LRijkstra.ml 35.8 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
(* The purpose of this algorithm is to find, for each pair of a state [s]
   and a terminal symbol [z] such that looking at [z] in state [s] causes
   an error, a minimal path (starting in some initial state) that actually
   triggers this error. *)

(* This is potentially useful for grammar designers who wish to better
   understand the properties of their grammar, or who wish to produce a
   list of all possible syntax errors (or, at least, one syntax error in
   each automaton state where an error may occur). *)

(* The problem seems rather tricky. One might think that it suffices to
   compute shortest paths in the automaton, and to use [Analysis.minimal] to
   replace each non-terminal symbol in a path with a minimal word that this
   symbol generates. One can indeed do so, but this yields only a lower bound
   on the actual shortest path to the error at [s, z]. Indeed, two
   difficulties arise:

   - Some states have a default reduction. Thus, they will not trigger
     an error, even though they should. The error is triggered in some
     other state, after reduction takes place.

   - If the grammar has conflicts, conflict resolution removes some
     (shift or reduce) actions, hence may suppress the shortest path. *)

25 26 27 28 29 30 31 32 33 34 35
(* We explicitly choose to ignore the [error] token. Thus, we disregard any
   reductions or transitions that take place when the lookahead symbol is
   [error]. As a result, any state whose incoming symbol is [error] is found
   unreachable. It would be too complicated to have to create a first error in
   order to be able to take certain transitions or drop certain parts of the
   input. *)

(* We never work with the terminal symbol [#] either. This symbol never
   appears in the maps returned by [Lr1.transitions] and [Lr1.reductions].
   Thus, in principle, we work with ``real'' terminal symbols only. However,
   we encode [any] as [#] -- see below. *)
36

37 38 39 40 41
(* ------------------------------------------------------------------------ *)

(* To delay the side effects performed by this module, we wrap everything in
   in a big functor without arguments. *)

42
module Run (X : sig val verbose: bool end) = struct
43

44
open Grammar
45 46 47

(* ------------------------------------------------------------------------ *)

48 49
(* Because of our encoding of terminal symbols as 8-bit characters, this
   algorithm supports at most 256 terminal symbols. *)
50 51

let () =
52
  if Terminal.n > 256 then
53
    Error.error [] (Printf.sprintf
54
      "--list-errors supports at most 256 terminal symbols.\n\
55 56 57 58 59
       The grammar has %d terminal symbols." Terminal.n
    )

(* ------------------------------------------------------------------------ *)

60 61 62 63 64
(* Build a module that represents words as (hash-consed) strings. Note:
   this functor application has a side effect (it allocates memory, and
   more importantly, it may fail). *)

module W = Terminal.Word(struct end)
65

66 67
(* ------------------------------------------------------------------------ *)

68 69
(* The [error] token may appear in the maps returned by [Lr1.transitions]
   and [Lr1.reductions], so we sometimes need to explicitly check for it. *)
70

71
let non_error z =
72
  not (Terminal.equal z Terminal.error)
73

74 75 76 77
(* We introduce a pseudo-terminal symbol [any]. It is used in several places
   later on, in particular in the field [fact.lookahead], to encode the
   absence of a lookahead hypothesis -- i.e., any terminal symbol will do. *)

78 79 80 81 82
(* We choose to encode [any] as [#]. There is no risk of confusion, since we
   do not use [#] anywhere. Thus, the assertion [Terminal.real z] implies
   [z <> any]. *)

let any =
83
  Terminal.sharp
84

85 86
(* ------------------------------------------------------------------------ *)

87 88 89 90 91
(* We begin with a number of auxiliary functions that provide information
   about the LR(1) automaton. These functions could perhaps be moved to a
   separate module. We keep them here, for the moment, because they are not
   used anywhere else. *)

POTTIER Francois's avatar
POTTIER Francois committed
92 93 94
(* [reductions_on s z] is the list of reductions permitted in state [s] when
   the lookahead symbol is [z]. This is a list of zero or one elements. This
   does not take default reductions into account. *)
95

POTTIER Francois's avatar
POTTIER Francois committed
96
let reductions_on s z : Production.index list =
97
  assert (Terminal.real z);
98 99 100 101 102
  try
    TerminalMap.find z (Lr1.reductions s)
  with Not_found ->
    []

