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{
Yacc closure and first set construction algorithms. See Aho/Sethi/Ullman,
1986, Sections 4.4 and 4.7, for further explanation.
Copyright (c) 1990-92 Albert Graef <ag@muwiinfa.geschichte.uni-mainz.de>
Copyright (C) 1996 Berend de Boer <berend@pobox.com>
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
$Revision: 1.2 $
$Modtime: 96-07-31 14:09 $
$History: YACCCLOS.PAS $
*
* ***************** Version 2 *****************
* User: Berend Date: 96-10-10 Time: 21:16
* Updated in $/Lex and Yacc/tply
* Updated for protected mode, windows and Delphi 1.X and 2.X.
}
unit YaccClos;
interface
procedure closures;
(* compute the closure sets *)
procedure first_sets;
(* compute first sets and nullable flags *)
implementation
uses YaccBase, YaccTabl;
procedure closures;
(* The closure set of a nonterminal X is the set of all nonterminals Y
s.t. Y appears as the first symbol in a rightmost derivation from the
nonterminal X (i.e. X =>+ Y ... in a rightmost derivation). We can
easily compute closure sets as follows:
- Initialize the closure set for any nonterminal X to contain all
nonterminals Y for which there is a rule X : Y ...
- Now repeatedly pass over the already constructed sets, and for
any nonterminal Y which has already been added to the closure set
of some nonterminal X, also include the closure elements of Y in
the closure set of X.
The algorithm terminates as soon as no additional symbols have been
added during the previous pass. *)
var sym, i, count, prev_count : Integer;
act_syms : IntSet;
begin
(* initialize closure sets: *)
prev_count := 0;
count := 0;
for sym := 1 to n_nts do
begin
closure_table^[sym] := newEmptyIntSet;
with rule_offs^[sym] do
for i := rule_lo to rule_hi do
with rule_table^[rule_no^[i]]^ do
if (rhs_len>0) and (rhs_sym[1]<0) then
include(closure_table^[sym]^, rhs_sym[1]);
inc(count, size(closure_table^[sym]^));
end;
(* repeated passes until no more symbols have been added during the last
pass: *)
while prev_count<count do
begin
prev_count := count;
count := 0;
for sym := 1 to n_nts do
begin
act_syms := closure_table^[sym]^;
for i := 1 to size(act_syms) do
setunion(closure_table^[sym]^, closure_table^[-act_syms[i]]^);
inc(count, size(closure_table^[sym]^));
end;
end;
end(*closures*);
procedure first_sets;
(* The first set of a nonterminal X is the set of all literal symbols
y s.t. X =>+ y ... in some derivation of the nonterminal X. In
addition, X is nullable if the empty string can be derived from X.
Using the first set construction algorithm of Aho/Sethi/Ullman,
Section 4.4, the first sets and nullable flags are computed as
follows:
For any production X -> y1 ... yn, where the yi are grammar symbols,
add the symbols in the first set of y1 (y1 itself if it is a literal)
to the first set of X; if y1 is a nullable nonterminal, then proceed
with y2, etc., until either all yi have been considered or yi is non-
nullable (or a literal symbol). If all of the yi are nullable (in
particular, if n=0), then also set nullable[X] to true.
This procedure is repeated until no more symbols have been added to any
first set and none of the nullable flags have been changed during the
previous pass. *)
var i, j, l, sym : Integer;
n, null, done : Boolean;
begin
(* initialize tables: *)
for sym := 1 to n_nts do
begin
nullable^[sym] := false;
first_set_table^[sym] := newEmptyIntSet;
end;
(* repeated passes until no more symbols added and no nullable flags
modified: *)
repeat
done := true;
for i := 1 to n_rules do
with rule_table^[i]^ do
begin
l := size(first_set_table^[-lhs_sym]^);
n := nullable^[-lhs_sym];
null := true;
j := 1;
while (j<=rhs_len) and null do
begin
if rhs_sym[j]<0 then
begin
setunion( first_set_table^[-lhs_sym]^,
first_set_table^[-rhs_sym[j]]^ );
null := nullable^[-rhs_sym[j]];
end
else
begin
include( first_set_table^[-lhs_sym]^,
rhs_sym[j] );
null := false;
end;
inc(j);
end;
if null then nullable^[-lhs_sym] := true;
if (l<size(first_set_table^[-lhs_sym]^)) or
(n<>nullable^[-lhs_sym]) then
done := false;
end;
until done;
end(*first_sets*);
end(*YaccClosure*).
|
