open UnparameterizedSyntax
open Syntax
open Positions
(* ------------------------------------------------------------------------ *)
(* Precedence levels for tokens or pseudo-tokens alike. *)
module TokPrecedence = struct
(* This set records, on a token by token basis, whether the token's
precedence level is ever useful. This allows emitting warnings
about useless precedence declarations. *)
let ever_useful : StringSet.t ref =
ref StringSet.empty
let use id =
ever_useful := StringSet.add id !ever_useful
(* This function is invoked when someone wants to consult a token's
precedence level. This does not yet mean that this level is
useful, though. Indeed, if it is subsequently compared against
[UndefinedPrecedence], it will not allow solving a conflict. So,
in addition to the desired precedence level, we return a delayed
computation which, when evaluated, records that this precedence
level was useful. *)
let levelip id properties =
lazy (use id), properties.tk_precedence
let leveli id =
let properties =
try
StringMap.find id Front.grammar.tokens
with Not_found ->
assert false (* well-formedness check has been performed earlier *)
in
levelip id properties
(* This function is invoked after the automaton has been constructed.
It warns about unused precedence levels. *)
let diagnostics () =
StringMap.iter (fun id properties ->
if not (StringSet.mem id !ever_useful) then
match properties.tk_precedence with
| UndefinedPrecedence ->
()
| PrecedenceLevel (_, _, pos1, pos2) ->
Error.grammar_warning (Positions.two pos1 pos2)
"the precedence level assigned to %s is never useful." id
) Front.grammar.tokens
end
(* ------------------------------------------------------------------------ *)
(* Nonterminals. *)
module Nonterminal = struct
type t = int
let n2i i = i
let compare = (-)
(* Determine how many nonterminals we have and build mappings
both ways between names and indices. A new nonterminal is
created for every start symbol. *)
let new_start_nonterminals =
StringSet.fold (fun symbol ss -> (symbol ^ "'") :: ss) Front.grammar.start_symbols []
let original_nonterminals =
nonterminals Front.grammar
let start =
List.length new_start_nonterminals
let (n : int), (name : string array), (map : int StringMap.t) =
Misc.index (new_start_nonterminals @ original_nonterminals)
let () =
Error.logG 1 (fun f ->
Printf.fprintf f
"Grammar has %d nonterminal symbols, among which %d start symbols.\n"
(n - start) start
)
let is_start nt =
nt < start
let print normalize nt =
if normalize then
Misc.normalize name.(nt)
else
name.(nt)
let lookup name =
StringMap.find name map
let positions nt =
(StringMap.find (print false nt) Front.grammar.rules).positions
let iter f =
Misc.iteri n f
let fold f accu =
Misc.foldi n f accu
let map f =
Misc.mapi n f
let iterx f =
for nt = start to n - 1 do
f nt
done
let foldx f accu =
Misc.foldij start n f accu
let ocamltype nt =
assert (not (is_start nt));
try
Some (StringMap.find (print false nt) Front.grammar.types)
with Not_found ->
None
let ocamltype_of_start_symbol nt =
match ocamltype nt with
| Some typ ->
typ
| None ->
(* Every start symbol has a type. *)
assert false
let tabulate f =
Array.get (Array.init n f)
end
(* Sets and maps over nonterminals, used only below. *)
module NonterminalMap = Patricia.Big
module NonterminalSet = Patricia.Big.Domain
(* ------------------------------------------------------------------------ *)
(* Terminals. *)
module Terminal = struct
type t = int
let t2i i = i
let i2t i = i
let compare = (-)
let equal (tok1 : t) (tok2 : t) =
tok1 = tok2
(* Determine how many terminals we have and build mappings
both ways between names and indices. A new terminal "#"
is created. A new terminal "error" is created. The fact
that the integer code assigned to the "#" pseudo-terminal
is the last one is exploited in the table-based back-end.
(The right-most row of the action table is not created.)
Pseudo-tokens (used in %prec declarations, but never
declared using %token) are filtered out. *)
(* In principle, the number of the [error] token is irrelevant.
It is currently 0, but we do not rely on that. *)
let (n : int), (name : string array), (map : int StringMap.t) =
let tokens = tokens Front.grammar in
match tokens with
| [] ->
Error.error [] "no tokens have been declared."
