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|
;;;-*-Mode:LISP; Package: CHAOS; Base:10; Syntax:Common-lisp -*-
;;;
;;; Copyright (c) 2000-2015, Toshimi Sawada. All rights reserved.
;;;
;;; Redistribution and use in source and binary forms, with or without
;;; modification, are permitted provided that the following conditions
;;; are met:
;;;
;;; * Redistributions of source code must retain the above copyright
;;; notice, this list of conditions and the following disclaimer.
;;;
;;; * Redistributions in binary form must reproduce the above
;;; copyright notice, this list of conditions and the following
;;; disclaimer in the documentation and/or other materials
;;; provided with the distribution.
;;;
;;; THIS SOFTWARE IS PROVIDED BY THE AUTHOR 'AS IS' AND ANY EXPRESSED
;;; OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
;;; WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
;;; ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
;;; DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
;;; DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
;;; GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
;;; INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
;;; WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
;;; NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
;;; SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
;;;
;;;
(in-package :chaos)
#|=============================================================================
System:Chaos
Module:BigPink
File:modconv.lisp
=============================================================================|#
#-:chaos-debug
(declaim (optimize (speed 3) (safety 0) #-GCL (debug 0)))
#+:chaos-debug
(declaim (optimize (speed 1) (safety 3) #-GCL (debug 3)))
;;; -----------------------------------------------
;;; CONVERTERS : CafeOBJ Axioms --> Fopl Sentences
;;; -----------------------------------------------
;;; MAKE-PIGNOSE-AXIOM
;;;
(defun make-pignose-axiom (lhs &key behavioural (type :pignose-axiom) label)
(make-rule :lhs lhs
:rhs *bool-true*
:condition *bool-true*
:labels label
:behavioural behavioural
:type type)
)
;;; AXIOM->FORMULA : Axiom -> FoplSentence
;;; convert CafeoBJ axiom (eq, ceq, beq, and cbeq) to FoplSentence
;;;
(declaim (special *elim-tf-in-axioms*))
(defvar *elim-tf-in-axioms* t)
(defun pn-set-tf-flag (value)
(declare (ignore value))
(if (pn-flag meta-paramod)
(setq *elim-tf-in-axioms* nil)
(setq *elim-tf-in-axioms* t)))
(defun pn-method-is-of-same-operator (m1 m2)
(declare (type method m1 m2))
(eq (method-operator m1)
(method-operator m2)))
#||
(eval-when (:execute :load-toplevel)
(setq .pn-ignore-ops.
(list *bool-and* ; _and_
*bool-or* ; _or_
*bool-not* ; not_
*sort-membership* ; _:<SortId>
*bool-if* ; if_then_else_fi
*bool-imply* ; _implies_
*bool-iff* ; _iff_
*bool-xor* ; _xor_
*bool-equal* ; _==_
*beh-equal* ; _=b=_
*bool-nonequal* ; _=/=_
*beh-eq-pred* ; _=*=_
*bool-and-also* ; _and-also_
*bool-or-else*))) ; _or-else_
||#
(defun axiom->formula (ax)
(declare (type axiom ax))
(when *debug-formula*
(format t "~%>> start axiom->formula conversion <<")
(print-next)
(print-chaos-object ax))
;; we ignore axioms of built-in Boolean operations
;; and, or, not, xor, ==, =/=, =b=, =*=, etc. user should be noticed.
(let* ((lhs (axiom-lhs ax))
(head (if (term-is-applform? lhs)
(term-head (axiom-lhs ax))
nil))
(type (axiom-type ax)))
(declare (type (or null method) head)
(type symbol type))
(when (and head
(member head .pn-ignore-ops.
:test #'pn-method-is-of-same-operator))
(when *chaos-verbose*
(with-output-chaos-warning ()
(format t "axiom to formula translation: ignoring axiom")
(print-next)
(print-chaos-object ax)))
(return-from axiom->formula nil))
;;
(case type
((:equation :pignose-axiom :pignose-goal)
#|| too early !!!
