pgen.c

/***********************************************************
Copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam,
The Netherlands.

                        All Rights Reserved

Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that
both that copyright notice and this permission notice appear in
supporting documentation, and that the names of Stichting Mathematisch
Centrum or CWI or Corporation for National Research Initiatives or
CNRI not be used in advertising or publicity pertaining to
distribution of the software without specific, written prior
permission.

While CWI is the initial source for this software, a modified version
is made available by the Corporation for National Research Initiatives
(CNRI) at the Internet address ftp://ftp.python.org.

STICHTING MATHEMATISCH CENTRUM AND CNRI DISCLAIM ALL WARRANTIES WITH
REGARD TO THIS SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL STICHTING MATHEMATISCH
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TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR
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******************************************************************/

/* Parser generator */
/* XXX This file is not yet fully PROTOized */

/* For a description, see the comments at end of this file */

#include "pgenheaders.h"
#include "assert.h"
#include "token.h"
#include "node.h"
#include "grammar.h"
#include "metagrammar.h"
#include "pgen.h"

extern int Py_DebugFlag;


/* PART ONE -- CONSTRUCT NFA -- Cf. Algorithm 3.2 from [Aho&Ullman 77] */

typedef struct _nfaarc {
	int	ar_label;
	int	ar_arrow;
} nfaarc;

typedef struct _nfastate {
	int	st_narcs;
	nfaarc	*st_arc;
} nfastate;

typedef struct _nfa {
	int		nf_type;
	char		*nf_name;
	int		nf_nstates;
	nfastate	*nf_state;
	int		nf_start, nf_finish;
} nfa;

/* Forward */
static void compile_rhs Py_PROTO((labellist *ll,
			       nfa *nf, node *n, int *pa, int *pb));
static void compile_alt Py_PROTO((labellist *ll,
			       nfa *nf, node *n, int *pa, int *pb));
static void compile_item Py_PROTO((labellist *ll,
				nfa *nf, node *n, int *pa, int *pb));
static void compile_atom Py_PROTO((labellist *ll,
				nfa *nf, node *n, int *pa, int *pb));

static int
addnfastate(nf)
	nfa *nf;
{
	nfastate *st;
	
	PyMem_RESIZE(nf->nf_state, nfastate, nf->nf_nstates + 1);
	if (nf->nf_state == NULL)
		Py_FatalError("out of mem");
	st = &nf->nf_state[nf->nf_nstates++];
	st->st_narcs = 0;
	st->st_arc = NULL;
	return st - nf->nf_state;
}

static void
addnfaarc(nf, from, to, lbl)
	nfa *nf;
	int from, to, lbl;
{
	nfastate *st;
	nfaarc *ar;
	
	st = &nf->nf_state[from];
	PyMem_RESIZE(st->st_arc, nfaarc, st->st_narcs + 1);
	if (st->st_arc == NULL)
		Py_FatalError("out of mem");
	ar = &st->st_arc[st->st_narcs++];
	ar->ar_label = lbl;
	ar->ar_arrow = to;
}

static nfa *
newnfa(name)
	char *name;
{
	nfa *nf;
	static int type = NT_OFFSET; /* All types will be disjunct */
	
	nf = PyMem_NEW(nfa, 1);
	if (nf == NULL)
		Py_FatalError("no mem for new nfa");
	nf->nf_type = type++;
	nf->nf_name = name; /* XXX strdup(name) ??? */
	nf->nf_nstates = 0;
	nf->nf_state = NULL;
	nf->nf_start = nf->nf_finish = -1;
	return nf;
}

typedef struct _nfagrammar {
	int		gr_nnfas;
	nfa		**gr_nfa;
	labellist	gr_ll;
} nfagrammar;

/* Forward */
static void compile_rule Py_PROTO((nfagrammar *gr, node *n));

static nfagrammar *
newnfagrammar()
{
	nfagrammar *gr;
	
	gr = PyMem_NEW(nfagrammar, 1);
	if (gr == NULL)
		Py_FatalError("no mem for new nfa grammar");
	gr->gr_nnfas = 0;
	gr->gr_nfa = NULL;
	gr->gr_ll.ll_nlabels = 0;
	gr->gr_ll.ll_label = NULL;
	addlabel(&gr->gr_ll, ENDMARKER, "EMPTY");
	return gr;
}

static nfa *
addnfa(gr, name)
	nfagrammar *gr;
	char *name;
{
	nfa *nf;
	
	nf = newnfa(name);
	PyMem_RESIZE(gr->gr_nfa, nfa *, gr->gr_nnfas + 1);
	if (gr->gr_nfa == NULL)
		Py_FatalError("out of mem");
	gr->gr_nfa[gr->gr_nnfas++] = nf;
	addlabel(&gr->gr_ll, NAME, nf->nf_name);
	return nf;
}