| _ ->
Misc.index ("error" :: tokens @ [ "#" ])
let print tok =
name.(tok)
let lookup name =
StringMap.find name map
let sharp =
lookup "#"
let error =
lookup "error"
let pseudo tok =
(tok = sharp) || (tok = error)
let real t =
error <> t && t <> sharp
let token_properties =
let not_so_dummy_properties = (* applicable to [error] and [#] *)
{
tk_filename = "__primitives__";
tk_precedence = UndefinedPrecedence;
tk_associativity = UndefinedAssoc;
tk_ocamltype = None;
tk_is_declared = true;
tk_position = Positions.dummy;
}
in
Array.init n (fun tok ->
try
StringMap.find name.(tok) Front.grammar.tokens
with Not_found ->
assert (tok = sharp || tok = error);
not_so_dummy_properties
)
let () =
Error.logG 1 (fun f ->
Printf.fprintf f "Grammar has %d terminal symbols.\n" (n - 2)
)
let precedence_level tok =
TokPrecedence.levelip (print tok) token_properties.(tok)
let associativity tok =
token_properties.(tok).tk_associativity
let ocamltype tok =
token_properties.(tok).tk_ocamltype
let iter f =
Misc.iteri n f
let fold f accu =
Misc.foldi n f accu
let map f =
Misc.mapi n f
let () =
assert (sharp = n - 1)
let mapx f =
Misc.mapi sharp f
let () =
assert (error = 0)
let iter_real f =
for i = 1 to n-2 do
f i
done
(* If a token named [EOF] exists, then it is assumed to represent
ocamllex's [eof] pattern. *)
let eof =
try
Some (lookup "EOF")
with Not_found ->
None
(* The sub-module [Word] offers an implementation of words (that is,
sequences) of terminal symbols. It is used by [LRijkstra]. We
make it a functor, because it has internal state (a hash table)
and a side effect (failure if there are more than 256 terminal
symbols). *)
module Word (X : sig end) = struct
(* We could use lists, or perhaps the sequences offered by the module
[Seq], which support constant time concatenation. However, we need a
much more compact representation: [LRijkstra] stores tens of millions
of such words. We use strings, because they are very compact (8 bits
per symbol), and on top of that, we use a hash-consing facility. In
practice, hash-consing allows us to save 1000x in space. *)
(* A drawback of this approach is that it works only if the number of
terminal symbols is at most 256. For the moment, this is good enough.
[LRijkstra] already has difficulty at 100 terminal symbols or so. *)
let () =
assert (n <= 256)
let (encode : string -> int), (decode : int -> string), verbose =
Misc.new_encode_decode 1024
type word =
int
let epsilon =
encode ""
let singleton t =
encode (String.make 1 (Char.chr t))
let append i1 i2 =
let w1 = decode i1
and w2 = decode i2 in
if String.length w1 = 0 then
i2
else if String.length w2 = 0 then
i1
else
encode (w1 ^ w2)
let length i =
String.length (decode i)
let first i z =
let w = decode i in
if String.length w > 0 then
Char.code w.[0]
else
z
let rec elements i n w =
if i = n then
[]
else
Char.code w.[i] :: elements (i + 1) n w
let elements i =
let w = decode i in
elements 0 (String.length w) w
let print i =
let w = decode i in
Misc.separated_iter_to_string
(fun c -> print (Char.code c))
" "
(fun f -> String.iter f w)
(* [Pervasives.compare] implements a lexicographic ordering on strings. *)
let compare i1 i2 =
Pervasives.compare (decode i1) (decode i2)
end
end
(* Sets of terminals are used intensively in the LR(1) construction,
so it is important that they be as efficient as possible. *)
module TerminalSet = struct
include CompressedBitSet
let print toks =
Misc.separated_iter_to_string Terminal.print " " (fun f -> iter f toks)
let universe =
remove Terminal.sharp (
remove Terminal.error (
Terminal.fold add empty
)
)
(* The following definitions are used in the computation of FIRST sets
below. They are not exported outside of this file. *)
type property =
t
let bottom =
empty
let is_maximal _ =
false
end
(* Maps over terminals. *)
module TerminalMap = Patricia.Big
(* ------------------------------------------------------------------------ *)
(* Symbols. *)
module Symbol = struct
type t =
| N of Nonterminal.t
| T of Terminal.t
let compare sym1 sym2 =
match sym1, sym2 with
| N nt1, N nt2 ->
Nonterminal.compare nt1 nt2
| T tok1, T tok2 ->
Terminal.compare tok1 tok2
| N _, T _ ->
1
| T _, N _ ->
-1
let equal sym1 sym2 =
compare sym1 sym2 = 0
let rec lequal syms1 syms2 =
match syms1, syms2 with
| [], [] ->
true
| sym1 :: syms1, sym2 :: syms2 ->
equal sym1 sym2 && lequal syms1 syms2
| _ :: _, []
| [], _ :: _ ->
false
let print = function
| N nt ->
Nonterminal.print false nt
| T tok ->
Terminal.print tok
let nonterminal = function
| T _ ->
false
| N _ ->
true
(* Printing an array of symbols. [offset] is the start offset -- we
print everything to its right. [dot] is the dot offset -- we
print a dot at this offset, if we find it. *)