103 104 105
(* [has_reduction s z] tells whether state [s] is willing to reduce some
   production (and if so, which one) when the lookahead symbol is [z]. It
   takes a possible default reduction into account. *)
106 107

let has_reduction s z : Production.index option =
108
  assert (Terminal.real z);
109 110 111 112
  match Invariant.has_default_reduction s with
  | Some (prod, _) ->
      Some prod
  | None ->
POTTIER Francois's avatar
POTTIER Francois committed
113
      match reductions_on s z with
114 115 116 117 118 119
      | prod :: prods ->
          assert (prods = []);
          Some prod
      | [] ->
          None

120 121 122 123 124 125 126 127 128
(* [can_reduce s prod] indicates whether state [s] is able to reduce
   production [prod] (either as a default reduction, or as a normal
   reduction). *)

let can_reduce s prod =
  match Invariant.has_default_reduction s with
  | Some (prod', _) when prod = prod' ->
      true
  | _ ->
129
      TerminalMap.fold (fun z prods accu ->
130 131
        (* A reduction on [#] is always a default reduction. (See [lr1.ml].) *)
        assert (not (Terminal.equal z Terminal.sharp));
132
        accu || non_error z && List.mem prod prods
133 134
      ) (Lr1.reductions s) false

135 136
(* [causes_an_error s z] tells whether state [s] will initiate an error on the
   lookahead symbol [z]. *)
137

138
let causes_an_error s z : bool =
139
  assert (Terminal.real z);
140 141 142 143
  match Invariant.has_default_reduction s with
  | Some _ ->
      false
  | None ->
POTTIER Francois's avatar
POTTIER Francois committed
144
      reductions_on s z = [] &&
145 146
      not (SymbolMap.mem (Symbol.T z) (Lr1.transitions s))

147
(* [foreach_terminal f] applies the function [f] to every terminal symbol in
148
   turn, except [error] and [#]. *)
149

150 151
let foreach_terminal =
  Terminal.iter_real
152

153 154 155
(* [foreach_terminal_not_causing_an_error s f] applies the function [f] to
   every terminal symbol [z] such that [causes_an_error s z] is false. This
   could be implemented in a naive manner using [foreach_terminal] and
POTTIER Francois's avatar
POTTIER Francois committed
156
   [causes_an_error]. This implementation is significantly more efficient. *)
157

158 159 160
let foreach_terminal_not_causing_an_error s f =
  match Invariant.has_default_reduction s with
  | Some _ ->
161
      (* There is a default reduction. No symbol causes an error. *)
162 163
      foreach_terminal f
  | None ->
164 165 166
      (* Enumerate every terminal symbol [z] for which there is a
         reduction. *)
      TerminalMap.iter (fun z _ ->
167 168 169
        (* A reduction on [#] is always a default reduction. (See [lr1.ml].) *)
        assert (not (Terminal.equal z Terminal.sharp));
        if non_error z then
170
          f z
171
      ) (Lr1.reductions s);
172 173
      (* Enumerate every terminal symbol [z] for which there is a
         transition. *)
174 175
      SymbolMap.iter (fun sym _ ->
        match sym with
176
        | Symbol.T z ->
177 178
            assert (not (Terminal.equal z Terminal.sharp));
            if non_error z then
179
              f z
180 181 182 183
        | Symbol.N _ ->
            ()
      ) (Lr1.transitions s)

184
(* Let us say a state [s] is solid if its incoming symbol is a terminal symbol
POTTIER Francois's avatar
POTTIER Francois committed
185 186
   (or if it has no incoming symbol at all, i.e., it is an initial state). It
   is fragile if its incoming symbol is a non-terminal symbol. *)
187 188 189 190 191

let is_solid s =
  match Lr1.incoming_symbol s with
  | None
  | Some (Symbol.T _) ->
POTTIER Francois's avatar
POTTIER Francois committed
192
    true
193
  | Some (Symbol.N _) ->
POTTIER Francois's avatar
POTTIER Francois committed
194
    false
195

196 197
(* ------------------------------------------------------------------------ *)