(when (eq type :pignose-goal)
;; we negate it before taking univeraly quantified closure:
(setq lhs (copy-term-reusing-variables lhs
(term-variables lhs)))
(setq lhs
(make-term-with-sort-check *fopl-neg*
(list lhs))))
||#
(let ((frm-lhs (cafeobj-term->formula lhs))
(frm-rhs (if (eq type :equation)
(cafeobj-term->formula (axiom-rhs ax))))
(frm-cond (if (eq type :equation)
(if (term-is-similar? *bool-true*
(axiom-condition ax))
nil
(cafeobj-term->formula (axiom-condition ax)))))
(frm nil)
(*elim-tf-in-axioms*
(if (not (eq (axiom-type ax) :equation))
t
*elim-tf-in-axioms*)))
(declare (type (or null term)
frm-lhs frm-rhs frm-cond frm))
;;
(when *elim-tf-in-axioms*
(when (term-is-similar? *bool-true* frm-lhs)
(setq frm-lhs nil))
(when (term-is-similar? *bool-true* frm-rhs)
(setq frm-rhs nil))
(when (term-is-similar? *bool-false* frm-lhs)
(setq frm-lhs nil)
(setq frm-rhs (make-term-with-sort-check
*fopl-neg*
(list frm-rhs))))
(when (term-is-similar? *bool-false* frm-rhs)
(setq frm-rhs nil)
(setq frm-lhs (make-term-with-sort-check
*fopl-neg*
(list frm-lhs))))
(unless frm-lhs
(setq frm-lhs frm-rhs)
(setq frm-rhs nil)))
;;
(if (and frm-lhs frm-rhs)
(if frm-cond
;; ~cond | lhs = rhs (cond -> lhs = rhs)
(setq frm (make-term-with-sort-check
*fopl-or*
(list (make-term-with-sort-check
*fopl-neg*
(list frm-cond))
(make-term-with-sort-check
(if (and *fopl-two-equalities*
(axiom-is-behavioural ax))
*fopl-beq*
*fopl-eq*)
(list frm-lhs frm-rhs)))))
;; lhs = rhs
(setq frm (make-term-with-sort-check
(if (and *fopl-two-equalities*
(axiom-is-behavioural ax))
*fopl-beq*
*fopl-eq*)
(list frm-lhs frm-rhs))))
;;
(if frm-cond
;; ~cond | lhs
(setq frm (make-term-with-sort-check
*fopl-or*
(list (make-term-with-sort-check
*fopl-neg*
(list frm-cond))
frm-lhs)))
;; lhs
(setq frm frm-lhs))
)
;;
(when *debug-formula*
(format t "~%>> done <<")
(print-next)
(term-print frm))
;; if the axioms is :pignose-goal, i.e. declared by
;; `goal', negate it.
(when (eq type :pignose-goal)
(setq frm (copy-term-reusing-variables frm
(term-variables frm)))
(normalize-quantifiers frm)
(setq frm (make-term-with-sort-check *fopl-neg*
(list frm))))
;;
frm))
(otherwise
(with-output-chaos-error ()
(format t "sorry, but transitions are not supported yet.")
(print-next)
(print-chaos-object ax)))
)))
;;; MODULE-AXIOMS->CLAUSE : Module -> List[Clause]
;;;
(defun module-all-equations (mod)
(declare (type module mod)
(values list))
(let ((*seen* nil))
(declare (special *seen*)
(type list *seen*))
(labels ((all-own-equations (mod)
(declare (type module mod))
(reverse (module-equations mod)))
(imported-equations (mod)
(declare (type module mod))
(let ((res nil)
(subs (nreverse (module-direct-submodules mod))))
(declare (type list res subs))
(dolist (sub subs)
(block next-sub
(let ((sm (car sub)))
(declare (type module sm))
(when (memq sm *seen*)
(return-from next-sub nil))
(push sm *seen*)
(when (eq :using (cdr sub))
(return-from next-sub nil))
(let ((sub-ax nil)
(to-be-fixed (module-axioms-to-be-fixed mod)))
(dolist (ax (all-own-equations sm))
(push (or (cdr (assq ax to-be-fixed))
ax)
sub-ax))
(setq res
(nconc res
(nconc (nreverse sub-ax)
(mapcar #'(lambda (x)
(or (cdr (assq x to-be-fixed))
x))
(imported-equations sm)))
))))))
;;
(delete-duplicates res :test #'eq))))
;;
(setq *seen* nil)
(nconc (all-own-equations mod)
(imported-equations mod))
)))
;;; MODULE-INCLUDES-FORMULA : Module -> Bool
;;; t iff module imports (semi)built-in FOPL module.
;;;
(defun module-includes-formula (mod)
(declare (type module mod))
(assq *fopl-sentence-module* (module-all-submodules mod)))
;;; MAKE-PN-APPL (mod method)
;;;
(defun make-pn-appl-pat (mod method)
(with-in-module (mod)
(make-term-with-sort-check
method
(mapcar #'(lambda (x)
(pn-make-var-on-the-fly x))
(method-arity method)))))
;;; COVER-SET-OF-SORT
;;;
(defun cover-set-of-sort (mod sort)
(declare (type module mod)
(type sort* sort)
(values list))
(let ((constructors (sort-constructors sort))
(res nil))
(declare (type list constructors res))
(dolist (constr constructors)
(push (make-pn-appl-pat mod constr) res))
res))
;;; MODULE-COVER-SETS : mod -> list ( < sort . cover-set >) ...)