let printaod offset dot symbols =
let buffer = Buffer.create 512 in
let length = Array.length symbols in
for i = offset to length do
if i = dot then
Buffer.add_string buffer ". ";
if i < length then begin
Buffer.add_string buffer (print symbols.(i));
Buffer.add_char buffer ' '
end
done;
Buffer.contents buffer
let printao offset symbols =
printaod offset (-1) symbols
let printa symbols =
printao 0 symbols
let printl symbols =
printa (Array.of_list symbols)
let lookup name =
try
T (Terminal.lookup name)
with Not_found ->
try
N (Nonterminal.lookup name)
with Not_found ->
assert false (* well-formedness check has been performed earlier *)
end
(* Sets of symbols. *)
module SymbolSet = struct
include Set.Make(Symbol)
let print symbols =
Symbol.printl (elements symbols)
(* The following definitions are used in the computation of symbolic FOLLOW
sets below. They are not exported outside of this file. *)
type property =
t
let bottom =
empty
let is_maximal _ =
false
end
(* Maps over symbols. *)
module SymbolMap = struct
include Map.Make(Symbol)
let domain m =
fold (fun symbol _ accu ->
symbol :: accu
) m []
let purelynonterminal m =
fold (fun symbol _ accu ->
accu && Symbol.nonterminal symbol
) m true
end
(* ------------------------------------------------------------------------ *)
(* Productions. *)
module Production = struct
type index =
int
let compare =
(-)
(* Create an array of productions. Record which productions are
associated with every nonterminal. A new production S' -> S
is created for every start symbol S. It is known as a
start production. *)
let n : int =
let n = StringMap.fold (fun _ { branches = branches } n ->
n + List.length branches
) Front.grammar.rules 0 in
Error.logG 1 (fun f -> Printf.fprintf f "Grammar has %d productions.\n" n);
n + StringSet.cardinal Front.grammar.start_symbols
let p2i prod =
prod
let i2p prod =
assert (prod >= 0 && prod < n);
prod
let table : (Nonterminal.t * Symbol.t array) array =
Array.make n (-1, [||])
let identifiers : identifier array array =
Array.make n [||]
let actions : action option array =
Array.make n None
let ntprods : (int * int) array =
Array.make Nonterminal.n (-1, -1)
let positions : Positions.t list array =
Array.make n []
let (start : int),
(startprods : index NonterminalMap.t) =
StringSet.fold (fun nonterminal (k, startprods) ->
let nt = Nonterminal.lookup nonterminal
and nt' = Nonterminal.lookup (nonterminal ^ "'") in
table.(k) <- (nt', [| Symbol.N nt |]);
identifiers.(k) <- [| "_1" |];
ntprods.(nt') <- (k, k+1);
positions.(k) <- Nonterminal.positions nt;
k+1,
NonterminalMap.add nt k startprods
) Front.grammar.start_symbols (0, NonterminalMap.empty)
let prec_decl : symbol located option array =
Array.make n None
let production_level : branch_production_level array =
(* The start productions should receive this dummy level, I suppose.
We use a fresh mark, so a reduce/reduce conflict that involves a
start production will not be solved. *)
let dummy = ProductionLevel (Mark.fresh(), 0) in
Array.make n dummy
let (_ : int) = StringMap.fold (fun nonterminal { branches = branches } k ->
let nt = Nonterminal.lookup nonterminal in
let k' = List.fold_left (fun k branch ->
let symbols = Array.of_list branch.producers in
table.(k) <- (nt, Array.map (fun (v, _) -> Symbol.lookup v) symbols);
identifiers.(k) <- Array.map snd symbols;
actions.(k) <- Some branch.action;
production_level.(k) <- branch.branch_production_level;
prec_decl.(k) <- branch.branch_prec_annotation;
positions.(k) <- [ branch.branch_position ];
k+1
) k branches in
ntprods.(nt) <- (k, k');
k'
) Front.grammar.rules start
(* Iteration over the productions associated with a specific
nonterminal. *)
let iternt nt f =
let k, k' = ntprods.(nt) in
for prod = k to k' - 1 do
f prod
done
let foldnt (nt : Nonterminal.t) (accu : 'a) (f : index -> 'a -> 'a) : 'a =
let k, k' = ntprods.(nt) in
let rec loop accu prod =
if prod < k' then
loop (f prod accu) (prod + 1)
else
accu
in
loop accu k
(* This funny variant is lazy. If at some point [f] does not demand its
second argument, then iteration stops. *)
let foldnt_lazy (nt : Nonterminal.t) (f : index -> (unit -> 'a) -> 'a) (seed : 'a) : 'a =
let k, k' = ntprods.(nt) in
let rec loop prod seed =
if prod < k' then
f prod (fun () -> loop (prod + 1) seed)
else
seed
in
loop k seed
(* Accessors. *)
let def prod =
table.(prod)
let nt prod =
let nt, _ = table.(prod) in
nt
let rhs prod =
let _, rhs = table.(prod) in
rhs
let length prod =
Array.length (rhs prod)
let identifiers prod =
identifiers.(prod)
let is_start prod =
prod < start
let classify prod =
if is_start prod then
match (rhs prod).(0) with
| Symbol.N nt ->
Some nt
| Symbol.T _ ->
assert false
else
None
