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572 lines
14 KiB
572 lines
14 KiB
/***** ltl2ba : parse.c *****/
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/* Written by Denis Oddoux, LIAFA, France */
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/* Copyright (c) 2001 Denis Oddoux */
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/* Modified by Paul Gastin, LSV, France */
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/* Copyright (c) 2007 Paul Gastin */
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/* */
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/* This program is free software; you can redistribute it and/or modify */
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/* it under the terms of the GNU General Public License as published by */
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/* the Free Software Foundation; either version 2 of the License, or */
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/* (at your option) any later version. */
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/* */
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/* This program is distributed in the hope that it will be useful, */
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/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
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/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
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/* GNU General Public License for more details. */
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/* */
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/* You should have received a copy of the GNU General Public License */
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/* along with this program; if not, write to the Free Software */
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/* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA*/
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/* */
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/* Based on the translation algorithm by Gastin and Oddoux, */
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/* presented at the 13th International Conference on Computer Aided */
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/* Verification, CAV 2001, Paris, France. */
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/* Proceedings - LNCS 2102, pp. 53-65 */
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/* */
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/* Send bug-reports and/or questions to Paul Gastin */
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/* http://www.lsv.ens-cachan.fr/~gastin */
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/* */
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/* Some of the code in this file was taken from the Spin software */
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/* Written by Gerard J. Holzmann, Bell Laboratories, U.S.A. */
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#include "ltl2ba.h"
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extern int tl_yylex(void);
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extern int tl_verbose, tl_simp_log;
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int tl_yychar = 0;
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YYSTYPE tl_yylval;
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static Node *tl_formula(void);
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static Node *tl_factor(void);
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static Node *tl_level(int);
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static int prec[2][4] = {
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{ U_OPER, V_OPER, 0, 0}, /* left associative */
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{ OR, AND, IMPLIES, EQUIV, }, /* left associative */
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};
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static int
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implies(Node *a, Node *b)
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{
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return
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(isequal(a,b) ||
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b->ntyp == TRUE ||
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a->ntyp == FALSE ||
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(b->ntyp == AND && implies(a, b->lft) && implies(a, b->rgt)) ||
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(a->ntyp == OR && implies(a->lft, b) && implies(a->rgt, b)) ||
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(a->ntyp == AND && (implies(a->lft, b) || implies(a->rgt, b))) ||
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(b->ntyp == OR && (implies(a, b->lft) || implies(a, b->rgt))) ||
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(b->ntyp == U_OPER && implies(a, b->rgt)) ||
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(a->ntyp == V_OPER && implies(a->rgt, b)) ||
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(a->ntyp == U_OPER && implies(a->lft, b) && implies(a->rgt, b)) ||
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(b->ntyp == V_OPER && implies(a, b->lft) && implies(a, b->rgt)) ||
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((a->ntyp == U_OPER || a->ntyp == V_OPER) && a->ntyp == b->ntyp &&
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implies(a->lft, b->lft) && implies(a->rgt, b->rgt)));
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}
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static Node *
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bin_simpler(Node *ptr)
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{ Node *a, *b;
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if (ptr)
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switch (ptr->ntyp) {
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case U_OPER:
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if (ptr->rgt->ntyp == TRUE
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|| ptr->rgt->ntyp == FALSE
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|| ptr->lft->ntyp == FALSE)
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{ ptr = ptr->rgt;
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break;
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}
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if (implies(ptr->lft, ptr->rgt)) /* NEW */
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{ ptr = ptr->rgt;
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break;
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}
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if (ptr->lft->ntyp == U_OPER
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&& isequal(ptr->lft->lft, ptr->rgt))
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{ /* (p U q) U p = (q U p) */
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ptr->lft = ptr->lft->rgt;
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break;
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}