POTTIER Francois's avatar
POTTIER Francois committed
198 199 200 201 202 203 204 205 206
(* Suppose [s] is a state that carries an outgoing edge labeled with a
   non-terminal symbol [nt]. We are interested in finding out how this edge
   can be taken. In order to do that, we must determine how, by starting in
   [s], one can follow a path that corresponds to (the right-hand side of) a
   production [prod] associated with [nt]. There are in general several such
   productions. The paths that they determine in the automaton form a "star".
   We represent the star rooted at [s] as a trie. For every state [s], the
   star rooted at [s] is constructed in advance, before the algorithm runs.
   While the algorithm runs, a point in the trie (that is, a sub-trie) tells
POTTIER Francois's avatar
Typo.  
POTTIER Francois committed
207
   us where we come from, where we are, and which production(s) we are hoping
POTTIER Francois's avatar
POTTIER Francois committed
208 209
   to reduce in the future. *)

210 211 212
module Trie : sig

  type trie
213 214 215 216

  (* [star s] creates a (new) trie whose source is [s], populated with its
     branches. (There is one branch for every production [prod] associated
     with every non-terminal symbol [nt] for which [s] carries an outgoing
217
     edge.) If the star turns out to be trivial then [None] is returned. *)
218 219
  val star: Lr1.node -> trie option

220 221 222 223
  (* After [star s] has been called, [size (Lr1.number s)] reports the size
     of the trie that has been constructed for state [s]. *)
  val size: int -> int

224 225 226 227 228 229 230 231
  (* Every (sub-)trie has a unique identity. (One can think of it as its
     address.) [compare] compares the identity of two tries. This can be
     used, e.g., to set up a map whose keys are tries. *)
  val compare: trie -> trie -> int

  (* [source t] returns the source state of the (sub-)trie [t]. This is
     the root of the star of which [t] is a sub-trie. In other words, this
     tells us "where we come from". *)
232
  val source: trie -> Lr1.node
POTTIER Francois's avatar
POTTIER Francois committed
233 234

  (* [current t] returns the current state of the (sub-)trie [t]. This is
235 236
     the root of the sub-trie [t]. In other words, this tells us "where
     we are". *)
POTTIER Francois's avatar
POTTIER Francois committed
237
  val current: trie -> Lr1.node
238

239 240 241 242 243
  (* [accepts prod t] tells whether the current state of the trie [t] is
     the end of a branch associated with production [prod]. If so, this
     means that we have successfully followed a path that corresponds to
     the right-hand side of production [prod]. *)
  val accepts: Production.index -> trie -> bool
244

245 246 247 248 249 250 251 252
  (* [step sym t] is the immediate sub-trie of [t] along the symbol [sym].
     This function raises [Not_found] if [t] has no child labeled [sym]. *)
  val step: Symbol.t -> trie -> trie

  (* [verbose()] outputs debugging & performance information. *)
  val verbose: unit -> unit

end = struct
253

254 255
  (* A trie has the following structure. *)

256
  type trie = {
257 258 259
    (* A unique identity, used by [compare]. The trie construction code
       ensures that these numbers are indeed unique: see [fresh], [insert],
       [star]. *)
260
    identity: int;
261
    (* The root state of this star: "where we come from". *)
262
    source: Lr1.node;
263
    (* The current state, i.e., the root of this sub-trie: "where we are". *)
POTTIER Francois's avatar
POTTIER Francois committed
264
    current: Lr1.node;
265 266 267
    (* The productions that we can reduce in the current state. In other
       words, if this list is nonempty, then the current state is the end
       of one (or several) branches. It can nonetheless have children. *)
268
    productions: Production.index list;
269 270
    (* The children, or sub-tries. *)
    transitions: trie SymbolMap.t
271
  }
272

273
  (* This counter is used by [mktrie] to produce unique identities. *)
274 275
  let c = ref 0

276
  (* This smart constructor creates a new trie with a unique identity. *)
POTTIER Francois's avatar
POTTIER Francois committed
277
  let mktrie source current productions transitions =
278
    let identity = Misc.postincrement c in
POTTIER Francois's avatar
POTTIER Francois committed
279
    { identity; source; current; productions; transitions }
280