let action prod =
match actions.(prod) with
| Some action ->
action
| None ->
(* Start productions have no action. *)
assert (is_start prod);
assert false
let positions prod =
positions.(prod)
let startsymbol2startprod nt =
try
NonterminalMap.find nt startprods
with Not_found ->
assert false (* [nt] is not a start symbol *)
(* Iteration. *)
let iter f =
Misc.iteri n f
let fold f accu =
Misc.foldi n f accu
let map f =
Misc.mapi n f
let amap f =
Array.init n f
let iterx f =
for prod = start to n - 1 do
f prod
done
let foldx f accu =
Misc.foldij start n f accu
let mapx f =
Misc.mapij start n f
(* Printing a production. *)
let print prod =
assert (not (is_start prod));
let nt, rhs = table.(prod) in
Printf.sprintf "%s -> %s" (Nonterminal.print false nt) (Symbol.printao 0 rhs)
(* Tabulation. *)
let tabulate f =
Misc.tabulate n f
let tabulateb f =
Misc.tabulateb n f
(* This array allows recording, for each %prec declaration, whether it is
ever useful. This allows us to emit a warning about useless %prec
declarations. *)
(* 2015/10/06: We take into account the fact that a %prec declaration can be
duplicated by inlining or by the expansion of parameterized non-terminal
symbols. Our table is not indexed by productions, but by positions (of
%prec declarations in the source). Thus, if a %prec declaration is
duplicated, at least one of its copies should be found useful for the
warning to be suppressed. *)
let ever_useful : (Positions.t, unit) Hashtbl.t =
(* assuming that generic hashing and equality on positions are OK *)
Hashtbl.create 16
let consult_prec_decl prod =
let osym = prec_decl.(prod) in
lazy (
Option.iter (fun sym ->
(* Mark this %prec declaration as useful. *)
let pos = Positions.position sym in
Hashtbl.add ever_useful pos ()
) osym
),
osym
let diagnostics () =
iterx (fun prod ->
let osym = prec_decl.(prod) in
Option.iter (fun sym ->
(* Check whether this %prec declaration was useless. *)
let pos = Positions.position sym in
if not (Hashtbl.mem ever_useful pos) then begin
Error.grammar_warning [pos] "this %%prec declaration is never useful.";
Hashtbl.add ever_useful pos () (* hack: avoid two warnings at the same position *)
end
) osym
)
(* Determining the precedence level of a production. If no %prec
declaration was explicitly supplied, it is the precedence level
of the rightmost terminal symbol in the production's right-hand
side. *)
type production_level =
| PNone
| PRightmostToken of Terminal.t
| PPrecDecl of symbol
let rightmost_terminal prod =
Array.fold_left (fun accu symbol ->
match symbol with
| Symbol.T tok ->
PRightmostToken tok
| Symbol.N _ ->
accu
) PNone (rhs prod)
let combine e1 e2 =
lazy (Lazy.force e1; Lazy.force e2)
let precedence prod =
let fact1, prec_decl = consult_prec_decl prod in
let oterminal =
match prec_decl with
| None ->
rightmost_terminal prod
| Some { value = terminal } ->
PPrecDecl terminal
in
match oterminal with
| PNone ->
fact1, UndefinedPrecedence
| PRightmostToken tok ->
let fact2, level = Terminal.precedence_level tok in
combine fact1 fact2, level
| PPrecDecl id ->
let fact2, level = TokPrecedence.leveli id in
combine fact1 fact2, level
end
(* ------------------------------------------------------------------------ *)
(* Maps over productions. *)
module ProductionMap = struct
include Patricia.Big
(* Iteration over the start productions only. *)
let start f =
Misc.foldi Production.start (fun prod m ->
add prod (f prod) m
) empty
end
(* ------------------------------------------------------------------------ *)
(* If requested, build and print the forward reference graph of the grammar.
There is an edge of a nonterminal symbol [nt1] to every nonterminal symbol
[nt2] that occurs in the definition of [nt1]. *)
let () =
if Settings.graph then begin
(* Allocate. *)
let forward : NonterminalSet.t array =
Array.make Nonterminal.n NonterminalSet.empty
in
(* Populate. *)
Array.iter (fun (nt1, rhs) ->
Array.iter (function
| Symbol.T _ ->
()
| Symbol.N nt2 ->
forward.(nt1) <- NonterminalSet.add nt2 forward.(nt1)
) rhs
) Production.table;
(* Print. *)
let module P = Dot.Print (struct
type vertex = Nonterminal.t
let name nt =
Printf.sprintf "nt%d" nt
let successors (f : ?style:Dot.style -> label:string -> vertex -> unit) nt =
NonterminalSet.iter (fun successor ->
f ~label:"" successor
) forward.(nt)
let iter (f : ?shape:Dot.shape -> ?style:Dot.style -> label:string -> vertex -> unit) =
Nonterminal.iter (fun nt ->
f ~label:(Nonterminal.print false nt) nt
)
end) in
let f = open_out (Settings.base ^ ".dot") in
P.print f;
close_out f
end
(* ------------------------------------------------------------------------ *)
(* Support for analyses of the grammar, expressed as fixed point computations.
