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menhir
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POTTIER Francois
menhir
Commits
74b133ce
Commit
74b133ce
authored
Jul 02, 2015
by
POTTIER Francois
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Replaced the old FOLLOW computation with the new one.
parent
8e270475
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src/grammar.ml
src/grammar.ml
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src/grammar.ml
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74b133ce
...
...
@@ -936,38 +936,6 @@ let solve (eqs : equations) : Nonterminal.t -> TerminalSet.t =
F
.
lfp
nonterminal
(* ------------------------------------------------------------------------ *)
(* Generic support for fixpoint computations.
A fixpoint computation associates a property with every nonterminal.
A monotone function tells how properties are computed. [compute nt]
updates the property associated with nonterminal [nt] and returns a
flag that tells whether the property actually needed an update. The
state of the computation is maintained entirely inside [compute] and
is invisible here.
Whenever a property of [nt] is updated, the properties of the
terminals whose definitions depend on [nt] are updated. The
dependency graph must be explicitly supplied. *)
let
fixpoint
(
dependencies
:
NonterminalSet
.
t
array
)
(
compute
:
Nonterminal
.
t
->
bool
)
:
unit
=
let
queue
:
Nonterminal
.
t
Queue
.
t
=
Queue
.
create
()
in
let
onqueue
:
bool
array
=
Array
.
make
Nonterminal
.
n
true
in
for
i
=
0
to
Nonterminal
.
n
-
1
do
Queue
.
add
i
queue
done
;
Misc
.
qiter
(
fun
nt
->
onqueue
.
(
nt
)
<-
false
;
let
changed
=
compute
nt
in
if
changed
then
NonterminalSet
.
iter
(
fun
nt
->
if
not
onqueue
.
(
nt
)
then
begin
Queue
.
add
nt
queue
;
onqueue
.
(
nt
)
<-
true
end
)
dependencies
.
(
nt
)
)
queue
(* ------------------------------------------------------------------------ *)
(* Compute which nonterminals are nonempty, that is, recognize a
nonempty language. Also, compute which nonterminals are
...
...
@@ -1080,76 +1048,49 @@ let () =
this is useful for the SLR(1) test. Thus, we perform this analysis only
on demand. *)
let
follow
:
TerminalSet
.
t
array
Lazy
.
t
=
lazy
(
let
follow
=
Array
.
make
Nonterminal
.
n
TerminalSet
.
empty
and
forward
:
NonterminalSet
.
t
array
=
Array
.
make
Nonterminal
.
n
NonterminalSet
.
empty
and
backward
:
NonterminalSet
.
t
array
=
Array
.
make
Nonterminal
.
n
NonterminalSet
.
empty
in
(* Iterate over all start symbols. *)
for
nt
=
0
to
Nonterminal
.
start
-
1
do
assert
(
Nonterminal
.
is_start
nt
);
(* Add # to FOLLOW(nt). *)
follow
.
(
nt
)
<-
TerminalSet
.
singleton
Terminal
.
sharp
done
;
(* We need to do this explicitly because our start productions are
of the form S' -> S, not S' -> S #, so # will not automatically
appear into FOLLOW(S) when the start productions are examined. *)
(* Iterate over all productions. *)
Array
.
iteri
(
fun
prod
(
nt1
,
rhs
)
->
(* Iterate over all nonterminal symbols [nt2] in the right-hand side. *)
Array
.
iteri
(
fun
i
symbol
->
match
symbol
with
|
Symbol
.
T
_
->
()
|
Symbol
.
N
nt2
->
let
nullable
=
NULLABLE
.
production
prod
(
i
+
1
)
and
first
=
FIRST
.
production
prod
(
i
+
1
)
in
(* The FIRST set of the remainder of the right-hand side
contributes to the FOLLOW set of [nt2]. *)
follow
.
(
nt2
)
<-
TerminalSet
.
union
first
follow
.
(
nt2
);
(* If the remainder of the right-hand side is nullable,
FOLLOW(nt1) contributes to FOLLOW(nt2). *)
if
nullable
then
begin
forward
.
(
nt1
)
<-
NonterminalSet
.
add
nt2
forward
.
(
nt1
);
backward
.
(
nt2
)
<-
NonterminalSet
.
add
nt1
backward
.
(
nt2
)
end
)
rhs
)
Production
.
table
;
let
follow
:
Nonterminal
.
t
->
TerminalSet
.
t
=
(* The fixpoint computation used here is not the most efficient
algorithm -- one could do better by first collapsing the
strongly connected components, then walking the graph in
topological order. But this will do. *)
(* First pass. Build a system of equations between sets of nonterminal
symbols. *)
fixpoint
forward
(
fun
nt
->
let
original
=
follow
.