281 282
  exception DeadBranch

283
  let rec insert w prod t =
284 285
    match w with
    | [] ->
POTTIER Francois's avatar
POTTIER Francois committed
286
        (* We check whether the current state [t.current] is able to reduce
287 288 289 290 291
           production [prod]. (If [prod] cannot be reduced, the reduction
           action must have been suppressed by conflict resolution.) If not,
           then this branch is dead. This test is superfluous (i.e., it would
           be OK to conservatively assume that [prod] can be reduced) but
           allows us to build a slightly smaller star in some cases. *)
POTTIER Francois's avatar
POTTIER Francois committed
292
        if can_reduce t.current prod then
293 294 295 296 297 298
          (* We consume (update) the trie [t], so there is no need to allocate
             a new stamp. (Of course we could allocate a new stamp, but I prefer
             to be precise.) *)
          { t with productions = prod :: t.productions }
        else
          raise DeadBranch
299
    | (Symbol.T t) :: _ when Terminal.equal t Terminal.error ->
300
         raise DeadBranch
301
    | a :: w ->
POTTIER Francois's avatar
POTTIER Francois committed
302
        (* Check if there is a transition labeled [a] out of [t.current]. If
303 304
           there is, we add a child to the trie [t]. If there isn't, then it
           must have been removed by conflict resolution. (Indeed, it must be
305 306 307
           present in a canonical automaton.) We could in this case return an
           unchanged sub-trie. We can do slightly better: we abort the whole
           insertion, so as to return an unchanged toplevel trie. *)
POTTIER Francois's avatar
POTTIER Francois committed
308
        match SymbolMap.find a (Lr1.transitions t.current) with
309
        | successor ->
310 311 312 313 314 315 316 317
            (* Find our child at [a], or create it. *)
            let t' =
              try
                SymbolMap.find a t.transitions
              with Not_found ->
                mktrie t.source successor [] SymbolMap.empty
            in
            (* Update the child [t']. *)
318
            let t' = insert w prod t' in
319 320
            (* Update [t]. Again, no need to allocate a new stamp. *)
            { t with transitions = SymbolMap.add a t' t.transitions }
321
        | exception Not_found ->
322
            raise DeadBranch
323

324 325 326 327 328
  (* [insert prod t] inserts a new branch, corresponding to production
     [prod], into the trie [t]. This function consumes its argument,
     which should no longer be used afterwards. *)
  let insert prod t =
    let w = Array.to_list (Production.rhs prod) in
329 330 331 332 333 334
    let save = !c in
    try
      insert w prod t
    with DeadBranch ->
      c := save;
      t
335

336 337 338 339
  (* [fresh s] creates a new empty trie whose source is [s]. *)
  let fresh source =
    mktrie source source [] SymbolMap.empty

340 341 342
  (* The star at [s] is obtained by starting with a fresh empty trie and
     inserting into it every production [prod] whose left-hand side [nt]
     is the label of an outgoing edge at [s]. *)
343 344 345 346 347 348 349 350 351
  let star s =
    SymbolMap.fold (fun sym _ accu ->
      match sym with
      | Symbol.T _ ->
          accu
      | Symbol.N nt ->
          Production.foldnt nt accu insert
    ) (Lr1.transitions s) (fresh s)

352 353 354 355 356 357 358
  (* A trie [t] is nontrivial if it has at least one branch, i.e., contains at
     least one sub-trie whose [productions] field is nonempty. Trivia: a trie
     of size greater than 1 is necessarily nontrivial, but the converse is not
     true: a nontrivial trie can have size 1. (This occurs if all productions
     have zero length.) *)
  let trivial t =
    t.productions = [] && SymbolMap.is_empty t.transitions
359

360 361
  (* Redefine [star] to include a [nontrivial] test and to record the size of
     the newly built trie. *)
362 363 364 365

  let size =
    Array.make Lr1.n (-1)

366
  let star s =
367
    let initial = !c in
368
    let t = star s in
369 370
    let final = !c in
    size.(Lr1.number s) <- final - initial;
371
    if trivial t then None else Some t
372

373 374 375 376
  let size s =
    assert (size.(s) >= 0);
    size.(s)

POTTIER Francois's avatar
POTTIER Francois committed
377
  let compare t1 t2 =
378
    Pervasives.compare t1.identity t2.identity
379