;;;
(defun module-cover-sets (mod &optional (no-built-in t))
(declare (type module mod)
(values list))
(let ((res nil))
(dolist (sort (module-all-sorts mod))
(declare (type sort* sort))
(block next
(when (and no-built-in
(let ((smod (sort-module sort)))
(or (module-is-hard-wired smod)
(module-is-system-module smod))))
(return-from next nil))
(let ((cset (cover-set-of-sort mod sort)))
(when cset
(push (cons sort cset) res))))
)
res))
(defun get-all-methods-of-sort-strict (sort module)
(declare (type sort* sort)
(type module module))
(let ((res nil))
(declare (type list res))
(dolist (info (module-all-operators module))
(dolist (m (opinfo-methods info))
(unless (or (eq *void-method* m)
(is-skolem m module))
(when (sort= (method-coarity m) sort)
(push m res)))))
res))
;;; INTRO-EXISTS : formula ex-vars -> formula
;;;
(defun intro-exists (form vars)
(declare (type term form)
(type list vars))
(if (null vars)
form
(let ((var-decl nil))
(declare (type (or null term)))
(if (cdr vars)
(setq var-decl
(make-right-assoc-normal-form *var-decl-list*
vars))
(setq var-decl (car vars)))
(make-term-with-sort-check *fopl-exists*
(list var-decl form)))))
;;; PN-NO-JUNK
;;; genarates axioms of no-junk.
;;;
(defun pn-no-junk (mod)
(declare (type module mod))
#+:chaos-debug
(declare (notinline op-lex-compare))
(let ((csets (module-cover-sets mod))
(all-axioms nil))
(declare (type list csets))
(with-in-module (mod)
(dolist (cset csets)
(declare (type list cset))
(block next
(let* ((sort (car cset))
(covers (cdr cset))
(axioms nil))
(declare (type sort* sort)
(type list covers axioms))
(let ((constrs (sort-constructors sort))
(methods (get-all-methods-of-sort-strict sort mod))
(gen-methods nil))
(declare (type list constrs methods gen-methods))
;;
#|
(dolist (const constrs)
(when (method-arity const) (return-from next nil)))
|#
;;
(dolist (method methods)
(unless (memq method constrs)
(let* ((arg-1 (make-pn-appl-pat mod method))
(vars (term-variables arg-1))
(pat nil)
(axiom-lhs nil))
(declare (type term arg-1)
(list vars pat)
(type (or null term) axiom-lhs))
(dolist (cover covers)
(let* ((real-cover (term-unique-vars cover))
(cover-vars (term-variables real-cover))
(eq-pat (make-term-with-sort-check
*fopl-eq*
(list
(copy-term-reusing-variables arg-1 vars)
real-cover))))
(if (null cover-vars)
(push eq-pat pat)
;; cover pat contains vars.
;; introduce existential quantifier.
(push (intro-exists eq-pat cover-vars) pat))))
(if (cdr pat) ; more than one pat
(setq axiom-lhs
(make-right-assoc-normal-form *fopl-or*
pat))
(setq axiom-lhs (car pat)))
;;
(push (make-pignose-axiom axiom-lhs :label 'no-junk)
axioms)
(push method gen-methods)))
) ; done for all methods for a sort
;; redunduncy check. this is important
;; if there are some axioms of the form
;; foo(X) = bar(X)
;; and
;; foo > bar
;; foo from axioms.
(let ((do-delete nil))
(declare (type list do-delete))
(dolist (ax axioms)
(let* ((lhs (axiom-lhs ax))
(type (fopl-sentence-type lhs))
(lhs-meth nil)
(rules nil))
;; lhs ::=
;; | meth(x) = constr1 ...
;; | \E[...] X = Y ...
(when (eq type :or)
(setq lhs (term-arg-1 lhs))
(setq type (fopl-sentence-type lhs)))
(case type
(:eq (setq lhs (term-arg-1 lhs))
(setq lhs-meth (term-head lhs)))
(:exists (setq lhs (term-arg-1 (term-arg-2 lhs)))
(setq lhs-meth (term-head lhs)))
(otherwise
(with-output-panic-message ()
(format t "pn-no-junk: illegal type ~s" type)))
)
(when lhs-meth
(setq rules (method-rules-with-different-top lhs-meth)))
;;
(dolist (rule rules)
(let* ((rhs (rule-rhs rule)))
(when (and (term-is-application-form? rhs)
(let ((rhs-meth (term-head rhs)))
(and (memq rhs-meth gen-methods)
(eq :greater
(op-lex-compare lhs-meth
(term-head rhs))))
))
;;
(pushnew ax do-delete))))))
(dolist (ax do-delete)
(setq axioms (delete ax axioms))))
#||
(unless axioms
;; we make
;; var = consr1 | var = constr2 ...