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if (ptr->rgt->ntyp == U_OPER
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&& implies(ptr->lft, ptr->rgt->lft))
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{ /* NEW */
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ptr = ptr->rgt;
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break;
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}
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#ifdef NXT
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/* X p U X q == X (p U q) */
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if (ptr->rgt->ntyp == NEXT
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&& ptr->lft->ntyp == NEXT)
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{ ptr = tl_nn(NEXT,
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tl_nn(U_OPER,
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ptr->lft->lft,
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ptr->rgt->lft), ZN);
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break;
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}
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/* NEW : F X p == X F p */
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if (ptr->lft->ntyp == TRUE &&
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ptr->rgt->ntyp == NEXT) {
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ptr = tl_nn(NEXT, tl_nn(U_OPER, True, ptr->rgt->lft), ZN);
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break;
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}
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#endif
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/* NEW : F G F p == G F p */
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if (ptr->lft->ntyp == TRUE &&
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ptr->rgt->ntyp == V_OPER &&
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ptr->rgt->lft->ntyp == FALSE &&
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ptr->rgt->rgt->ntyp == U_OPER &&
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ptr->rgt->rgt->lft->ntyp == TRUE) {
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ptr = ptr->rgt;
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break;
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}
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/* NEW */
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if (ptr->lft->ntyp != TRUE &&
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implies(push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN)),
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ptr->lft))
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{ ptr->lft = True;
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break;
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}
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break;
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case V_OPER:
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if (ptr->rgt->ntyp == FALSE
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|| ptr->rgt->ntyp == TRUE
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|| ptr->lft->ntyp == TRUE)
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{ ptr = ptr->rgt;
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break;
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}
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if (implies(ptr->rgt, ptr->lft))
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{ /* p V p = p */
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ptr = ptr->rgt;
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break;
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}
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/* F V (p V q) == F V q */
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if (ptr->lft->ntyp == FALSE
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&& ptr->rgt->ntyp == V_OPER)
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{ ptr->rgt = ptr->rgt->rgt;
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break;
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}
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#ifdef NXT
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/* NEW : G X p == X G p */
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if (ptr->lft->ntyp == FALSE &&
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ptr->rgt->ntyp == NEXT) {
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ptr = tl_nn(NEXT, tl_nn(V_OPER, False, ptr->rgt->lft), ZN);
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break;
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}
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#endif
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/* NEW : G F G p == F G p */
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if (ptr->lft->ntyp == FALSE &&
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ptr->rgt->ntyp == U_OPER &&
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ptr->rgt->lft->ntyp == TRUE &&
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ptr->rgt->rgt->ntyp == V_OPER &&
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ptr->rgt->rgt->lft->ntyp == FALSE) {
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ptr = ptr->rgt;
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break;
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}
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/* NEW */
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if (ptr->rgt->ntyp == V_OPER
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&& implies(ptr->rgt->lft, ptr->lft))
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{ ptr = ptr->rgt;
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break;
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}
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/* NEW */
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if (ptr->lft->ntyp != FALSE &&
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implies(ptr->lft,
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push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN))))
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{ ptr->lft = False;
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break;
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}
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break;
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#ifdef NXT
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case NEXT:
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/* NEW : X G F p == G F p */
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if (ptr->lft->ntyp == V_OPER &&
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ptr->lft->lft->ntyp == FALSE &&
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ptr->lft->rgt->ntyp == U_OPER &&
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ptr->lft->rgt->lft->ntyp == TRUE) {
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ptr = ptr->lft;
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break;
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}