380 381 382
  let source t =
    t.source

POTTIER Francois's avatar
POTTIER Francois committed
383 384
  let current t =
    t.current
385

386 387 388
  let accepts prod t =
    List.mem prod t.productions

389
  let step a t =
390
    SymbolMap.find a t.transitions (* careful: may raise [Not_found] *)
391

392
  let verbose () =
393
    Printf.eprintf "Cumulated star size: %d\n%!" !c
394

395 396
end

POTTIER Francois's avatar
POTTIER Francois committed
397 398
(* ------------------------------------------------------------------------ *)

POTTIER Francois's avatar
POTTIER Francois committed
399 400 401 402 403 404
(* The main algorithm, [LRijkstra], accumulates facts. A fact is a triple of a
   position (that is, a sub-trie), a word, and a lookahead assumption. Such a
   fact means that this position can be reached, from the source state
   [Trie.source fact.position], by consuming [fact.word], under the assumption
   that the next input symbol is [fact.lookahead]. *)

405 406
(* We allow [fact.lookahead] to be [any] so as to indicate that this fact does
   not have a lookahead assumption. *)
POTTIER Francois's avatar
POTTIER Francois committed
407

408
type fact = {
409
  position: Trie.trie;
410
  word: W.word;
411
  lookahead: Terminal.t (* may be [any] *)
412 413
}

414 415
(* Accessors. *)

416
let source fact =
417
  Trie.source fact.position
418

POTTIER Francois's avatar
POTTIER Francois committed
419
let current fact =
420
  Trie.current fact.position
421

422 423
(* Two invariants reduce the number of facts that we consider:

424 425 426
   1. If [fact.lookahead] is a real terminal symbol [z] (i.e., not [any]),
      then [z] does not cause an error in the current state [current fact].
      It would be useless to consider a fact that violates this property;
POTTIER Francois's avatar
POTTIER Francois committed
427 428 429
      this cannot possibly lead to a successful reduction. In practice,
      this refinement allows reducing the number of facts that go through
      the queue by a factor of two.
430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447

   2. [fact.lookahead] is [any] iff the current state [current fact] is
      solid. This sounds rather reasonable (when a state is entered
      by shifting, it is entered regardless of which symbol follows)
      and simplifies the implementation of the sub-module [T].

*)

let invariant1 fact =
  fact.lookahead = any || not (causes_an_error (current fact) fact.lookahead)

let invariant2 fact =
  (fact.lookahead = any) = is_solid (current fact)

(* [compatible z a] checks whether the terminal symbol [a] satisfies the
   lookahead assumption [z] -- which can be [any]. *)

let compatible z a =
448 449
  assert (non_error z);
  assert (Terminal.real a);
450 451
  z = any || z = a

POTTIER Francois's avatar
POTTIER Francois committed
452
(* ------------------------------------------------------------------------ *)
453

454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476
(* As in Dijkstra's algorithm, a priority queue contains the facts that await
   examination. The length of [fact.word] serves as the priority of a fact.
   This guarantees that we discover shortest paths. (We never insert into the
   queue a fact whose priority is less than the priority of the last fact
   extracted out of the queue.) *)

(* [LowIntegerPriorityQueue] offers very efficient operations (essentially
   constant time, for a small constant). It exploits the fact that priorities
   are low nonnegative integers. *)

module Q = LowIntegerPriorityQueue

let q =
  Q.create()

(* In principle, there is no need to insert the fact into the queue if [T]
   already stores a comparable fact. We could perform this test in [add].
   However, a quick experiment suggests that this is not worthwhile. The run
   time augments (because membership in [T] is tested twice, upon inserting
   and upon extracting) and the memory consumption does not seem to go down
   significantly. *)

let add fact =
POTTIER Francois's avatar
POTTIER Francois committed
477
  (* [fact.lookahead] can be [any], but cannot be [error] *)
478
  assert (non_error fact.lookahead);
479 480
  assert (invariant1 fact);
  assert (invariant2 fact);
481 482 483 484 485 486
  (* The length of [fact.word] serves as the priority of this fact. *)
  Q.add q fact (W.length fact.word)