#ifdef Py_DEBUG

static char REQNFMT[] = "metacompile: less than %d children\n";

#define REQN(i, count) \
 	if (i < count) { \
		fprintf(stderr, REQNFMT, count); \
		Py_FatalError("REQN"); \
	} else

#else
#define REQN(i, count)	/* empty */
#endif

static nfagrammar *
metacompile(n)
	node *n;
{
	nfagrammar *gr;
	int i;
	
	printf("Compiling (meta-) parse tree into NFA grammar\n");
	gr = newnfagrammar();
	REQ(n, MSTART);
	i = n->n_nchildren - 1; /* Last child is ENDMARKER */
	n = n->n_child;
	for (; --i >= 0; n++) {
		if (n->n_type != NEWLINE)
			compile_rule(gr, n);
	}
	return gr;
}

static void
compile_rule(gr, n)
	nfagrammar *gr;
	node *n;
{
	nfa *nf;
	
	REQ(n, RULE);
	REQN(n->n_nchildren, 4);
	n = n->n_child;
	REQ(n, NAME);
	nf = addnfa(gr, n->n_str);
	n++;
	REQ(n, COLON);
	n++;
	REQ(n, RHS);
	compile_rhs(&gr->gr_ll, nf, n, &nf->nf_start, &nf->nf_finish);
	n++;
	REQ(n, NEWLINE);
}

static void
compile_rhs(ll, nf, n, pa, pb)
	labellist *ll;
	nfa *nf;
	node *n;
	int *pa, *pb;
{
	int i;
	int a, b;
	
	REQ(n, RHS);
	i = n->n_nchildren;
	REQN(i, 1);
	n = n->n_child;
	REQ(n, ALT);
	compile_alt(ll, nf, n, pa, pb);
	if (--i <= 0)
		return;
	n++;
	a = *pa;
	b = *pb;
	*pa = addnfastate(nf);
	*pb = addnfastate(nf);
	addnfaarc(nf, *pa, a, EMPTY);
	addnfaarc(nf, b, *pb, EMPTY);
	for (; --i >= 0; n++) {
		REQ(n, VBAR);
		REQN(i, 1);
		--i;
		n++;
		REQ(n, ALT);
		compile_alt(ll, nf, n, &a, &b);
		addnfaarc(nf, *pa, a, EMPTY);
		addnfaarc(nf, b, *pb, EMPTY);
	}
}

static void
compile_alt(ll, nf, n, pa, pb)
	labellist *ll;
	nfa *nf;
	node *n;
	int *pa, *pb;
{
	int i;
	int a, b;
	
	REQ(n, ALT);
	i = n->n_nchildren;
	REQN(i, 1);
	n = n->n_child;
	REQ(n, ITEM);
	compile_item(ll, nf, n, pa, pb);
	--i;
	n++;
	for (; --i >= 0; n++) {
		if (n->n_type == COMMA) { /* XXX Temporary */
			REQN(i, 1);
			--i;
			n++;
		}
		REQ(n, ITEM);
		compile_item(ll, nf, n, &a, &b);
		addnfaarc(nf, *pb, a, EMPTY);
		*pb = b;
	}
}

static void
compile_item(ll, nf, n, pa, pb)
	labellist *ll;
	nfa *nf;
	node *n;
	int *pa, *pb;
{
	int i;
	int a, b;
	
	REQ(n, ITEM);
	i = n->n_nchildren;
	REQN(i, 1);
	n = n->n_child;
	if (n->n_type == LSQB) {
		REQN(i, 3);
		n++;
		REQ(n, RHS);
		*pa = addnfastate(nf);
		*pb = addnfastate(nf);
		addnfaarc(nf, *pa, *pb, EMPTY);
		compile_rhs(ll, nf, n, &a, &b);
		addnfaarc(nf, *pa, a, EMPTY);
		addnfaarc(nf, b, *pb, EMPTY);
		REQN(i, 1);
		n++;
		REQ(n, RSQB);
	}
	else {
		compile_atom(ll, nf, n, pa, pb);
		if (--i <= 0)
			return;
		n++;
		addnfaarc(nf, *pb, *pa, EMPTY);
		if (n->n_type == STAR)
			*pb = *pa;
		else
			REQ(n, PLUS);
	}
}

static void
compile_atom(ll, nf, n, pa, pb)
	labellist *ll;
	nfa *nf;
	node *n;
	int *pa, *pb;
{
	int i;
	
