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YACCLOOK.PAS
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Pascal/Delphi Source File
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1993-01-24
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381 lines
unit YaccLookaheads;
(* 3-1-91 AG *)
(* Copyright (c) 1990,91 by Albert Graef, Schillerstr. 18,
6509 Schornsheim/Germany
All rights reserved *)
interface
(* Yacc lookahead computation. This implementation is based on the
lookahead set algorithm described in Aho/Sethi/Ullman, 1986,
Section 4.7. *)
procedure lookaheads;
(* computes the LALR lookahead sets and enters corresponding reductions
into the redn table (sorted w.r.t. rule numbers) *)
implementation
uses YaccBase, YaccTables;
(* This implementation is based on algorithms 4.12 and 4.13 in Aho/Sethi/
Ullman 1986 (with some optimizations added), which avoid the need to
construct the full LR(1) set, and are able to compute lookaheads from
LR(0) kernel items only.
We start off with the LR(0) state set together with corresponding (shift
and goto) transitions already computed. We compute the LALR(1) lookahead
sets for kernel items and also record all corresponding reduce actions
in the reduction table (where we also have to consider nonkernel items
with empty right-hand side; these items also call for a reduction, but
never appear in the kernel item table).
This implementation uses some simple optimizations to speed up the
algorithm. The lookahead sets are represented by (IntSet) pointers.
Lookahead sets are associated with each kernel item in the item table,
and with each reduction in the reduction table. A kernel item
calling for a reduction shares its lookahead set pointer with the
corresponding entry in the reduction table. The lookahead set for
a nonkernel reduction item (item with empty right-hand side) only
appears in the reduction table.
The algorithm consists of two phases:
1. Initialization:
The initialization phase consists of a single traversal of the LR(0)
set, where we compute lookahead sets generated spontaneously (lookaheads
which are passed on from nonkernel items to the corresponding items in
successor states), initialize lookahead sets and enter them into the
lookahead and reduction table. Furthermore, during the initialization
phase we also initialize the links for the propagation of lookaheads
in the second phase.
To determine lookaheads and propagation links, we compute the look-
aheads for the closures of single LR(0) sets "in the small", according
to the method in Aho/Sethi/Ullman 1986 (with some modifications),
where we associate with each kernel item i a corresponding endmarker
symbol #i as its lookahead symbol.
The initialization phase proceeds as follows:
1) Initialize all nonkernel item lookahead sets to empty.
Now we pass over each state s in the LR0 set, repeating steps 2) thru
5) specified below:
2) Compute the closure closure(K(s)) of the states's kernel set K(s).
3) Compute the lookahead sets for closure(K(s)) (described in detail
below) where each kernel item i is associated with a special
endmarker symbol #i as lookahead.
Now the lookahead symbols, reductions and propagation links are entered
into the corresponding tables as follows:
4) Process kernel items: Add a propagation link from the kernel item
to the lookahead set of the linked item in the corresponding
successor state (as specified by the next field). If there is no
successor item (kernel item calling for a reduction), add a
corresponding entry into the reduction table instead.
5) Process nonkernel items: find the corresponding kernel item in the
successor state which is generated spontaneously from the nonkernel
item. Add the spontaneous lookahead symbols (except endmarker
symbols) of the nonkernel item determined in step 3) to the kernel
item. If the nonkernel item has an empty right-hand side (nonkernel
item calling for a reduction), add a corresponding entry into the
reduction table instead. Furthermore, for each endmarker symbol
#i in the spontaneous lookahead set of the nonkernel item, add
a corresponding propagation link from the ith kernel item to the
lookahead set of the spontaneous kernel item.
To compute the spontaneous lookaheads (step 3)), we proceed as follows:
3a) First compute the first sets of tail strings of all items in
closure(K(s)). The "tail string" of an item [ X -> v.Yw ], where
Y is a nonterminal, is the symbol sequence w, whose first set
induces corresponding spontaneous lookaheads in the nonkernel
items of the state with left-hand side Y; note that the first
sets of "tail strings" in items [ X -> v.yw ], where y is a
*terminal* symbol, are not required and hence it is not
necessary to compute them. We also record for each item whether
its tail string is "nullable", i.e., may be derived to the empty
string. In this case, the item also passes on its own lookaheads,
in addition to the first symbols of its tail string. First sets
and nullable flags are computed using the information in YaccTable's
first and nullable tables.