(let ((var (pn-make-var-on-the-fly sort))
(pat nil)
(axiom-lhs nil))
(declare (type term var))
(dolist (cover covers)
(push
(make-term-with-sort-check
*fopl-eq*
(list
var
(term-unique-vars cover)))
pat))
(if (cdr pat) ; more than one pat
(setq axiom-lhs
(make-right-assoc-normal-form *fopl-or*
pat))
(setq axiom-lhs (car pat)))
;;
(push (make-pignose-axiom axiom-lhs :label 'no-junk)
axioms)))
||#
)
;;
(setq all-axioms (nconc all-axioms axioms))
))) ; done for a sort
all-axioms
)))
;;; PN-NO-CONFUSION
;;; generates axioms (clauses) of no-confusion.
;;;
(defun pn-no-confusion (mod)
(declare (type module mod))
(let ((csets (module-cover-sets mod))
(axioms nil))
(declare (type list csets axioms))
(with-in-module (mod)
(dolist (cset csets)
(declare (type list cset))
(let ((covers (cdr cset)))
(do ((pat-list covers (cdr pat-list)))
((endp pat-list))
(dolist (pat2 (cdr pat-list))
#||
;; ~(a = b)
(push (make-pignose-axiom
(make-term-with-sort-check
*fopl-neg*
(list (make-term-with-sort-check
*fopl-eq*
(list (term-unique-vars (car pat-list))
(term-unique-vars pat2)))))
:label 'no-conf)
axioms)
||#
;; (a = b) = false
(push (make-pignose-axiom
(make-term-with-sort-check
*fopl-eq*
(list (make-term-with-sort-check
*fopl-eq*
(list (term-unique-vars (car pat-list))
(term-unique-vars pat2)))
*bool-false*))
:label 'no-conf)
axioms)
))))
axioms
)))
;;; MODULE-AXIOMS->CLAUSE : Proof-sytem -> List[Clause]
;;;
(defun module-axioms->clause (psys &aux (mod (psystem-module psys)))
(declare (type psystem psys)
(type module mod))
(include-FOPL mod)
(compile-module mod)
(unless (module-includes-formula mod)
(with-output-chaos-error ('formula-error)
(princ "module does not import FOPL-CLAUSE module.")))
;;
(flet ((clause-is-valid-for-resolution (clause)
(declare (type clause clause))
(if (unit-clause? clause)
(let ((lit (car (clause-literals clause))))
(declare (type literal lit))
(if (positive-eq-literal? lit)
(if (term-is-lisp-form? (term-arg-2 (literal-atom lit)))
nil
t)
t))
t)))
(with-in-module (mod)
(let ((axs (module-all-equations mod))
(ax-clauses nil)
(demods nil)
(bi-demods nil))
(declare (type list axs ax-clauses demods))
(dolist (ax axs)
(let ((cls nil)
(bi-demod nil)
(demod nil))
(declare (type list cls demod))
(let ((lhs (axiom-lhs ax)))
(when (or (not (term-is-applform? lhs))
(not (method-is-meta-demod (term-head lhs))))
(dolist (cl (formula->clause-1
(axiom->formula ax)
psys
ax))
(declare (type clause cl))
(if (clause-is-builtin-demod cl)
(push cl bi-demod)
(if (clause-axiom-declared-as-demodulator cl)
(push cl demod)
(when (clause-is-valid-for-resolution cl)
(push cl cls)))))))
(setq ax-clauses (nconc ax-clauses (nreverse cls)))
(setq demods (nconc demods (nreverse demod)))
(setq bi-demods (nconc bi-demods (nreverse bi-demod)))))
(setf (psystem-axioms psys) ax-clauses)
(setf (psystem-demods psys) demods)
(setf (psystem-bi-demods psys) bi-demods))
;; no junk/ no confusion axioms if required
(when (pn-flag no-junk)
(let ((axs (pn-no-junk mod)))
(dolist (ax axs)
(dolist (cl (formula->clause-1
(axiom->formula ax)
psys
ax))
(declare (type clause cl))
(push cl (psystem-axioms psys))))))
(when (pn-flag no-confusion)
(let ((axs (pn-no-confusion mod)))
(dolist (ax axs)
(dolist (cl (formula->clause-1
(axiom->formula ax)
psys
ax))
(declare (type clause cl))
(push cl (psystem-axioms psys))))))
)))
;;; EOF
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