	REQ(n, ATOM);
	i = n->n_nchildren;
	REQN(i, 1);
	n = n->n_child;
	if (n->n_type == LPAR) {
		REQN(i, 3);
		n++;
		REQ(n, RHS);
		compile_rhs(ll, nf, n, pa, pb);
		n++;
		REQ(n, RPAR);
	}
	else if (n->n_type == NAME || n->n_type == STRING) {
		*pa = addnfastate(nf);
		*pb = addnfastate(nf);
		addnfaarc(nf, *pa, *pb, addlabel(ll, n->n_type, n->n_str));
	}
	else
		REQ(n, NAME);
}

static void
dumpstate(ll, nf, istate)
	labellist *ll;
	nfa *nf;
	int istate;
{
	nfastate *st;
	int i;
	nfaarc *ar;
	
	printf("%c%2d%c",
		istate == nf->nf_start ? '*' : ' ',
		istate,
		istate == nf->nf_finish ? '.' : ' ');
	st = &nf->nf_state[istate];
	ar = st->st_arc;
	for (i = 0; i < st->st_narcs; i++) {
		if (i > 0)
			printf("\n    ");
		printf("-> %2d  %s", ar->ar_arrow,
			PyGrammar_LabelRepr(&ll->ll_label[ar->ar_label]));
		ar++;
	}
	printf("\n");
}

static void
dumpnfa(ll, nf)
	labellist *ll;
	nfa *nf;
{
	int i;
	
	printf("NFA '%s' has %d states; start %d, finish %d\n",
		nf->nf_name, nf->nf_nstates, nf->nf_start, nf->nf_finish);
	for (i = 0; i < nf->nf_nstates; i++)
		dumpstate(ll, nf, i);
}


/* PART TWO -- CONSTRUCT DFA -- Algorithm 3.1 from [Aho&Ullman 77] */

static void
addclosure(ss, nf, istate)
	bitset ss;
	nfa *nf;
	int istate;
{
	if (addbit(ss, istate)) {
		nfastate *st = &nf->nf_state[istate];
		nfaarc *ar = st->st_arc;
		int i;
		
		for (i = st->st_narcs; --i >= 0; ) {
			if (ar->ar_label == EMPTY)
				addclosure(ss, nf, ar->ar_arrow);
			ar++;
		}
	}
}

typedef struct _ss_arc {
	bitset	sa_bitset;
	int	sa_arrow;
	int	sa_label;
} ss_arc;

typedef struct _ss_state {
	bitset	ss_ss;
	int	ss_narcs;
	ss_arc	*ss_arc;
	int	ss_deleted;
	int	ss_finish;
	int	ss_rename;
} ss_state;

typedef struct _ss_dfa {
	int	sd_nstates;
	ss_state *sd_state;
} ss_dfa;

/* Forward */
static void printssdfa Py_PROTO((int xx_nstates, ss_state *xx_state, int nbits,
			      labellist *ll, char *msg));
static void simplify Py_PROTO((int xx_nstates, ss_state *xx_state));
static void convert Py_PROTO((dfa *d, int xx_nstates, ss_state *xx_state));

static void
makedfa(gr, nf, d)
	nfagrammar *gr;
	nfa *nf;
	dfa *d;
{
	int nbits = nf->nf_nstates;
	bitset ss;
	int xx_nstates;
	ss_state *xx_state, *yy;
	ss_arc *zz;
	int istate, jstate, iarc, jarc, ibit;
	nfastate *st;
	nfaarc *ar;
	
	ss = newbitset(nbits);
	addclosure(ss, nf, nf->nf_start);
	xx_state = PyMem_NEW(ss_state, 1);
	if (xx_state == NULL)
		Py_FatalError("no mem for xx_state in makedfa");
	xx_nstates = 1;
	yy = &xx_state[0];
	yy->ss_ss = ss;
	yy->ss_narcs = 0;
	yy->ss_arc = NULL;
	yy->ss_deleted = 0;
	yy->ss_finish = testbit(ss, nf->nf_finish);
	if (yy->ss_finish)
		printf("Error: nonterminal '%s' may produce empty.\n",
			nf->nf_name);
	
	/* This algorithm is from a book written before
	   the invention of structured programming... */