(* Construct the [star] of every state [s]. Initialize the priority queue. *)

let () =
POTTIER Francois's avatar
POTTIER Francois committed
487
  (* For every state [s]... *)
488
  Lr1.iter (fun s ->
POTTIER Francois's avatar
POTTIER Francois committed
489
    (* If the trie rooted at [s] is nontrivial...*)
490
    match Trie.star s with
POTTIER Francois's avatar
POTTIER Francois committed
491 492 493 494 495 496 497 498 499 500
    | None ->
        ()
    | Some position ->
        (* ...then insert an initial fact into the priority queue. *)
        (* In order to respect invariants 1 and 2, we must distinguish two
           cases. If [s] is solid, then we insert a single fact, whose
           lookahead assumption is [any]. Otherwise, we must insert one
           initial fact for every terminal symbol [z] that does not cause
           an error in state [s]. *)
        let word = W.epsilon in
501
        if is_solid s then
POTTIER Francois's avatar
POTTIER Francois committed
502
          add { position; word; lookahead = any }
503 504
        else
          foreach_terminal_not_causing_an_error s (fun z ->
POTTIER Francois's avatar
POTTIER Francois committed
505
            add { position; word; lookahead = z }
506
          )
507 508 509 510
  )

(* ------------------------------------------------------------------------ *)

511 512 513 514 515 516 517 518 519 520
(* The first symbol of the input, [W.first fact.word fact.lookahead], plays a
   special role. Indeed, for every position, for every first symbol, and for
   every lookahead symbol, we keep track of at most one fact. Thus, the total
   number of facts accumulated by the algorithm is at most [T.n^2], where [T]
   is the total size of the tries that we have constructed, and [n] is the
   number of terminal symbols. (This number can be quite large. [T] can be in
   the tens of thousands, and [n] can be over one hundred. These figures lead
   to a theoretical upper bound of 100M. In practice, for T=25K and n=108, we
   observe that the algorithm gathers about 7M facts.) *)

521
module T : sig
522 523

  (* [register fact] registers the fact [fact]. It returns [true] if this fact
POTTIER Francois's avatar
POTTIER Francois committed
524 525
     is new, i.e., no fact concerning the same triple of [position], [a], and
     [z] was previously known. *)
526 527
  val register: fact -> bool

POTTIER Francois's avatar
POTTIER Francois committed
528 529
  (* [query current z f] enumerates all known facts whose current state is
     [current] and whose lookahead assumption is [z]. *)
530
  val query: Lr1.node -> Terminal.t -> (fact -> unit) -> unit
531

532
  val verbose: unit -> unit
533

534
end = struct
535

536
  (* This module implements a set of facts. Two facts are considered equal
537
     (for the purposes of this set) if they have the same [position], [a], and
538 539 540 541 542 543
     [z] fields. The [word] is not considered. Indeed, we are not interested
     in keeping track of several words that produce the same effect. Only the
     shortest such word is of interest. *)

  (* We need to query the set of facts in two ways. In [register], we need to
     test whether a fact is in the set. In [query], we need to find all facts
POTTIER Francois's avatar
POTTIER Francois committed
544 545
     that match a pair [current, z]. For this reason, we use a two-level table.
     The first level is a matrix indexed by [current] and [z]. At the second
546
     level, we find sets of facts. *)
547 548 549
(**)

  module M =
550
    MySet.Make(struct
551 552
      type t = fact
      let compare fact1 fact2 =
553
        let c = Trie.compare fact1.position fact2.position in
554
        if c <> 0 then c else
555 556
        let a1 = W.first fact1.word fact1.lookahead
        and a2 = W.first fact2.word fact2.lookahead in
557
        (* note: [a1] and [a2] can be [any] here *)
558 559
        Terminal.compare a1 a2
    end)
560

561
  let table = (* a pretty large table... *)
562
    Array.make (Lr1.n * Terminal.n) M.empty
563
  (* TEMPORARY this space is wasted for solid states *)
564

POTTIER Francois's avatar
POTTIER Francois committed
565
  let index current z =
566
    Terminal.n * (Lr1.number current) + Terminal.t2i z
567

