cpython/Parser/pgen.c

/* Parser generator */

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

#include <stdio.h>
#include "assert.h"

#include "PROTO.h"
#include "malloc.h"
#include "token.h"
#include "node.h"
#include "grammar.h"
#include "metagrammar.h"
#include "pgen.h"

extern int debugging;


/* 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;

static int
addnfastate(nf)
	nfa *nf;
{
	nfastate *st;
	
	RESIZE(nf->nf_state, nfastate, nf->nf_nstates + 1);
	if (nf->nf_state == NULL)
		fatal("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];
	RESIZE(st->st_arc, nfaarc, st->st_narcs + 1);
	if (st->st_arc == NULL)
		fatal("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 type = NT_OFFSET; /* All types will be disjunct */
	
	nf = NEW(nfa, 1);
	if (nf == NULL)
		fatal("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;

static nfagrammar *
newnfagrammar()
{
	nfagrammar *gr;
	
	gr = NEW(nfagrammar, 1);
	if (gr == NULL)
		fatal("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);
	RESIZE(gr->gr_nfa, nfa *, gr->gr_nnfas + 1);
	if (gr->gr_nfa == NULL)
		fatal("out of mem");
	gr->gr_nfa[gr->gr_nnfas++] = nf;
	addlabel(&gr->gr_ll, NAME, nf->nf_name);
	return nf;
}

#ifdef DEBUG

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

#define REQN(i, count) \
 	if (i < count) { \
		fprintf(stderr, REQNFMT, count); \
		abort(); \
	} 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
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
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
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
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
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,
			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 int
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;

static
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 = NEW(ss_state, 1);
	if (xx_state == NULL)
		fatal("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 */
				RESIZE(yy->ss_arc, ss_arc, yy->ss_narcs + 1);
				if (yy->ss_arc == NULL)
					fatal("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;
				}
			}
			RESIZE(xx_state, ss_state, xx_nstates + 1);
			if (xx_state == NULL)
				fatal("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 (debugging)
		printssdfa(xx_nstates, xx_state, nbits, &gr->gr_ll,
						"before minimizing");
	
	simplify(xx_nstates, xx_state);
	
	if (debugging)
		printssdfa(xx_nstates, xx_state, nbits, &gr->gr_ll,
						"after minimizing");
	
	convert(d, xx_nstates, xx_state);
	
	/* XXX cleanup */
}

static
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,
				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 (debugging)
		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
simplify(xx_nstates, xx_state)
	int xx_nstates;
	ss_state *xx_state;
{
	int changes;
	int i, j, k;
	
	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
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 (debugging) {
			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)

*/