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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 "waterfall-steps")
(%interactive)
(%autoadmit rw.flag-waterfall)
(%autoadmit rw.waterfall)
(%autoadmit rw.waterfall-list)
(%autoprove definition-of-rw.waterfall
(%restrict default rw.flag-waterfall (and (equal x 'x) (equal steps 'steps)))
(%enable default rw.waterfall rw.waterfall-list))
(%autoprove definition-of-rw.waterfall-list
(%restrict default rw.flag-waterfall (and (equal x 'x) (equal steps 'steps)))
(%enable default rw.waterfall rw.waterfall-list))
(%autoprove rw.flag-waterfall-of-clause
(%enable default rw.waterfall))
(%autoprove rw.flag-waterfall-of-list
(%enable default rw.waterfall-list))
(%autoprove rw.waterfall-list-when-not-consp
(%restrict default definition-of-rw.waterfall-list (equal x 'x)))
(%autoprove rw.waterfall-list-of-cons
(%restrict default definition-of-rw.waterfall-list (equal x '(cons a x))))
(%defprojection :list (rw.waterfall-list x theoryname cfastp ufastp world steps strategy n)
:element (rw.waterfall x theoryname cfastp ufastp world steps strategy n)
:nil-preservingp nil)
;; BOZO. Wow, these, uh, completely do not belong here at all...
(%autoprove true-listp-of-clause.make-clause-from-arbitrary-formula
(%enable default clause.make-clause-from-arbitrary-formula))
(%autoprove true-list-listp-of-clause.make-clauses-from-arbitrary-formulas
(%autoinduct clause.make-clauses-from-arbitrary-formulas)
(%restrict default clause.make-clauses-from-arbitrary-formulas (equal x 'x)))
(%autoprove lemma-2-for-rw.waterstepp-of-rw.waterfall
;; disabled!
(%enable default
rw.make-crewrite-clause-plan
rw.crewrite-clause-plan->clause-prime))
(%autoprove lemma-for-rw.waterstepp-of-rw.waterfall
(%autoinduct rw.flag-waterfall)
(%forcingp nil)
(%waterfall default 40)
(%restrict default definition-of-rw.waterfall (and (equal x 'x)
(equal steps 'steps)))
(%enable default lemma-2-for-rw.waterstepp-of-rw.waterfall)
(%waterfall default 40))
(%autoprove rw.waterstepp-of-rw.waterfall
(%use (%instance (%thm lemma-for-rw.waterstepp-of-rw.waterfall)
(flag 'clause))))
(%autoprove rw.waterstep-listp-of-rw.waterfall-list
(%use (%instance (%thm lemma-for-rw.waterstepp-of-rw.waterfall)
(flag 'list))))
(%autoprove lemma-1-for-rw.waterstep-atblp-of-rw.waterfall
(%enable default rw.ccstep->clause-prime))
(%autoprove lemma-2-for-rw.waterstep-atblp-of-rw.waterfall
(%autoinduct rw.ccstep-list-gather-traces)
(%restrict default rw.ccstep-list-gather-traces (equal x 'x))
(%enable default rw.ccstep->provedp rw.ccstep->contradiction))
(%autoprove lemma-3-for-rw.waterstep-atblp-of-rw.waterfall
(%autoinduct rw.ccstep-list-hypboxes)
(%restrict default rw.ccstep-list-hypboxes (equal x 'x)))
(%autoprove lemma-4-for-rw.waterstep-atblp-of-rw.waterfall
(%enable default lemma-1-for-rw.waterstep-atblp-of-rw.waterfall))
(%autoprove lemma-5-for-rw.waterstep-atblp-of-rw.waterfall
(%enable default
rw.crewrite-clause-planp
rw.crewrite-clause-plan-atblp
rw.crewrite-clause-plan-okp
rw.crewrite-clause-plan->clause
rw.crewrite-clause-plan->clause-prime
lemma-1-for-rw.waterstep-atblp-of-rw.waterfall
lemma-2-for-rw.waterstep-atblp-of-rw.waterfall
lemma-3-for-rw.waterstep-atblp-of-rw.waterfall
lemma-4-for-rw.waterstep-atblp-of-rw.waterfall)
;; huh.. acl2 had to fertilize? we don't?
)
;; The acl2 proof below uses restrict hints to fix problems with free var matching
;; our system doesn't work quite the same -- we'll introduce alt-rules instead.