We exploit the generic fixed point algorithm in [Fix]. *)
(* We perform memoization only at nonterminal symbols. We assume that the
analysis of a symbol is the analysis of its definition (as opposed to,
say, a computation that depends on the occurrences of this symbol in
the grammar). *)
module GenericAnalysis
(P : Fix.PROPERTY)
(S : sig
open P
(* An analysis is specified by the following functions. *)
(* [terminal] maps a terminal symbol to a property. *)
val terminal: Terminal.t -> property
(* [disjunction] abstracts a binary alternative. That is, when we analyze
an alternative between several productions, we compute a property for
each of them independently, then we combine these properties using
[disjunction]. *)
val disjunction: property -> (unit -> property) -> property
(* [P.bottom] should be a neutral element for [disjunction]. We use it in
the analysis of an alternative with zero branches. *)
(* [conjunction] abstracts a binary sequence. That is, when we analyze a
sequence, we compute a property for each member independently, then we
combine these properties using [conjunction]. In general, conjunction
needs access to the first member of the sequence (a symbol), not just
to its analysis (a property). *)
val conjunction: Symbol.t -> property -> (unit -> property) -> property
(* [epsilon] abstracts the empty sequence. It should be a neutral element
for [conjunction]. *)
val epsilon: property
end)
: sig
open P
(* The results of the analysis take the following form. *)
(* To every nonterminal symbol, we associate a property. *)
val nonterminal: Nonterminal.t -> property
(* To every symbol, we associate a property. *)
val symbol: Symbol.t -> property
(* To every suffix of every production, we associate a property.
The offset [i], which determines the beginning of the suffix,
must be contained between [0] and [n], inclusive, where [n]
is the length of the production. *)
val production: Production.index -> int -> property
end = struct
open P
(* The following analysis functions are parameterized over [get], which allows
making a recursive call to the analysis at a nonterminal symbol. [get] maps
a nonterminal symbol to a property. *)
(* Analysis of a symbol. *)
let symbol sym get : property =
match sym with
| Symbol.T tok ->
S.terminal tok
| Symbol.N nt ->
(* Recursive call to the analysis, via [get]. *)
get nt
(* Analysis of (a suffix of) a production [prod], starting at index [i]. *)
let production prod i get : property =
let rhs = Production.rhs prod in
let n = Array.length rhs in
(* Conjunction over all symbols in the right-hand side. This can be viewed
as a version of [Array.fold_right], which does not necessarily begin at
index [0]. Note that, because [conjunction] is lazy, it is possible
to stop early. *)
let rec loop i =
if i = n then
S.epsilon
else
let sym = rhs.(i) in
S.conjunction sym
(symbol sym get)
(fun () -> loop (i+1))
in
loop i
(* The analysis is the least fixed point of the following function, which
analyzes a nonterminal symbol by looking up and analyzing its definition
as a disjunction of conjunctions of symbols. *)
let nonterminal nt get : property =
(* Disjunction over all productions for this nonterminal symbol. *)
Production.foldnt_lazy nt (fun prod rest ->
S.disjunction
(production prod 0 get)
rest
) P.bottom
(* The least fixed point is taken as follows. Note that it is computed
on demand, as [lfp] is called by the user. *)
module F =
Fix.Make
(Maps.ArrayAsImperativeMaps(Nonterminal))
(P)
let nonterminal =
F.lfp nonterminal
(* The auxiliary functions can be published too. *)
let symbol sym =
symbol sym nonterminal
let production prod i =
production prod i nonterminal
end
(* ------------------------------------------------------------------------ *)
(* The computation of FOLLOW sets does not follow the above model. Instead, we
need to explicitly compute a system of equations over sets of terminal
symbols (in a first pass), then solve the constraints (in a second
pass). *)
(* The computation of the symbolic FOLLOW sets follows the same pattern, but
produces sets of symbols, instead of sets of terminals. For this reason,
we parameterize this little equation solver over a module [P], which we
later instantiate with [TerminalSet] and [SymbolSet]. *)
module Solve (P : sig
include Fix.PROPERTY
val union: property -> property -> property
end) = struct
(* An equation's right-hand side is a set expression. *)
type expr =
| EVar of Nonterminal.t
| EConstant of P.property
| EUnion of expr * expr
(* A system of equations is represented as an array, which maps nonterminal
symbols to expressions. *)
type equations =
expr array
(* This solver computes the least solution of a set of equations. *)
let solve (eqs : equations) : Nonterminal.t -> P.property =
let rec expr e get =
match e with
| EVar nt ->