	/* For each unmarked state... */
	for (istate = 0; istate < xx_nstates; ++istate) {
		yy = &xx_state[istate];
		ss = yy->ss_ss;
		/* For all its states... */
		for (ibit = 0; ibit < nf->nf_nstates; ++ibit) {
			if (!testbit(ss, ibit))
				continue;
			st = &nf->nf_state[ibit];
			/* For all non-empty arcs from this state... */
			for (iarc = 0; iarc < st->st_narcs; iarc++) {
				ar = &st->st_arc[iarc];
				if (ar->ar_label == EMPTY)
					continue;
				/* Look up in list of arcs from this state */
				for (jarc = 0; jarc < yy->ss_narcs; ++jarc) {
					zz = &yy->ss_arc[jarc];
					if (ar->ar_label == zz->sa_label)
						goto found;
				}
				/* Add new arc for this state */
				PyMem_RESIZE(yy->ss_arc, ss_arc,
					     yy->ss_narcs + 1);
				if (yy->ss_arc == NULL)
					Py_FatalError("out of mem");
				zz = &yy->ss_arc[yy->ss_narcs++];
				zz->sa_label = ar->ar_label;
				zz->sa_bitset = newbitset(nbits);
				zz->sa_arrow = -1;
			 found:	;
				/* Add destination */
				addclosure(zz->sa_bitset, nf, ar->ar_arrow);
			}
		}
		/* Now look up all the arrow states */
		for (jarc = 0; jarc < xx_state[istate].ss_narcs; jarc++) {
			zz = &xx_state[istate].ss_arc[jarc];
			for (jstate = 0; jstate < xx_nstates; jstate++) {
				if (samebitset(zz->sa_bitset,
					xx_state[jstate].ss_ss, nbits)) {
					zz->sa_arrow = jstate;
					goto done;
				}
			}
			PyMem_RESIZE(xx_state, ss_state, xx_nstates + 1);
			if (xx_state == NULL)
				Py_FatalError("out of mem");
			zz->sa_arrow = xx_nstates;
			yy = &xx_state[xx_nstates++];
			yy->ss_ss = zz->sa_bitset;
			yy->ss_narcs = 0;
			yy->ss_arc = NULL;
			yy->ss_deleted = 0;
			yy->ss_finish = testbit(yy->ss_ss, nf->nf_finish);
		 done:	;
		}
	}
	
	if (Py_DebugFlag)
		printssdfa(xx_nstates, xx_state, nbits, &gr->gr_ll,
						"before minimizing");
	
	simplify(xx_nstates, xx_state);
	
	if (Py_DebugFlag)
		printssdfa(xx_nstates, xx_state, nbits, &gr->gr_ll,
						"after minimizing");
	
	convert(d, xx_nstates, xx_state);
	
	/* XXX cleanup */
}

static void
printssdfa(xx_nstates, xx_state, nbits, ll, msg)
	int xx_nstates;
	ss_state *xx_state;
	int nbits;
	labellist *ll;
	char *msg;
{
	int i, ibit, iarc;
	ss_state *yy;
	ss_arc *zz;
	
	printf("Subset DFA %s\n", msg);
	for (i = 0; i < xx_nstates; i++) {
		yy = &xx_state[i];
		if (yy->ss_deleted)
			continue;
		printf(" Subset %d", i);
		if (yy->ss_finish)
			printf(" (finish)");
		printf(" { ");
		for (ibit = 0; ibit < nbits; ibit++) {
			if (testbit(yy->ss_ss, ibit))
				printf("%d ", ibit);
		}
		printf("}\n");
		for (iarc = 0; iarc < yy->ss_narcs; iarc++) {
			zz = &yy->ss_arc[iarc];
			printf("  Arc to state %d, label %s\n",
				zz->sa_arrow,
				PyGrammar_LabelRepr(
					&ll->ll_label[zz->sa_label]));
		}
	}
}


/* PART THREE -- SIMPLIFY DFA */

/* Simplify the DFA by repeatedly eliminating states that are
   equivalent to another oner.  This is NOT Algorithm 3.3 from
   [Aho&Ullman 77].  It does not always finds the minimal DFA,
   but it does usually make a much smaller one...  (For an example
   of sub-optimal behaviour, try S: x a b+ | y a b+.)
*/

static int
samestate(s1, s2)
	ss_state *s1, *s2;
{
	int i;
	
	if (s1->ss_narcs != s2->ss_narcs || s1->ss_finish != s2->ss_finish)
		return 0;
	for (i = 0; i < s1->ss_narcs; i++) {
		if (s1->ss_arc[i].sa_arrow != s2->ss_arc[i].sa_arrow ||
			s1->ss_arc[i].sa_label != s2->ss_arc[i].sa_label)
			return 0;
	}
	return 1;
}

