tl_parse.c

这是一个同样来自贝尔实验室的和UNIX有着渊源的操作系统, 其简洁的设计和实现易于我们学习和理解

/***** tl_spin: tl_parse.c *****/

/* Copyright (c) 1995-2003 by Lucent Technologies, Bell Laboratories.     */
/* All Rights Reserved.  This software is for educational purposes only.  */
/* No guarantee whatsoever is expressed or implied by the distribution of */
/* this code.  Permission is given to distribute this code provided that  */
/* this introductory message is not removed and no monies are exchanged.  */
/* Software written by Gerard J. Holzmann.  For tool documentation see:   */
/*             http://spinroot.com/                                       */
/* Send all bug-reports and/or questions to: [e-mail]            */

/* Based on the translation algorithm by Gerth, Peled, Vardi, and Wolper, */
/* presented at the PSTV Conference, held in 1995, Warsaw, Poland 1995.   */

#include "tl.h"

extern int	tl_yylex(void);
extern int	tl_verbose;

int	tl_yychar = 0;
YYSTYPE	tl_yylval;

static Node	*tl_formula(void);
static Node	*tl_factor(void);
static Node	*tl_level(int);

static int	prec[2][4] = {
	{ U_OPER,  V_OPER, 0, 0 },	/* left associative */
	{ OR, AND, IMPLIES, EQUIV, },	/* left associative */
};

static Node *
tl_factor(void)
{	Node *ptr = ZN;

	switch (tl_yychar) {
	case '(':
		ptr = tl_formula();
		if (tl_yychar != ')')
			tl_yyerror("expected ')'");
		tl_yychar = tl_yylex();
		break;
	case NOT:
		ptr = tl_yylval;
		tl_yychar = tl_yylex();
		ptr->lft = tl_factor();
		ptr = push_negation(ptr);
		break;
	case ALWAYS:
		tl_yychar = tl_yylex();

		ptr = tl_factor();
#ifndef NO_OPT
		if (ptr->ntyp == FALSE
		||  ptr->ntyp == TRUE)
			break;	/* [] false == false */

		if (ptr->ntyp == V_OPER)
		{	if (ptr->lft->ntyp == FALSE)
				break;	/* [][]p = []p */

			ptr = ptr->rgt;	/* [] (p V q) = [] q */
		}
#endif
		ptr = tl_nn(V_OPER, False, ptr);
		break;
#ifdef NXT
	case NEXT:
		tl_yychar = tl_yylex();
		ptr = tl_factor();
		if (ptr->ntyp == TRUE)
			break;	/* X true = true */
		ptr = tl_nn(NEXT, ptr, ZN);
		break;
#endif
	case EVENTUALLY:
		tl_yychar = tl_yylex();

		ptr = tl_factor();
#ifndef NO_OPT
		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 */
		}
#endif
		ptr = tl_nn(U_OPER, True, 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 *
bin_simpler(Node *ptr)
{	Node *a, *b;

	if (ptr)
	switch (ptr->ntyp) {
	case U_OPER:
#ifndef NO_OPT
		if (ptr->rgt->ntyp == TRUE
		||  ptr->rgt->ntyp == FALSE
		||  ptr->lft->ntyp == FALSE)
		{	ptr = ptr->rgt;
			break;
		}
		if (isequal(ptr->lft, ptr->rgt))
		{	/* p U p = p */	
			ptr = ptr->rgt;
			break;
		}
		if (ptr->lft->ntyp == U_OPER
		&&  isequal(ptr->lft->lft, ptr->rgt))
		{	/* (p U q) U p = (q U p) */
			ptr->lft = ptr->lft->rgt;
			break;
		}
		if (ptr->rgt->ntyp == U_OPER
		&&  ptr->rgt->lft->ntyp == TRUE)
		{	/* p U (T U q)  = (T U q) */
			ptr = ptr->rgt;
			break;
		}
#ifdef NXT
		/* X p U X q == X (p U q) */
		if (ptr->rgt->ntyp == NEXT
		&&  ptr->lft->ntyp == NEXT)
		{	ptr = tl_nn(NEXT,
				tl_nn(U_OPER,
					ptr->lft->lft,
					ptr->rgt->lft), ZN);
		}
#endif
#endif
		break;
	case V_OPER:
#ifndef NO_OPT
		if (ptr->rgt->ntyp == FALSE
		||  ptr->rgt->ntyp == TRUE
		||  ptr->lft->ntyp == TRUE)
		{	ptr = ptr->rgt;
			break;
		}
		if (isequal(ptr->lft, ptr->rgt))
		{	/* p V p = p */	
			ptr = ptr->rgt;
			break;
		}
		/* F V (p V q) == F V q */
		if (ptr->lft->ntyp == FALSE
		&&  ptr->rgt->ntyp == V_OPER)
		{	ptr->rgt = ptr->rgt->rgt;
			break;
		}
		/* p V (F V q) == F V q */
		if (ptr->rgt->ntyp == V_OPER
		&&  ptr->rgt->lft->ntyp == FALSE)
		{	ptr->lft = False;
			ptr->rgt = ptr->rgt->rgt;
			break;
		}
#endif
		break;
	case IMPLIES:
#ifndef NO_OPT
		if (isequal(ptr->lft, ptr->rgt))
		{	ptr = True;
			break;
		}
#endif
		ptr = tl_nn(OR, Not(ptr->lft), ptr->rgt);
		ptr = rewrite(ptr);
		break;
	case EQUIV:
#ifndef NO_OPT
		if (isequal(ptr->lft, ptr->rgt))
		{	ptr = True;
			break;
		}
#endif
		a = rewrite(tl_nn(AND,
			dupnode(ptr->lft),
			dupnode(ptr->rgt)));
		b = rewrite(tl_nn(AND,
			Not(ptr->lft),
			Not(ptr->rgt)));
		ptr = tl_nn(OR, a, b);
		ptr = rewrite(ptr);
		break;
	case AND:
#ifndef NO_OPT
		/* p && (q U p) = p */
		if (ptr->rgt->ntyp == U_OPER
		&&  isequal(ptr->rgt->rgt, ptr->lft))
		{	ptr = ptr->lft;
			break;
		}
		if (ptr->lft->ntyp == U_OPER
		&&  isequal(ptr->lft->rgt, ptr->rgt))
		{	ptr = ptr->rgt;
			break;
		}