get nt
| EConstant c ->
c
| EUnion (e1, e2) ->
P.union (expr e1 get) (expr e2 get)
in
let nonterminal nt get =
expr eqs.(nt) get
in
let module F =
Fix.Make
(Maps.ArrayAsImperativeMaps(Nonterminal))
(P)
in
F.lfp nonterminal
end
(* ------------------------------------------------------------------------ *)
(* Compute which nonterminals are nonempty, that is, recognize a
nonempty language. Also, compute which nonterminals are
nullable. The two computations are almost identical. The only
difference is in the base case: a single terminal symbol is not
nullable, but is nonempty. *)
module NONEMPTY =
GenericAnalysis
(Boolean)
(struct
(* A terminal symbol is nonempty. *)
let terminal _ = true
(* An alternative is nonempty if at least one branch is nonempty. *)
let disjunction p q = p || q()
(* A sequence is nonempty if both members are nonempty. *)
let conjunction _ p q = p && q()
(* The sequence epsilon is nonempty. It generates the singleton
language {epsilon}. *)
let epsilon = true
end)
module NULLABLE =
GenericAnalysis
(Boolean)
(struct
(* A terminal symbol is not nullable. *)
let terminal _ = false
(* An alternative is nullable if at least one branch is nullable. *)
let disjunction p q = p || q()
(* A sequence is nullable if both members are nullable. *)
let conjunction _ p q = p && q()
(* The sequence epsilon is nullable. *)
let epsilon = true
end)
(* ------------------------------------------------------------------------ *)
(* Compute FIRST sets. *)
module FIRST =
GenericAnalysis
(TerminalSet)
(struct
(* A terminal symbol has a singleton FIRST set. *)
let terminal = TerminalSet.singleton
(* The FIRST set of an alternative is the union of the FIRST sets. *)
let disjunction p q = TerminalSet.union p (q())
(* The FIRST set of a sequence is the union of:
the FIRST set of the first member, and
the FIRST set of the second member, if the first member is nullable. *)
let conjunction symbol p q =
if NULLABLE.symbol symbol then
TerminalSet.union p (q())
else
p
(* The FIRST set of the empty sequence is empty. *)
let epsilon = TerminalSet.empty
end)
(* ------------------------------------------------------------------------ *)
let () =
(* If a start symbol generates the empty language or generates
the language {epsilon}, report an error. In principle, this
could be just a warning. However, in [Engine], in the function
[start], it is convenient to assume that neither of these
situations can arise. This means that at least one token must
be read. *)
StringSet.iter (fun symbol ->
let nt = Nonterminal.lookup symbol in
if not (NONEMPTY.nonterminal nt) then
Error.error
(Nonterminal.positions nt)
"%s generates the empty language." (Nonterminal.print false nt);
if TerminalSet.is_empty (FIRST.nonterminal nt) then
Error.error
(Nonterminal.positions nt)
"%s generates the language {epsilon}." (Nonterminal.print false nt)
) Front.grammar.start_symbols;
(* If a nonterminal symbol generates the empty language, issue a warning. *)
for nt = Nonterminal.start to Nonterminal.n - 1 do
if not (NONEMPTY.nonterminal nt) then
Error.grammar_warning
(Nonterminal.positions nt)
"%s generates the empty language." (Nonterminal.print false nt);
done
(* ------------------------------------------------------------------------ *)
(* For every nonterminal symbol [nt], compute a word of minimal length
generated by [nt]. This analysis subsumes [NONEMPTY] and [NULLABLE].
Indeed, [nt] produces a nonempty language if only if the minimal length is
finite; [nt] is nullable if only if the minimal length is zero. *)
(* This analysis is in principle more costly than the [NONEMPTY] and
[NULLABLE], so it is performed only on demand. In practice, it seems
to be very cheap: its cost is not measurable for any of the grammars
in our benchmark suite. *)
module MINIMAL =
GenericAnalysis
(struct
include CompletedNatWitness
type property = Terminal.t t
end)
(struct
open CompletedNatWitness
(* A terminal symbol has length 1. *)
let terminal = singleton
(* The length of an alternative is the minimum length of any branch. *)
let disjunction = min_lazy
(* The length of a sequence is the sum of the lengths of the members. *)
let conjunction _ = add_lazy
(* The epsilon sequence has length 0. *)
let epsilon = epsilon
end)
(* ------------------------------------------------------------------------ *)
(* Dump the analysis results. *)
let () =
Error.logG 2 (fun f ->
for nt = Nonterminal.start to Nonterminal.n - 1 do
Printf.fprintf f "nullable(%s) = %b\n"
(Nonterminal.print false nt)
(NULLABLE.nonterminal nt)
done;
for nt = Nonterminal.start to Nonterminal.n - 1 do
Printf.fprintf f "first(%s) = %s\n"
(Nonterminal.print false nt)
(TerminalSet.print (FIRST.nonterminal nt))
done;
for nt = Nonterminal.start to Nonterminal.n - 1 do
Printf.fprintf f "minimal(%s) = %s\n"