3b) Now follows an initialization part in which each item [ X -> v.Yw ]
passes on the first symbols of its tail string to the lookahead
sets of each corresponding nonkernel item [ Y -> .u ].
3c) Finally, we repeatedly pass over the item set, passing on
lookaheads from items with nullable tail strings. Each item
[ X -> v.Yw ] with nullable w propagates its own lookaheads to
all corresponding nonkernel items [ Y -> .u]. Step 3c) terminates
as soon as no lookahead sets have been modified during the previous
pass.
2. Propagation:
The second phase of the lookahead computation algorithm now is quite
simple. We repeatedly pass over all kernel items, propagating lookaheads
according to the propagation links determined in the initialization
phase. The algorithm terminates as soon as no lookahead sets have been
modified during the previous pass. *)
(* Data structures used in lookahead computation: *)
type
SymSetArray = array [1..max_set_items] of IntSet;
BoolArray = array [1..max_set_items] of Boolean;
var
item_set : ItemSet;
lookahead_set : SymSetArray;
n_kernel_items : Integer;
procedure spontaneous_lookaheads;
(* compute spontaneous lookaheads for item_set; negative symbols are
used for endmarkers (-i denotes endmarker #i) *)
var count, last_count, i : Integer;
first_syms : SymSetArray;
nullable : BoolArray;
function sym_count ( n : Integer ) : Integer;
(* count lookahead symbols *)
var count, i : Integer;
begin
count := 0;
for i := 1 to n do
inc(count, size(lookahead_set[i]));
sym_count := count;
end(*sym_count*);
procedure compute_first_syms ( i : Integer );
(* compute first set and nullable flag for tail string of item
number i *)
var j : Integer;
begin
empty(first_syms[i]); nullable[i] := true;
with item_set, item[i], rule_table^[rule_no]^ do
if (pos_no<=rhs_len) and (rhs_sym[pos_no]<0) then
begin
j := pos_no+1;
while (j<=rhs_len) and nullable[i] do
begin
if rhs_sym[j]<0 then
begin
setunion(first_syms[i], first_set_table^[-rhs_sym[j]]^);
nullable[i] := YaccTables.nullable^[-rhs_sym[j]];
end
else
begin
include(first_syms[i], rhs_sym[j]);
nullable[i] := false;
end;
inc(j);
end;
end;
end(*compute_first_syms*);
procedure init_lookaheads ( i : Integer );
(* compute initial lookaheads induced by first sets of tail string
of item i *)
var sym, j : Integer;
begin
with item_set, item[i], rule_table^[rule_no]^ do
if (pos_no<=rhs_len) and (rhs_sym[pos_no]<0) then
begin
sym := rhs_sym[pos_no];
for j := n_kernel_items+1 to n_items do
with item[j], rule_table^[rule_no]^ do
if lhs_sym=sym then
setunion(lookahead_set[j], first_syms[i]);
end
end(*initial_lookaheads*);
procedure propagate ( i : Integer );
(* propagate lookahead symbols of item i *)
var sym, j : Integer;
begin
with item_set, item[i], rule_table^[rule_no]^ do
if (pos_no<=rhs_len) and (rhs_sym[pos_no]<0) and nullable[i] then
begin
sym := rhs_sym[pos_no];
for j := n_kernel_items+1 to n_items do
with item[j], rule_table^[rule_no]^ do
if lhs_sym=sym then
setunion(lookahead_set[j], lookahead_set[i]);
end
end(*propagate*);
begin(*spontaneous_lookaheads*)
with item_set do
begin
(* initialize kernel lookahead sets: *)
for i := 1 to n_kernel_items do singleton(lookahead_set[i], -i);
(* compute first sets and nullable flags: *)
for i := 1 to n_items do compute_first_syms(i);
(* initialize nonkernel lookahead sets: *)
for i := n_kernel_items+1 to n_items do empty(lookahead_set[i]);
for i := 1 to n_items do init_lookaheads(i);
(* repeated passes until no more lookaheads have been added