		/* p && (q V p) == q V p */
		if (ptr->rgt->ntyp == V_OPER
		&&  isequal(ptr->rgt->rgt, ptr->lft))
		{	ptr = ptr->rgt;
			break;
		}
		if (ptr->lft->ntyp == V_OPER
		&&  isequal(ptr->lft->rgt, ptr->rgt))
		{	ptr = ptr->lft;
			break;
		}

		/* (p U q) && (r U q) = (p && r) U q*/
		if (ptr->rgt->ntyp == U_OPER
		&&  ptr->lft->ntyp == U_OPER
		&&  isequal(ptr->rgt->rgt, ptr->lft->rgt))
		{	ptr = tl_nn(U_OPER,
				tl_nn(AND, ptr->lft->lft, ptr->rgt->lft),
				ptr->lft->rgt);
			break;
		}

		/* (p V q) && (p V r) = p V (q && r) */
		if (ptr->rgt->ntyp == V_OPER
		&&  ptr->lft->ntyp == V_OPER
		&&  isequal(ptr->rgt->lft, ptr->lft->lft))
		{	ptr = tl_nn(V_OPER,
				ptr->rgt->lft,
				tl_nn(AND, ptr->lft->rgt, ptr->rgt->rgt));
			break;
		}
#ifdef NXT
		/* X p && X q == X (p && q) */
		if (ptr->rgt->ntyp == NEXT
		&&  ptr->lft->ntyp == NEXT)
		{	ptr = tl_nn(NEXT,
				tl_nn(AND,
					ptr->rgt->lft,
					ptr->lft->lft), ZN);
			break;
		}
#endif

		if (isequal(ptr->lft, ptr->rgt)	/* (p && p) == p */
		||  ptr->rgt->ntyp == FALSE	/* (p && F) == F */
		||  ptr->lft->ntyp == TRUE)	/* (T && p) == p */
		{	ptr = ptr->rgt;
			break;
		}	
		if (ptr->rgt->ntyp == TRUE	/* (p && T) == p */
		||  ptr->lft->ntyp == FALSE)	/* (F && p) == F */
		{	ptr = ptr->lft;
			break;
		}

		/* (p V q) && (r U q) == p V q */
		if (ptr->rgt->ntyp == U_OPER
		&&  ptr->lft->ntyp == V_OPER
		&&  isequal(ptr->lft->rgt, ptr->rgt->rgt))
		{	ptr = ptr->lft;
			break;
		}
#endif
		break;

	case OR:
#ifndef NO_OPT
		/* p || (q U p) == q U p */
		if (ptr->rgt->ntyp == U_OPER
		&&  isequal(ptr->rgt->rgt, ptr->lft))
		{	ptr = ptr->rgt;
			break;
		}

		/* p || (q V p) == p */
		if (ptr->rgt->ntyp == V_OPER
		&&  isequal(ptr->rgt->rgt, ptr->lft))
		{	ptr = ptr->lft;
			break;
		}

		/* (p U q) || (p U r) = p U (q || r) */
		if (ptr->rgt->ntyp == U_OPER
		&&  ptr->lft->ntyp == U_OPER
		&&  isequal(ptr->rgt->lft, ptr->lft->lft))
		{	ptr = tl_nn(U_OPER,
				ptr->rgt->lft,
				tl_nn(OR, ptr->lft->rgt, ptr->rgt->rgt));
			break;
		}

		if (isequal(ptr->lft, ptr->rgt)	/* (p || p) == p */
		||  ptr->rgt->ntyp == FALSE	/* (p || F) == p */
		||  ptr->lft->ntyp == TRUE)	/* (T || p) == T */
		{	ptr = ptr->lft;
			break;
		}	
		if (ptr->rgt->ntyp == TRUE	/* (p || T) == T */
		||  ptr->lft->ntyp == FALSE)	/* (F || p) == p */
		{	ptr = ptr->rgt;
			break;
		}

		/* (p V q) || (r V q) = (p || r) V q */
		if (ptr->rgt->ntyp == V_OPER
		&&  ptr->lft->ntyp == V_OPER
		&&  isequal(ptr->lft->rgt, ptr->rgt->rgt))
		{	ptr = tl_nn(V_OPER,
				tl_nn(OR, ptr->lft->lft, ptr->rgt->lft),
				ptr->rgt->rgt);
			break;
		}

		/* (p V q) || (r U q) == r U q */
		if (ptr->rgt->ntyp == U_OPER
		&&  ptr->lft->ntyp == V_OPER
		&&  isequal(ptr->lft->rgt, ptr->rgt->rgt))
		{	ptr = ptr->rgt;
			break;
		}		
#endif
		break;
	}
	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));
			ptr = bin_simpler(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: ");
		dump(n);
		printf("\n");
	}
	trans(n);
}