static void
renamestates(xx_nstates, xx_state, from, to)
	int xx_nstates;
	ss_state *xx_state;
	int from, to;
{
	int i, j;
	
	if (Py_DebugFlag)
		printf("Rename state %d to %d.\n", from, to);
	for (i = 0; i < xx_nstates; i++) {
		if (xx_state[i].ss_deleted)
			continue;
		for (j = 0; j < xx_state[i].ss_narcs; j++) {
			if (xx_state[i].ss_arc[j].sa_arrow == from)
				xx_state[i].ss_arc[j].sa_arrow = to;
		}
	}
}

static void
simplify(xx_nstates, xx_state)
	int xx_nstates;
	ss_state *xx_state;
{
	int changes;
	int i, j;
	
	do {
		changes = 0;
		for (i = 1; i < xx_nstates; i++) {
			if (xx_state[i].ss_deleted)
				continue;
			for (j = 0; j < i; j++) {
				if (xx_state[j].ss_deleted)
					continue;
				if (samestate(&xx_state[i], &xx_state[j])) {
					xx_state[i].ss_deleted++;
					renamestates(xx_nstates, xx_state,
						     i, j);
					changes++;
					break;
				}
			}
		}
	} while (changes);
}


/* PART FOUR -- GENERATE PARSING TABLES */

/* Convert the DFA into a grammar that can be used by our parser */

static void
convert(d, xx_nstates, xx_state)
	dfa *d;
	int xx_nstates;
	ss_state *xx_state;
{
	int i, j;
	ss_state *yy;
	ss_arc *zz;
	
	for (i = 0; i < xx_nstates; i++) {
		yy = &xx_state[i];
		if (yy->ss_deleted)
			continue;
		yy->ss_rename = addstate(d);
	}
	
	for (i = 0; i < xx_nstates; i++) {
		yy = &xx_state[i];
		if (yy->ss_deleted)
			continue;
		for (j = 0; j < yy->ss_narcs; j++) {
			zz = &yy->ss_arc[j];
			addarc(d, yy->ss_rename,
				xx_state[zz->sa_arrow].ss_rename,
				zz->sa_label);
		}
		if (yy->ss_finish)
			addarc(d, yy->ss_rename, yy->ss_rename, 0);
	}
	
	d->d_initial = 0;
}


/* PART FIVE -- GLUE IT ALL TOGETHER */

static grammar *
maketables(gr)
	nfagrammar *gr;
{
	int i;
	nfa *nf;
	dfa *d;
	grammar *g;
	
	if (gr->gr_nnfas == 0)
		return NULL;
	g = newgrammar(gr->gr_nfa[0]->nf_type);
			/* XXX first rule must be start rule */
	g->g_ll = gr->gr_ll;
	
	for (i = 0; i < gr->gr_nnfas; i++) {
		nf = gr->gr_nfa[i];
		if (Py_DebugFlag) {
			printf("Dump of NFA for '%s' ...\n", nf->nf_name);
			dumpnfa(&gr->gr_ll, nf);
		}
		printf("Making DFA for '%s' ...\n", nf->nf_name);
		d = adddfa(g, nf->nf_type, nf->nf_name);
		makedfa(gr, gr->gr_nfa[i], d);
	}
	
	return g;
}

grammar *
pgen(n)
	node *n;
{
	nfagrammar *gr;
	grammar *g;
	
	gr = metacompile(n);
	g = maketables(gr);
	translatelabels(g);
	addfirstsets(g);
	return g;
}


/*

Description
-----------

Input is a grammar in extended BNF (using * for repetition, + for
at-least-once repetition, [] for optional parts, | for alternatives and
() for grouping).  This has already been parsed and turned into a parse
tree.

Each rule is considered as a regular expression in its own right.
It is turned into a Non-deterministic Finite Automaton (NFA), which
is then turned into a Deterministic Finite Automaton (DFA), which is then
optimized to reduce the number of states.  See [Aho&Ullman 77] chapter 3,
or similar compiler books (this technique is more often used for lexical
analyzers).

The DFA's are used by the parser as parsing tables in a special way
that's probably unique.  Before they are usable, the FIRST sets of all
non-terminals are computed.

Reference
---------

[Aho&Ullman 77]
	Aho&Ullman, Principles of Compiler Design, Addison-Wesley 1977
	(first edition)

*/