during the previous pass: *)
count := sym_count(n_items);
repeat
last_count := count;
for i := 1 to n_items do
propagate(i);
count := sym_count(n_items);
until last_count=count;
end;
end(*spontaneous_lookaheads*);
{$F+}
function redns_less ( i, j : Integer ) : Boolean;
{$F-}
begin
redns_less := redn_table^[i].rule_no<redn_table^[j].rule_no
end(*redns_less*);
{$F+}
procedure redns_swap ( i, j : Integer );
{$F-}
var x : RednRec;
begin
x := redn_table^[i];
redn_table^[i] := redn_table^[j];
redn_table^[j] := x;
end(*redns_swap*);
procedure sort_redns;
(* sort reduction entries in act_state w.r.t. rule numbers *)
begin
with state_table^[act_state] do
quicksort(redns_lo, redns_hi, redns_less, redns_swap);
end(*sort_redns*);
procedure initialize;
(* initialization phase of lookahead computation algorithm *)
procedure add_prop ( i : Integer; symset : IntSetPtr );
(* add a propagation link to kernel item i *)
var prop : PropList;
begin
new(prop);
prop^.symset := symset;
prop^.next := prop_table^[i];
prop_table^[i] := prop;
end(*add_prop*);
var i, j, k : Integer;
lookaheads : IntSetPtr;
begin
(* initialize lookahead sets and propagation links: *)
for i := 1 to n_items do lookahead_table^[i] := newEmptyIntSet;
for i := 1 to n_items do prop_table^[i] := nil;
act_state := 0;
repeat
with state_table^[act_state], item_set do
begin
start_redns;
get_item_set(act_state, item_set);
n_kernel_items := n_items;
(* compute LR(0) closure: *)
closure(item_set);
(* compute spontaneous lookaheads: *)
spontaneous_lookaheads;
(* process kernel items: *)
for i := 1 to n_kernel_items do with item[i] do
if next>0 then
(* add propagation link: *)
add_prop(item_lo+i-1, lookahead_table^[next])
else
(* enter reduce action: *)
add_redn(lookahead_table^[item_lo+i-1], rule_no);
(* process nonkernel items: *)
(* find successor items: *)
for k := trans_lo to trans_hi do
with trans_table^[k] do
for i := n_kernel_items+1 to n_items do
with item[i], rule_table^[rule_no]^ do
if pos_no>rhs_len then
next := 0
else if rhs_sym[pos_no]=sym then
next := find_item(next_state, rule_no, pos_no+1);
(* add spontaneous lookaheads and propagation links: *)
for i := n_kernel_items+1 to n_items do with item[i] do
if next>0 then
(* lookaheads are generated spontaneously for successor
item: *)
for j := 1 to size(lookahead_set[i]) do
if lookahead_set[i][j]>=0 then
include(lookahead_table^[next]^, lookahead_set[i][j])
else
add_prop(item_lo+(-lookahead_set[i][j])-1,
lookahead_table^[next])
else
(* nonkernel reduction item: *)
begin
lookaheads := newEmptyIntSet;
for j := 1 to size(lookahead_set[i]) do
if lookahead_set[i][j]>=0 then
include(lookaheads^, lookahead_set[i][j])
else
add_prop(item_lo+(-lookahead_set[i][j])-1,
lookaheads);
add_redn(lookaheads, rule_no);
end;
end_redns;
sort_redns;
end;
inc(act_state);
until act_state=n_states;
end(*initialize*);
procedure propagate;
(* propagation phase of lookahead computation algorithm *)
var i, l : Integer;
done : Boolean;
prop : PropList;
begin
(* repeated passes over the kernel items table until no more lookaheads
could be added in the previous pass: *)
repeat
done := true;
for i := 1 to n_items do
begin
prop := prop_table^[i];
while prop<>nil do with prop^ do
begin
l := size(symset^);
setunion(symset^, lookahead_table^[i]^);
if size(symset^)>l then done := false;
prop := next;
end;
end;
until done;
end(*propagate*);
procedure lookaheads;
begin
initialize;
propagate;
end(*lookaheads*);
end(*YaccLookaheads*).