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/* NEW : X F G p == F G p */
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if (ptr->lft->ntyp == U_OPER &&
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ptr->lft->lft->ntyp == TRUE &&
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ptr->lft->rgt->ntyp == V_OPER &&
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ptr->lft->rgt->lft->ntyp == FALSE) {
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ptr = ptr->lft;
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break;
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}
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break;
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#endif
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case IMPLIES:
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if (implies(ptr->lft, ptr->rgt))
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{ ptr = True;
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break;
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}
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ptr = tl_nn(OR, Not(ptr->lft), ptr->rgt);
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ptr = rewrite(ptr);
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break;
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case EQUIV:
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if (implies(ptr->lft, ptr->rgt) &&
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implies(ptr->rgt, ptr->lft))
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{ ptr = True;
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break;
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}
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a = rewrite(tl_nn(AND,
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dupnode(ptr->lft),
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dupnode(ptr->rgt)));
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b = rewrite(tl_nn(AND,
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Not(ptr->lft),
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Not(ptr->rgt)));
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ptr = tl_nn(OR, a, b);
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ptr = rewrite(ptr);
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break;
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case AND:
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/* p && (q U p) = p */
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if (ptr->rgt->ntyp == U_OPER
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&& isequal(ptr->rgt->rgt, ptr->lft))
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{ ptr = ptr->lft;
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break;
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}
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if (ptr->lft->ntyp == U_OPER
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&& isequal(ptr->lft->rgt, ptr->rgt))
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{ ptr = ptr->rgt;
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break;
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}
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/* p && (q V p) == q V p */
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if (ptr->rgt->ntyp == V_OPER
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&& isequal(ptr->rgt->rgt, ptr->lft))
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{ ptr = ptr->rgt;
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break;
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}
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if (ptr->lft->ntyp == V_OPER
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&& isequal(ptr->lft->rgt, ptr->rgt))
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{ ptr = ptr->lft;
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break;
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}
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/* (p U q) && (r U q) = (p && r) U q*/
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if (ptr->rgt->ntyp == U_OPER
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&& ptr->lft->ntyp == U_OPER
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&& isequal(ptr->rgt->rgt, ptr->lft->rgt))
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{ ptr = tl_nn(U_OPER,
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tl_nn(AND, ptr->lft->lft, ptr->rgt->lft),
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ptr->lft->rgt);
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break;
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}
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/* (p V q) && (p V r) = p V (q && r) */
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if (ptr->rgt->ntyp == V_OPER
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&& ptr->lft->ntyp == V_OPER
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&& isequal(ptr->rgt->lft, ptr->lft->lft))
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{ ptr = tl_nn(V_OPER,
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ptr->rgt->lft,
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tl_nn(AND, ptr->lft->rgt, ptr->rgt->rgt));
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break;
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}
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#ifdef NXT
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/* X p && X q == X (p && q) */
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if (ptr->rgt->ntyp == NEXT
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&& ptr->lft->ntyp == NEXT)
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{ ptr = tl_nn(NEXT,
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tl_nn(AND,
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ptr->rgt->lft,
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ptr->lft->lft), ZN);
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break;
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}
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#endif
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/* (p V q) && (r U q) == p V q */
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if (ptr->rgt->ntyp == U_OPER
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&& ptr->lft->ntyp == V_OPER
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&& isequal(ptr->lft->rgt, ptr->rgt->rgt))
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{ ptr = ptr->lft;
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break;
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}
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if (isequal(ptr->lft, ptr->rgt) /* (p && p) == p */
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|| ptr->rgt->ntyp == FALSE /* (p && F) == F */
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|| ptr->lft->ntyp == TRUE /* (T && p) == p */
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|| implies(ptr->rgt, ptr->lft))/* NEW */
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{ ptr = ptr->rgt;
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break;