(
nt
)
in
(* union over all contributors *)
let
updated
=
NonterminalSet
.
fold
(
fun
nt'
accu
->
TerminalSet
.
union
follow
.
(
nt'
)
accu
)
backward
.
(
nt
)
original
in
follow
.
(
nt
)
<-
updated
;
TerminalSet
.
compare
original
updated
<>
0
);
let
follow
:
equations
=
Array
.
make
Nonterminal
.
n
[]
in
follow
(* Iterate over all start symbols. *)
let
sharp
=
MemberConstant
(
TerminalSet
.
singleton
Terminal
.
sharp
)
in
for
nt
=
0
to
Nonterminal
.
start
-
1
do
assert
(
Nonterminal
.
is_start
nt
);
(* Add # to FOLLOW(nt). *)
follow
.
(
nt
)
<-
sharp
::
follow
.
(
nt
)
done
;
(* We need to do this explicitly because our start productions are
of the form S' -> S, not S' -> S #, so # will not automatically
appear into FOLLOW(S) when the start productions are examined. *)
)
(* Iterate over all productions. *)
Array
.
iteri
(
fun
prod
(
nt1
,
rhs
)
->
(* Iterate over all nonterminal symbols [nt2] in the right-hand side. *)
Array
.
iteri
(
fun
i
symbol
->
match
symbol
with
|
Symbol
.
T
_
->
()
|
Symbol
.
N
nt2
->
let
nullable
=
NULLABLE
.
production
prod
(
i
+
1
)
and
first
=
FIRST
.
production
prod
(
i
+
1
)
in
(* The FIRST set of the remainder of the right-hand side
contributes to the FOLLOW set of [nt2]. *)
follow
.
(
nt2
)
<-
MemberConstant
first
::
follow
.
(
nt2
);
(* If the remainder of the right-hand side is nullable,
FOLLOW(nt1) contributes to FOLLOW(nt2). *)
if
nullable
then
follow
.
(
nt2
)
<-
MemberVar
nt1
::
follow
.
(
nt2
)
)
rhs
)
Production
.
table
;
(* Define an accessor that triggers the computation of the FOLLOW sets
if it has not been performed already. *)
(* Second pass. Solve the equations (on demand). *)
let
follow
nt
=
(
Lazy
.
force
follow
)
.
(
nt
)
solve
follow
(* At log level 2, display the FOLLOW sets. *)
...
...
@@ -1213,56 +1154,6 @@ let () =
done
)
(* ------------------------------------------------------------------------ *)
(* Compute FOLLOW sets. *)
let
follow'
=
let
follow
:
equations
=
Array
.
make
Nonterminal
.
n
[]
in
(* Iterate over all start symbols. *)
let
sharp
=
MemberConstant
(
TerminalSet
.
singleton
Terminal
.
sharp
)
in
for
nt
=
0
to
Nonterminal
.
start
-
1
do
assert
(
Nonterminal
.
is_start
nt
);
(* Add # to FOLLOW(nt). *)
follow
.
(
nt
)
<-
sharp
::
follow
.
(
nt
)
done
;
(* We need to do this explicitly because our start productions are
of the form S' -> S, not S' -> S #, so # will not automatically
appear into FOLLOW(S) when the start productions are examined. *)
(* Iterate over all productions. *)
Array
.
iteri
(
fun
prod
(
nt1
,
rhs
)
->
(* Iterate over all nonterminal symbols [nt2] in the right-hand side. *)
Array
.
iteri
(
fun
i
symbol
->
match
symbol
with
|
Symbol
.
T
_
->
()
|
Symbol
.
N
nt2
->
let
nullable
=
NULLABLE
.
production
prod
(
i
+
1
)
and
first
=
FIRST
.
production
prod
(
i
+
1
)
in
(* The FIRST set of the remainder of the right-hand side
contributes to the FOLLOW set of [nt2]. *)
follow
.
(
nt2
)
<-
MemberConstant
first
::
follow
.
(
nt2
);
(* If the remainder of the right-hand side is nullable,
FOLLOW(nt1) contributes to FOLLOW(nt2). *)
if
nullable
then
follow
.
(
nt2
)
<-
MemberVar
nt1
::
follow
.
(
nt2
)
)
rhs
)
Production
.
table
;
solve
follow
(* Sanity check. *)
let
()
=
for
nt
=
0
to
Nonterminal
.
n
-
1
do
let
f
=
follow
nt
and
f'
=
follow'
nt
in
assert
(
TerminalSet
.
equal
f
f'
)
done
(* ------------------------------------------------------------------------ *)
(* Provide explanations about FIRST sets. *)
...
...
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