(Nonterminal.print false nt)
(CompletedNatWitness.print Terminal.print (MINIMAL.nonterminal nt))
done
)
let () =
Time.tick "Analysis of the grammar"
(* ------------------------------------------------------------------------ *)
(* Compute FOLLOW sets. Unnecessary for us, but requested by a user. Also,
this is useful for the SLR(1) test. Thus, we perform this analysis only
on demand. *)
(* The computation of the symbolic FOLLOW sets follows exactly the same
pattern. We share code and parameterize this computation over a module [P],
just like the little equation solver above. *)
module FOLLOW (P : sig
include Fix.PROPERTY
val union: property -> property -> property
val terminal: Terminal.t -> property
val first: Production.index -> int -> property
end) = struct
module S = Solve(P)
open S
(* First pass. Build a system of equations. *)
let follow : equations =
Array.make Nonterminal.n (EConstant P.bottom)
(* Iterate over all start symbols. *)
let () =
let sharp = EConstant (P.terminal Terminal.sharp) in
for nt = 0 to Nonterminal.start - 1 do
assert (Nonterminal.is_start nt);
(* Add # to FOLLOW(nt). *)
follow.(nt) <- EUnion (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. *)
let () =
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 = P.first prod (i+1) in
(* The FIRST set of the remainder of the right-hand side
contributes to the FOLLOW set of [nt2]. *)
follow.(nt2) <- EUnion (EConstant first, follow.(nt2));
(* If the remainder of the right-hand side is nullable,
FOLLOW(nt1) contributes to FOLLOW(nt2). *)
if nullable then
follow.(nt2) <- EUnion (EVar nt1, follow.(nt2))
) rhs
) Production.table
(* Second pass. Solve the equations (on demand). *)
let follow : Nonterminal.t -> P.property =
solve follow
end
(* Use the above functor to obtain the standard (concrete) FOLLOW sets. *)
let follow : Nonterminal.t -> TerminalSet.t =
let module F = FOLLOW(struct
include TerminalSet
let terminal = singleton
let first = FIRST.production
end) in
F.follow
(* At log level 2, display the FOLLOW sets. *)
let () =
Error.logG 2 (fun f ->
for nt = Nonterminal.start to Nonterminal.n - 1 do
Printf.fprintf f "follow(%s) = %s\n"
(Nonterminal.print false nt)
(TerminalSet.print (follow nt))
done
)
(* Compute FOLLOW sets for the terminal symbols as well. Again, unnecessary
for us, but requested by a user. This is done in a single pass over the
grammar -- no new fixpoint computation is required. *)
let tfollow : TerminalSet.t array Lazy.t =
lazy (
let tfollow =
Array.make Terminal.n TerminalSet.empty
in
(* Iterate over all productions. *)
Array.iteri (fun prod (nt1, rhs) ->
(* Iterate over all terminal symbols [t2] in the right-hand side. *)
Array.iteri (fun i symbol ->
match symbol with
| Symbol.N _ ->
()
| Symbol.T t2 ->
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 [t2]. *)
tfollow.(t2) <- TerminalSet.union first tfollow.(t2);
(* If the remainder of the right-hand side is nullable,
FOLLOW(nt1) contributes to FOLLOW(t2). *)
if nullable then
tfollow.(t2) <- TerminalSet.union (follow nt1) tfollow.(t2)
) rhs
) Production.table;
tfollow
)
(* Define another accessor. *)
let tfollow t =
(Lazy.force tfollow).(t)
(* At log level 3, display the FOLLOW sets for terminal symbols. *)
let () =
Error.logG 3 (fun f ->
for t = 0 to Terminal.n - 1 do
Printf.fprintf f "follow(%s) = %s\n"
(Terminal.print t)
(TerminalSet.print (tfollow t))
done
)
(* ------------------------------------------------------------------------ *)
(* Compute symbolic FIRST and FOLLOW sets. *)
(* The symbolic FIRST set of the word determined by [prod/i] is defined
(and computed) as follows. *)
let sfirst prod i =
let rhs = Production.rhs prod in
let n = Array.length rhs in
let rec loop i =
if i = n then
(* If the word [prod/i] is empty, the set is empty. *)
SymbolSet.empty
else
let sym = rhs.(i) in
(* If the word [prod/i] begins with a symbol [sym], then [sym]
itself is part of the symbolic FIRST set, unconditionally. *)
SymbolSet.union
(SymbolSet.singleton sym)
(* Furthermore, if [sym] is nullable, then the symbolic
FIRST set of the sub-word [prod/i+1] contributes, too. *)
(if NULLABLE.symbol sym then loop (i + 1) else SymbolSet.empty)
in
loop i
(* The symbolic FOLLOW sets are computed just like the FOLLOW sets,
except we use a symbolic FIRST set instead of a standard FIRST
set. *)
let sfollow : Nonterminal.t -> SymbolSet.t =
let module F = FOLLOW(struct
include SymbolSet
let terminal t = SymbolSet.singleton (Symbol.T t)
let first = sfirst
end) in
F.follow
(* At log level 3, display the symbolic FOLLOW sets. *)
let () =
Error.logG 3 (fun f ->
for nt = Nonterminal.start to Nonterminal.n - 1 do
Printf.fprintf f "sfollow(%s) = %s\n"
(Nonterminal.print false nt)
(SymbolSet.print (sfollow nt))
done
)
(* ------------------------------------------------------------------------ *)