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}
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if (ptr->rgt->ntyp == TRUE /* (p && T) == p */
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|| ptr->lft->ntyp == FALSE /* (F && p) == F */
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|| implies(ptr->lft, ptr->rgt))/* NEW */
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{ ptr = ptr->lft;
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break;
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}
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/* NEW : F G p && F G q == F G (p && q) */
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if (ptr->lft->ntyp == U_OPER &&
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ptr->lft->lft->ntyp == TRUE &&
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ptr->lft->rgt->ntyp == V_OPER &&
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ptr->lft->rgt->lft->ntyp == FALSE &&
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ptr->rgt->ntyp == U_OPER &&
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ptr->rgt->lft->ntyp == TRUE &&
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ptr->rgt->rgt->ntyp == V_OPER &&
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ptr->rgt->rgt->lft->ntyp == FALSE)
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{
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ptr = tl_nn(U_OPER, True,
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tl_nn(V_OPER, False,
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tl_nn(AND, ptr->lft->rgt->rgt,
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ptr->rgt->rgt->rgt)));
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break;
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}
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/* NEW */
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if (implies(ptr->lft,
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push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN)))
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|| implies(ptr->rgt,
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push_negation(tl_nn(NOT, dupnode(ptr->lft), ZN))))
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{ ptr = False;
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break;
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}
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break;
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case OR:
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/* p || (q U p) == q U p */
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if (ptr->rgt->ntyp == U_OPER
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&& isequal(ptr->rgt->rgt, ptr->lft))
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{ ptr = ptr->rgt;
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break;
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}
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/* p || (q V p) == p */
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if (ptr->rgt->ntyp == V_OPER
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&& isequal(ptr->rgt->rgt, ptr->lft))
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{ ptr = ptr->lft;
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break;
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}
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/* (p U q) || (p U r) = p U (q || r) */
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if (ptr->rgt->ntyp == U_OPER
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&& ptr->lft->ntyp == U_OPER
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&& isequal(ptr->rgt->lft, ptr->lft->lft))
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{ ptr = tl_nn(U_OPER,
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ptr->rgt->lft,
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tl_nn(OR, ptr->lft->rgt, ptr->rgt->rgt));
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break;
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}
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if (isequal(ptr->lft, ptr->rgt) /* (p || p) == p */
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|| ptr->rgt->ntyp == FALSE /* (p || F) == p */
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|| ptr->lft->ntyp == TRUE /* (T || p) == T */
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|| implies(ptr->rgt, ptr->lft))/* NEW */
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{ ptr = ptr->lft;
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break;
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}
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if (ptr->rgt->ntyp == TRUE /* (p || T) == T */
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|| ptr->lft->ntyp == FALSE /* (F || p) == p */
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|| implies(ptr->lft, ptr->rgt))/* NEW */
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{ ptr = ptr->rgt;
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break;
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}
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/* (p V q) || (r V q) = (p || r) V q */
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if (ptr->rgt->ntyp == V_OPER
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&& ptr->lft->ntyp == V_OPER
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&& isequal(ptr->lft->rgt, ptr->rgt->rgt))
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{ ptr = tl_nn(V_OPER,
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tl_nn(OR, ptr->lft->lft, ptr->rgt->lft),
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ptr->rgt->rgt);
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break;
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}
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/* (p V q) || (r U q) == r U q */
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if (ptr->rgt->ntyp == U_OPER
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&& ptr->lft->ntyp == V_OPER
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&& isequal(ptr->lft->rgt, ptr->rgt->rgt))
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{ ptr = ptr->rgt;
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break;
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}
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/* NEW : G F p || G F q == G F (p || q) */
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if (ptr->lft->ntyp == V_OPER &&
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ptr->lft->lft->ntyp == FALSE &&
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ptr->lft->rgt->ntyp == U_OPER &&
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ptr->lft->rgt->lft->ntyp == TRUE &&
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ptr->rgt->ntyp == V_OPER &&
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ptr->rgt->lft->ntyp == FALSE &&
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ptr->rgt->rgt->ntyp == U_OPER &&
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ptr->rgt->rgt->lft->ntyp == TRUE)
