-logic.subproofs-when-logic.proofp
(%restrict default definition-of-logic.proofp (equal x 'x)))
|
