(* This module extends the LR(0) automaton with lookahead information in order
to construct an SLR(1) automaton. The lookahead information is obtained by
considering the FOLLOW sets. *)
(* This construction is not used by Menhir, but can be used to check whether
the grammar is in the class SLR(1). This check is performed when the log
level [lg] is at least 1. *)
open Grammar
(* This flag, which is reserved for internal use, causes more information
about SLR(1) conflict states to be printed. *)
let tell_me_everything =
false
(* The following function turns an LR(0) state into an SLR(1) state. *)
let make_slr_state (s : Lr0.node) : Lr0.concretelr1state =
(* Obtain the set of LR(0) items associated with the state [s]. *)
let items = Lr0.items s in
(* Unfortunately, this set is not closed. We do not have a function that
computes the closure of a set of LR(0) items -- we could build one using
[Item.Closure], but that would be overkill. So, we first convert this
set to a set of LR(1) items, then compute the closure at this level, and
finally we turn this LR(1) state into an SLR(1) state by letting the
lookahead sets be the FOLLOW sets. This is somewhat ugly and naïve, but
seems to work. *)
(* Convert this set to a set of LR(1) items. Here, we can use any set of
tokens as the lookahead set. We use the empty set. *)
let s = Item.Map.lift (fun _item -> TerminalSet.empty) items in
(* Compute the LR(1) closure. *)
let s = Lr0.closure s in
(* We now have an LR(1) state that has the correct set of LR(0) items but
phony lookahead information. We convert it into an SLR(1) state by
deciding that, for each item, the lookahead set is the FOLLOW set of the
symbol that appears on the left-hand side of the item. *)
Item.Map.fold (fun item toks accu ->
let _, nt, _, _, _ = Item.def item in
let follow_nt = Analysis.follow nt in
assert (TerminalSet.subset toks follow_nt); (* sanity check *)
Item.Map.add item follow_nt accu
) s Item.Map.empty
(* Insertion of a new reduce action into the table of reductions. Copied
from [Lr1] (boo, hiss). *)
let addl prod tok reductions =
let prods =
try
TerminalMap.lookup tok reductions
with Not_found ->
[]
in
TerminalMap.add tok (prod :: prods) reductions
(* Same thing, for a set of tokens. *)
let addl prod toks reductions =
TerminalSet.fold (addl prod) toks reductions
(* The following function turns a closed LR(1) state into a map of terminal
symbols to reduction actions. Copied from a related function in [Lr0]. *)
let reductions (s : Lr0.concretelr1state) : Production.index list TerminalMap.t =
Item.Map.fold (fun item toks reductions ->
match Item.classify item with
| Item.Reduce prod ->
addl prod toks reductions
| Item.Shift _ ->
reductions
) s TerminalMap.empty
(* The following function turns a closed LR(1) state into a set of shift
actions. *)
let transitions (s : Lr0.concretelr1state) : TerminalSet.t =
Item.Map.fold (fun item _ transitions ->
match Item.classify item with
| Item.Shift (Symbol.T tok, _) ->
TerminalSet.add tok transitions
| Item.Shift (Symbol.N _, _)
| Item.Reduce _ ->
transitions
) s TerminalSet.empty
(* This function computes the domain of a terminal map, producing a terminal
set. *)
let domain (m : 'a TerminalMap.t) : TerminalSet.t =
TerminalMap.fold (fun tok _ accu ->
TerminalSet.add tok accu
) m TerminalSet.empty
(* The following function checks whether a closed LR(1) state is free of
conflicts. *)
let state_is_ok (s : Lr0.concretelr1state) : bool =
let reductions = reductions s
and transitions = transitions s in
(* Check for shift/reduce conflicts. *)
TerminalSet.disjoint transitions (domain reductions) &&
(* Check for reduce/reduce conflicts. *)
TerminalMap.fold (fun _ prods ok ->
ok && match prods with
| []
| [ _ ] ->
true
| _ :: _ :: _ ->
false
) reductions true
(* The following function counts the number of states in the SLR(1) automaton
that have a conflict. *)
let count_slr_violations () : int =
let count = ref 0 in
for s = 0 to Lr0.n - 1 do
let s = make_slr_state s in
if not (state_is_ok s) then begin
incr count;
if tell_me_everything then
Printf.fprintf
stderr
"The following SLR(1) state has a conflict:\n%s"
(Lr0.print_concrete "" s)
end
done;
!count
(* At log level 1, indicate whether the grammar is SLR(1). *)
let () =
Error.logG 1 (fun f ->
let count = count_slr_violations() in
if count = 0 then
Printf.fprintf f "The grammar is SLR(1).\n"
else
Printf.fprintf f "The grammar is not SLR(1) -- %d states have a conflict.\n" count
)