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{
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ptr = tl_nn(V_OPER, False,
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tl_nn(U_OPER, True,
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tl_nn(OR, ptr->lft->rgt->rgt,
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ptr->rgt->rgt->rgt)));
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break;
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}
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/* NEW */
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if (implies(push_negation(tl_nn(NOT, dupnode(ptr->rgt), ZN)),
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ptr->lft)
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|| implies(push_negation(tl_nn(NOT, dupnode(ptr->lft), ZN)),
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ptr->rgt))
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{ ptr = True;
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break;
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}
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break;
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}
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return ptr;
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}
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|
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static Node *
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bin_minimal(Node *ptr)
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{ if (ptr)
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switch (ptr->ntyp) {
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case IMPLIES:
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return tl_nn(OR, Not(ptr->lft), ptr->rgt);
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case EQUIV:
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return tl_nn(OR,
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tl_nn(AND,dupnode(ptr->lft),dupnode(ptr->rgt)),
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tl_nn(AND,Not(ptr->lft),Not(ptr->rgt)));
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}
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return ptr;
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}
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static Node *
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tl_factor(void)
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{ Node *ptr = ZN;
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|
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switch (tl_yychar) {
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case '(':
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ptr = tl_formula();
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if (tl_yychar != ')')
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tl_yyerror("expected ')'");
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tl_yychar = tl_yylex();
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goto simpl;
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case NOT:
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ptr = tl_yylval;
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tl_yychar = tl_yylex();
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ptr->lft = tl_factor();
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ptr = push_negation(ptr);
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goto simpl;
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case ALWAYS:
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tl_yychar = tl_yylex();
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ptr = tl_factor();
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if(tl_simp_log) {
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if (ptr->ntyp == FALSE
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|| ptr->ntyp == TRUE)
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|
break; /* [] false == false */
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if (ptr->ntyp == V_OPER)
|
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{ if (ptr->lft->ntyp == FALSE)
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break; /* [][]p = []p */
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ptr = ptr->rgt; /* [] (p V q) = [] q */
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}
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}
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ptr = tl_nn(V_OPER, False, ptr);
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goto simpl;
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#ifdef NXT
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case NEXT:
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tl_yychar = tl_yylex();
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ptr = tl_factor();
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if ((ptr->ntyp == TRUE || ptr->ntyp == FALSE)&& tl_simp_log)
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break; /* X true = true , X false = false */
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ptr = tl_nn(NEXT, ptr, ZN);
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goto simpl;
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|
#endif
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case EVENTUALLY:
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|
tl_yychar = tl_yylex();
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|
|
|
ptr = tl_factor();
|
|
|
|
if(tl_simp_log) {
|
|
if (ptr->ntyp == TRUE
|
|
|| ptr->ntyp == FALSE)
|
|
break; /* <> true == true */
|
|
|
|
if (ptr->ntyp == U_OPER
|
|
&& ptr->lft->ntyp == TRUE)
|
|
break; /* <><>p = <>p */
|
|
|
|
if (ptr->ntyp == U_OPER)
|
|
{ /* <> (p U q) = <> q */
|
|
ptr = ptr->rgt;
|
|
/* fall thru */
|
|
}
|
|
}
|
|
|
|
ptr = tl_nn(U_OPER, True, ptr);
|
|
simpl:
|
|
if (tl_simp_log)
|
|
ptr = bin_simpler(ptr);
|
|
break;
|
|
case PREDICATE:
|
|
ptr = tl_yylval;
|
|
tl_yychar = tl_yylex();
|
|
break;
|
|
case TRUE:
|
|
case FALSE:
|
|
ptr = tl_yylval;
|
|
tl_yychar = tl_yylex();
|
|
break;
|
|
}
|
|
if (!ptr) tl_yyerror("expected predicate");
|
|
#if 0
|
|
printf("factor: ");
|
|
tl_explain(ptr->ntyp);
|
|
printf("\n");
|
|
#endif
|
|
return ptr;
|
|
}
|
|
|
|
static Node *
|
|
tl_level(int nr)
|
|
{ int i; Node *ptr = ZN;
|
|
|
|
if (nr < 0)
|
|
return tl_factor();
|
|
|
|
ptr = tl_level(nr-1);
|
|
again:
|
|
for (i = 0; i < 4; i++)
|
|
if (tl_yychar == prec[nr][i])
|
|
{ tl_yychar = tl_yylex();
|
|
ptr = tl_nn(prec[nr][i],
|
|
ptr, tl_level(nr-1));
|
|
if(tl_simp_log) ptr = bin_simpler(ptr);
|
|
else ptr = bin_minimal(ptr);
|
|
goto again;
|
|
}
|
|
if (!ptr) tl_yyerror("syntax error");
|
|
#if 0
|
|
printf("level %d: ", nr);
|
|
tl_explain(ptr->ntyp);
|
|
printf("\n");
|
|
#endif
|
|
return ptr;
|
|
}
|
|
|
|
static Node *
|
|
tl_formula(void)
|
|
{ tl_yychar = tl_yylex();
|
|
return tl_level(1); /* 2 precedence levels, 1 and 0 */
|
|
}
|
|
|
|
void
|
|
tl_parse(void)
|
|
{ Node *n = tl_formula();
|
|
if (tl_verbose)
|
|
{ printf("formula: ");
|
|
put_uform();
|
|
printf("\n");
|
|
}
|
|
trans(n);
|
|
}
|