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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 "colors")
(include-book "skeletonp")
(include-book "../clauses/split-bldr")
(set-verify-guards-eagerness 2)
(set-case-split-limitations nil)
(set-well-founded-relation ord<)
(set-measure-function rank)
(defund tactic.split-first-okp (x)
(declare (xargs :guard (tactic.skeletonp x)))
(let ((goals (tactic.skeleton->goals x))
(tacname (tactic.skeleton->tacname x))
(extras (tactic.skeleton->extras x))
(history (tactic.skeleton->history x)))
(and (equal tacname 'split-first)
(tuplep 4 extras)
(let ((old-goals (tactic.skeleton->goals history))
(liftp (first extras))
(liftlimit (second extras))
(splitlimit (third extras))
(split-len (fourth extras)))
(and (consp old-goals)
(booleanp liftp)
(natp liftlimit)
(natp splitlimit)
(let* ((clause1 (list-fix (car old-goals)))
(clause1-split (clause.split liftp liftlimit splitlimit clause1)))
(and (car clause1-split)
(equal split-len (len (cdr clause1-split)))
(equal (firstn split-len goals) (cdr clause1-split))
(equal (restn split-len goals) (cdr old-goals)))))))))
(defthm booleanp-of-tactic.split-first-okp
(equal (booleanp (tactic.split-first-okp x))
t)
:hints(("Goal" :in-theory (e/d (tactic.split-first-okp)
((:executable-counterpart acl2::force))))))
(defund tactic.split-first-tac (liftp liftlimit splitlimit x)
(declare (xargs :guard (and (booleanp liftp)
(natp liftlimit)
(natp splitlimit)
(tactic.skeletonp x))))
(let ((goals (tactic.skeleton->goals x)))
(if (not (consp goals))
(ACL2::cw "~s0Split-first-tac failure~s1: all clauses have already been proven.~%" *red* *black*)
(let* ((clause1 (list-fix (car goals)))
(clause1-split (clause.split liftp liftlimit splitlimit clause1))
(split-len (len (cdr clause1-split))))
(if (not (car clause1-split))
(ACL2::cw "~s0Split-first-tac failure~s1: the clause cannot be split further.~%" *red* *black*)
(tactic.extend-skeleton (app (cdr clause1-split) (cdr goals))
'split-first
(list liftp liftlimit splitlimit split-len)
x))))))
(defthm forcing-tactic.skeletonp-of-tactic.split-first-tac
(implies (and (tactic.split-first-tac liftp liftlimit splitlimit x)
(force (tactic.skeletonp x)))
(equal (tactic.skeletonp (tactic.split-first-tac liftp liftlimit splitlimit x))
t))
:hints(("Goal" :in-theory (enable tactic.split-first-tac))))
(defthm forcing-tactic.split-first-okp-of-tactic.split-first-tac
(implies (and (tactic.split-first-tac liftp liftlimit splitlimit x)
(force (booleanp liftp))
(force (natp liftlimit))
(force (natp splitlimit))
(force (tactic.skeletonp x)))
(equal (tactic.split-first-okp (tactic.split-first-tac liftp liftlimit splitlimit x))
t))
:hints(("Goal" :in-theory (enable tactic.split-first-tac tactic.split-first-okp))))
(defund tactic.split-first-compile (x proofs)
(declare (xargs :guard (and (tactic.skeletonp x)
(tactic.split-first-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs)))
:verify-guards nil))
(let* ((history (tactic.skeleton->history x))
(old-goals (tactic.skeleton->goals history))
(clause1 (list-fix (car old-goals)))
(extras (tactic.skeleton->extras x))
(liftp (first extras))
(liftlimit (second extras))
(splitlimit (third extras))
(len (fourth extras))
(split-proofs (firstn len proofs))
(other-proofs (restn len proofs))
(clause1-proof (clause.split-bldr liftp liftlimit splitlimit clause1 split-proofs)))
(cons clause1-proof other-proofs)))
(defobligations tactic.split-first-compile
(clause.split-bldr))
(encapsulate
()
(local (in-theory (enable tactic.split-first-okp tactic.split-first-compile)))
(local (defthm crock
(implies (and (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (firstn n goals) y))
(equal (logic.strip-conclusions (firstn n proofs))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas y))))
:hints(("Goal"
:in-theory (disable firstn-of-logic.disjoin-each-formula-list)
:use ((:instance firstn-of-logic.disjoin-each-formula-list
(x (logic.term-list-list-formulas goals))
(y n)))))))
(local (defthm crock2
(implies (and (equal (logic.disjoin-each-formula-list (logic.term-list-list-formulas goals))
(logic.strip-conclusions proofs))
(equal (restn n goals) y))
(equal (logic.strip-conclusions (restn n proofs))
(logic.disjoin-each-formula-list (logic.term-list-list-formulas y))))
:hints(("Goal"
:in-theory (disable restn-of-logic.disjoin-each-formula-list)
:use ((:instance restn-of-logic.disjoin-each-formula-list
(x (logic.term-list-list-formulas goals))
(y n)))))))
(verify-guards tactic.split-first-compile)
(defthm forcing-logic.appeal-listp-of-tactic.split-first-compile
(implies (force (and (tactic.skeletonp x)
(tactic.split-first-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs))))
(equal (logic.appeal-listp (tactic.split-first-compile x proofs))
t)))
(defthm forcing-logic.strip-conclusions-of-tactic.split-first-compile
(implies (force (and (tactic.skeletonp x)
(tactic.split-first-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs))))
(equal (logic.strip-conclusions (tactic.split-first-compile x proofs))
(clause.clause-list-formulas (tactic.skeleton->goals (tactic.skeleton->history x))))))
(defthm@ forcing-logic.proof-listp-of-tactic.split-first-compile
(implies (force (and (tactic.skeletonp x)
(tactic.split-first-okp x)
(logic.appeal-listp proofs)
(equal (clause.clause-list-formulas (tactic.skeleton->goals x))
(logic.strip-conclusions proofs))
;; ---
(tactic.skeleton-atblp x atbl)
(equal (cdr (lookup 'if atbl)) 3)
(equal (cdr (lookup 'iff atbl)) 2)
(equal (cdr (lookup 'not atbl)) 1)
(equal (cdr (lookup 'equal atbl)) 2)
(logic.proof-listp proofs axioms thms atbl)
(@obligations tactic.split-first-compile)))
(equal (logic.proof-listp (tactic.split-first-compile x proofs) axioms thms atbl)
t))))
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