(defthmd lemma-5-for-rw.waterstep-atblp-of-rw.waterfall-alt
(implies (force (and (tactic.worldp world)
(rw.crewrite-clause-planp x)
(rw.crewrite-clause-plan-atblp x atbl)
(rw.crewrite-clause-plan-okp x world)
(tactic.world-atblp world atbl)
(equal (cdr (lookup 'not atbl)) 1)
(equal (cdr (lookup 'equal atbl)) 2)
(equal (cdr (lookup 'iff atbl)) 2)
(equal (cdr (lookup 'if atbl)) 3)))
(equal (logic.term-list-atblp
(rw.crewrite-clause-plan->clause-prime x)
atbl)
t))
:hints(("goal" :in-theory (enable lemma-5-for-rw.waterstep-atblp-of-rw.waterfall))))
(%autoprove lemma-5-for-rw.waterstep-atblp-of-rw.waterfall-alt
(%enable default lemma-5-for-rw.waterstep-atblp-of-rw.waterfall))
(defthm logic.formula-list-atblp-of-rw.crewrite-clause-plan->forced-goals-alt
(implies (force (and (tactic.worldp world)
(rw.crewrite-clause-planp x)
(rw.crewrite-clause-plan-okp x world)
(rw.crewrite-clause-plan-atblp x atbl)
(tactic.world-atblp world atbl)
(equal (cdr (lookup 'not atbl)) 1)
(equal (cdr (lookup 'equal atbl)) 2)
(equal (cdr (lookup 'iff atbl)) 2)
(equal (cdr (lookup 'if atbl)) 3)))
(equal (logic.formula-list-atblp
(rw.crewrite-clause-plan->forced-goals x)
atbl)
t)))
(%autoprove logic.formula-list-atblp-of-rw.crewrite-clause-plan->forced-goals-alt)
(%autoprove lemma-for-rw.waterstep-atblp-of-rw.waterfall
(%autoinduct rw.flag-waterfall)
(%forcingp nil)
(%disable default
expensive-term/formula-inference
formula-decomposition
unusual-memberp-rules
unusual-subsetp-rules
unusual-consp-rules
type-set-like-rules
expensive-arithmetic-rules
expensive-arithmetic-rules-two
same-length-prefixes-equal-cheap)
(%waterfall default 40)
(%enable default
lemma-1-for-rw.waterstep-atblp-of-rw.waterfall
lemma-2-for-rw.waterstep-atblp-of-rw.waterfall
lemma-3-for-rw.waterstep-atblp-of-rw.waterfall
lemma-4-for-rw.waterstep-atblp-of-rw.waterfall
lemma-5-for-rw.waterstep-atblp-of-rw.waterfall
lemma-5-for-rw.waterstep-atblp-of-rw.waterfall-alt
lemma-2-for-rw.waterstepp-of-rw.waterfall)
(%restrict default definition-of-rw.waterfall (and (equal x 'x) (equal steps 'steps)))
(%waterfall default 40))
(%autoprove rw.waterstep-atblp-of-rw.waterfall
(%use (%instance (%thm lemma-for-rw.waterstep-atblp-of-rw.waterfall)
(flag 'clause))))
(%autoprove rw.waterstep-list-atblp-of-rw.waterfall-list
(%use (%instance (%thm lemma-for-rw.waterstep-atblp-of-rw.waterfall)
(flag 'list))))
(%autoprove lemma-for-rw.waterstep->clause-of-rw.waterfall
(%autoinduct rw.flag-waterfall)
(%forcingp nil)
(%waterfall default 40)
(%restrict default definition-of-rw.waterfall (and (equal x 'x) (equal steps 'steps))))
(%autoprove rw.waterstep->clause-of-rw.waterfall
(%use (%instance (%thm lemma-for-rw.waterstep->clause-of-rw.waterfall)
(flag 'clause))))
(%autoprove rw.waterstep-list->clauses-of-rw.waterfall-list
(%use (%instance (%thm lemma-for-rw.waterstep->clause-of-rw.waterfall)
(flag 'list))))
(%autoprove lemma-for-rw.waterstep-okp-of-rw.waterfall
(%autoinduct rw.flag-waterfall)
(%forcingp nil)
(%disable default
expensive-term/formula-inference
formula-decomposition
unusual-memberp-rules
unusual-subsetp-rules
unusual-consp-rules
type-set-like-rules
expensive-arithmetic-rules
expensive-arithmetic-rules-two
same-length-prefixes-equal-cheap)
(%waterfall default 40)
(%restrict default definition-of-rw.waterfall (and (equal x 'x) (equal steps 'steps)))
(%waterfall default 40)
(%enable default
definition-of-rw.waterstep-okp
rw.stop-waterstep-okp
rw.crewrite-waterstep-okp
rw.split-waterstep-okp
rw.urewrite-waterstep-okp
lemma-2-for-rw.waterstepp-of-rw.waterfall)
(%waterfall default 40)
(%forcingp t)
(%enable default
expensive-term/formula-inference
formula-decomposition
unusual-memberp-rules
unusual-subsetp-rules
unusual-consp-rules
type-set-like-rules
expensive-arithmetic-rules
expensive-arithmetic-rules-two
same-length-prefixes-equal-cheap)
(%auto))
(%autoprove rw.waterstep-okp-of-rw.waterfall
(%use (%instance (%thm lemma-for-rw.waterstep-okp-of-rw.waterfall)
(flag 'clause))))
(%autoprove rw.waterstep-list-okp-of-rw.waterfall-list
(%use (%instance (%thm lemma-for-rw.waterstep-okp-of-rw.waterfall)
(flag 'list))))
|