(* Provide explanations about FIRST sets. *)
(* The idea is to explain why a certain token appears in the FIRST set
for a certain sequence of symbols. Such an explanation involves
basic assertions of the form (i) symbol N is nullable and (ii) the
token appears in the FIRST set for symbol N. We choose to take
these basic facts for granted, instead of recursively explaining
them, so as to keep explanations short. *)
(* We first produce an explanation in abstract syntax, then
convert it to a human-readable string. *)
type explanation =
| EObvious (* sequence begins with desired token *)
| EFirst of Terminal.t * Nonterminal.t (* sequence begins with a nonterminal that produces desired token *)
| ENullable of Symbol.t list * explanation (* sequence begins with a list of nullable symbols and ... *)
let explain (tok : Terminal.t) (rhs : Symbol.t array) (i : int) =
let length = Array.length rhs in
let rec loop i =
assert (i < length);
let symbol = rhs.(i) in
match symbol with
| Symbol.T tok' ->
assert (Terminal.equal tok tok');
EObvious
| Symbol.N nt ->
if TerminalSet.mem tok (FIRST.nonterminal nt) then
EFirst (tok, nt)
else begin
assert (NULLABLE.nonterminal nt);
match loop (i + 1) with
| ENullable (symbols, e) ->
ENullable (symbol :: symbols, e)
| e ->
ENullable ([ symbol ], e)
end
in
loop i
let rec convert = function
| EObvious ->
""
| EFirst (tok, nt) ->
Printf.sprintf "%s can begin with %s"
(Nonterminal.print false nt)
(Terminal.print tok)
| ENullable (symbols, e) ->
let e = convert e in
Printf.sprintf "%scan vanish%s%s"
(Symbol.printl symbols)
(if e = "" then "" else " and ")
e
(* ------------------------------------------------------------------------ *)
(* Package the analysis results. *)
module Analysis = struct
let nullable = NULLABLE.nonterminal
let first = FIRST.nonterminal
(* An initial definition of [nullable_first_prod]. *)
let nullable_first_prod prod i =
NULLABLE.production prod i,
FIRST.production prod i
(* A memoised version, so as to avoid recomputing along a production's
right-hand side. *)
let nullable_first_prod =
Misc.tabulate Production.n (fun prod ->
Misc.tabulate (Production.length prod + 1) (fun i ->
nullable_first_prod prod i
)
)
let first_prod_lookahead prod i z =
let nullable, first = nullable_first_prod prod i in
if nullable then
TerminalSet.add z first
else
first
let explain_first_rhs (tok : Terminal.t) (rhs : Symbol.t array) (i : int) =
convert (explain tok rhs i)
let follow = follow
let minimal_symbol = MINIMAL.symbol
let minimal_prod = MINIMAL.production
end
(* ------------------------------------------------------------------------ *)
(* Conflict resolution via precedences. *)
module Precedence = struct
type choice =
| ChooseShift
| ChooseReduce
| ChooseNeither
| DontKnow
type order = Lt | Gt | Eq | Ic
let precedence_order p1 p2 =
match p1, p2 with
| UndefinedPrecedence, _
| _, UndefinedPrecedence ->
Ic
| PrecedenceLevel (m1, l1, _, _), PrecedenceLevel (m2, l2, _, _) ->
if not (Mark.same m1 m2) then
Ic
else
if l1 > l2 then
Gt
else if l1 < l2 then
Lt
else
Eq
let production_order p1 p2 =
match p1, p2 with
| ProductionLevel (m1, l1), ProductionLevel (m2, l2) ->
if not (Mark.same m1 m2) then
Ic
else
if l1 > l2 then
Gt
else if l1 < l2 then
Lt
else
Eq
let shift_reduce tok prod =
let fact1, tokp = Terminal.precedence_level tok
and fact2, prodp = Production.precedence prod in
match precedence_order tokp prodp with
(* Our information is inconclusive. Drop [fact1] and [fact2],
that is, do not record that this information was useful. *)
| Ic ->
DontKnow
(* Our information is useful. Record that fact by evaluating
[fact1] and [fact2]. *)
| (Eq | Lt | Gt) as c ->
Lazy.force fact1;
Lazy.force fact2;
match c with
| Ic ->
assert false (* already dispatched *)
| Eq ->
begin
match Terminal.associativity tok with
| LeftAssoc -> ChooseReduce
| RightAssoc -> ChooseShift
| NonAssoc -> ChooseNeither
| _ -> assert false
(* If [tok]'s precedence level is defined, then
its associativity must be defined as well. *)
end
| Lt ->
ChooseReduce
| Gt ->
ChooseShift
let reduce_reduce prod1 prod2 =
let pl1 = Production.production_level.(prod1)
and pl2 = Production.production_level.(prod2) in
match production_order pl1 pl2 with
| Lt ->
Some prod1
| Gt ->
Some prod2
| Eq ->
(* The order is strict except in the presence of parameterized
non-terminals and/or inlining. Two productions can have the same
precedence level if they originate, via macro-expansion or via
inlining, from a single production in the source grammar. *)
None
| Ic ->
None
end
let diagnostics () =
TokPrecedence.diagnostics();
Production.diagnostics()
(* ------------------------------------------------------------------------ *)
(* %on_error_reduce declarations. *)
module OnErrorReduce = struct
let declarations =
Front.grammar.on_error_reduce
end