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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 "formula-compiler")
(include-book "clause-basics")
(%interactive)
(%autoadmit clause.make-clause-from-arbitrary-formula)
(%autoprove consp-of-clause.make-clause-from-arbitrary-formula
(%enable default clause.make-clause-from-arbitrary-formula))
(%autoprove forcing-logic.term-listp-of-clause.make-clause-from-arbitrary-formula
(%enable default clause.make-clause-from-arbitrary-formula))
(%autoprove forcing-logic.term-list-atblp-of-clause.make-clause-from-arbitrary-formula
(%enable default clause.make-clause-from-arbitrary-formula))
(%autoadmit clause.prove-arbitrary-formula-from-its-clause)
(encapsulate
()
(local (%enable default
clause.prove-arbitrary-formula-from-its-clause
clause.make-clause-from-arbitrary-formula
logic.term-formula))
(%autoprove forcing-logic.appealp-of-clause.prove-arbitrary-formula-from-its-clause)
(%autoprove forcing-logic.conclusion-of-clause.prove-arbitrary-formula-from-its-clause)
(%autoprove forcing-logic.proofp-of-clause.prove-arbitrary-formula-from-its-clause))
(%defprojection :list (clause.make-clauses-from-arbitrary-formulas x)
:element (clause.make-clause-from-arbitrary-formula x)
:nil-preservingp nil)
(%autoprove consp-listp-of-clause.make-clauses-from-arbitrary-formulas
(%cdr-induction x))
(%autoprove forcing-logic.term-list-listp-of-clause.make-clauses-from-arbitrary-formulas
(%cdr-induction x))
(%autoprove forcing-logic.term-list-list-atblp-of-clause.make-clauses-from-arbitrary-formulas
(%cdr-induction x))
(%autoadmit clause.prove-arbitrary-formulas-from-their-clauses)
(%autoprove forcing-logic.appeal-listp-of-clause.prove-arbitrary-formulas-from-their-clauses
(%autoinduct clause.prove-arbitrary-formulas-from-their-clauses)
(%restrict default clause.prove-arbitrary-formulas-from-their-clauses
(equal fs 'fs)))
(%autoprove forcing-logic.strip-conclusions-of-clause.prove-arbitrary-formulas-from-their-clauses
(%autoinduct clause.prove-arbitrary-formulas-from-their-clauses)
(%restrict default clause.prove-arbitrary-formulas-from-their-clauses
(equal fs 'fs)))
(%autoprove forcing-logic.proofp-of-clause.prove-arbitrary-formulas-from-their-clauses
(%autoinduct clause.prove-arbitrary-formulas-from-their-clauses)
(%restrict default clause.prove-arbitrary-formulas-from-their-clauses
(equal fs 'fs)))
(%autoadmit clause.prove-arbitrary-formula-from-its-clause-okp)
(%autoadmit clause.prove-arbitrary-formula-from-its-clause-high)
(%autoprove clause.prove-arbitrary-formula-from-its-clause-okp-of-clause.prove-arbitrary-formula-from-its-clause-high
(%enable default clause.prove-arbitrary-formula-from-its-clause-okp
clause.prove-arbitrary-formula-from-its-clause-high))
(%autoprove hack-for-compile-formula-okp-1
(%autoinduct logic.compile-formula f)
(%restrict default logic.compile-formula (equal x 'f))
(%disable default
FORCING-LOGIC.FORMULA-ATBLP-OF-LOGIC.VRHS
FORCING-LOGIC.FORMULA-ATBLP-OF-LOGIC.VLHS
FORCING-LOGIC.FORMULA-ATBLP-OF-LOGIC.~ARG
FORCING-LOGIC.TERM-ATBLP-OF-LOGIC.=RHS
FORCING-LOGIC.TERM-ATBLP-OF-LOGIC.=LHS
FORCING-LOGIC.TERM-ATBLP-OF-LOGIC.FUNCTION
FORCING-LOGIC.TERM-ATBLP-OF-LOGIC.COMPILE-FORMULA)
(%restrict default logic.formula-atblp (equal x 'f))
(%restrict default definition-of-logic.term-atblp
(or (equal x '(LOGIC.FUNCTION 'IF
(CONS (LOGIC.COMPILE-FORMULA (LOGIC.~ARG F))
'('NIL 'T))))
(equal x '(LOGIC.FUNCTION 'EQUAL
(CONS (LOGIC.=LHS F)
(CONS (LOGIC.=RHS F) 'nil))))
(equal x '(LOGIC.FUNCTION 'IF
(CONS (LOGIC.COMPILE-FORMULA (LOGIC.VLHS F))
(CONS ''T
(CONS (LOGIC.COMPILE-FORMULA (LOGIC.VRHS F))
'NIL)))))))
(%forcingp nil))
(%autoprove hack-for-compile-formula-okp-2
(%enable default
clause.make-clause-from-arbitrary-formula
clause.prove-arbitrary-formula-from-its-clause-okp
logic.term-formula)
(%disable default
logic.formula-atblp-when-logic.provablep
logic.formula-list-atblp-of-when-logic.provable-listp)
(%forcingp nil)
(%use (%instance (%thm logic.formula-atblp-when-logic.provablep)
(x (logic.conclusion (car (logic.subproofs x))))))
(%use (%instance (%thm hack-for-compile-formula-okp-1)
(f (logic.conclusion x))))
(%auto)
(%fertilize (logic.compile-formula (logic.conclusion x))
(logic.=lhs
(logic.~arg (logic.conclusion (car (logic.subproofs x)))))))
(encapsulate
()
(local (%enable default clause.prove-arbitrary-formula-from-its-clause-okp))
(%autoprove booleanp-of-clause.prove-arbitrary-formula-from-its-clause-okp)
(%autoprove clause.prove-arbitrary-formula-from-its-clause-okp-of-logic.appeal-identity)
(%autoprove lemma-1-for-soundness-of-clause.prove-arbitrary-formula-from-its-clause-okp)
(%autoprove lemma-2-for-soundness-of-clause.prove-arbitrary-formula-from-its-clause-okp
(%enable default hack-for-compile-formula-okp-2))
(%autoprove forcing-soundness-of-clause.prove-arbitrary-formula-from-its-clause-okp
(%enable default
lemma-1-for-soundness-of-clause.prove-arbitrary-formula-from-its-clause-okp
lemma-2-for-soundness-of-clause.prove-arbitrary-formula-from-its-clause-okp)
(%use (%instance (%thm forcing-logic.provablep-when-logic.proofp)
(x (clause.prove-arbitrary-formula-from-its-clause
(logic.conclusion x)
(logic.provable-witness (logic.conclusion (car (logic.subproofs x)))
axioms thms atbl)))))))
(%ensure-exactly-these-rules-are-missing "../../clauses/compiler")
|