568 569
  let count = ref 0

570
  let register fact =
POTTIER Francois's avatar
POTTIER Francois committed
571
    let current = current fact in
572
    let z = fact.lookahead in
573
    assert (non_error z);
574 575
    (* [z] is [any] iff [current] is solid. *)
    assert ((z = any) = is_solid current);
POTTIER Francois's avatar
POTTIER Francois committed
576
    let i = index current z in
577 578 579 580 581 582 583 584 585 586 587 588
    let m = table.(i) in
    (* We crucially rely on the fact that [M.add] guarantees not to
       change the set if an ``equal'' fact already exists. Thus, a
       later, longer path is ignored in favor of an earlier, shorter
       path. *)
    let m' = M.add fact m in
    m != m' && begin
      incr count;
      table.(i) <- m';
      true
    end

POTTIER Francois's avatar
POTTIER Francois committed
589
  let query current z f =
590 591
    assert (z <> any);
    (* if [current] is solid then the facts that concern it are stored
POTTIER Francois's avatar
POTTIER Francois committed
592
       under [any], not under [z] *)
593
    let i = index current (if is_solid current then any else z) in
594 595
    let m = table.(i) in
    M.iter f m
596

597
  let verbose () =
598
    Printf.eprintf "T stores %d facts.\n%!" !count
599

600 601
end

POTTIER Francois's avatar
POTTIER Francois committed
602 603
(* ------------------------------------------------------------------------ *)

604 605 606 607 608 609 610
(* The module [E] is in charge of recording the non-terminal edges that we have
   discovered, or more precisely, the conditions under which these edges can be
   taken. *)

module E : sig

  (* [register s nt w z] records that, in state [s], the outgoing edge labeled
611 612 613
     [nt] can be taken by consuming the word [w], if the next symbol is [z].
     It returns [true] if this information is new. *)
  val register: Lr1.node -> Nonterminal.t -> W.word -> Terminal.t -> bool
614 615 616 617

  (* [query s nt a z] answers whether, in state [s], the outgoing edge labeled
     [nt] can be taken by consuming some word [w], under the assumption that
     the next symbol is [z], and under the constraint that the first symbol of
618 619
     [w.z] is [a]. *)
  val query: Lr1.node -> Nonterminal.t -> Terminal.t -> Terminal.t -> (W.word -> unit) -> unit
620

621
  val verbose: unit -> unit
622

623 624
end = struct

625 626 627 628 629 630 631 632 633 634
  (* At a high level, we must implement a mapping of [s, nt, a, z] to [w]. In
     practice, we can implement this specification using any combination of
     arrays, hash tables, balanced binary trees, and perfect hashing (i.e.,
     packing several of [s], [nt], [a], [z] in one word.) Here, we choose to
     use an array, indexed by [s], of hash tables, indexed by a key that packs
     [nt], [a], and [z] in one word. According to a quick experiment, the
     final population of the hash table [table.(index s)] seems to be roughly
     [Terminal.n * Trie.size s]. We note that using an initial capacity
     of 0 and relying on the hash table's resizing mechanism has a significant
     cost, which is why we try to guess a good initial capacity. *)
635

636
  module H = Hashtbl
637

638
  let table = (* a pretty large table... *)
639 640 641 642
    Array.init (Lr1.n) (fun i ->
      let size = Trie.size i in
      H.create (if size = 1 then 0 else Terminal.n * size)
    )
643 644 645

  let index s =
    Lr1.number s
646

647 648 649 650
  let pack nt a z : int =
    (Nonterminal.n2i nt lsl 16) lor
    (Terminal.t2i a lsl 8) lor
    (Terminal.t2i z)
651

652 653
  let count = ref 0

654
  let register s nt w z =
655
    assert (Terminal.real z);
656
    let i = index s in
657
    let m = table.(i) in
658
    let a = W.first w z in
659
    assert (not (causes_an_error s a));
660 661 662 663
    let key = pack nt a z in
    if H.mem m key then
      false
    else begin
664
      incr count;
665
      H.add m key w;
666 667
      true
    end
668

669
  let rec query s nt a z f =
670
    assert (Terminal.real z);
671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689
    (* [a] can be [any] *)
    if a <> any then begin
      let i = index s in
      let m = table.(i) in
      let key = pack nt a z in
      match H.find m key with
      | w -> f w
      | exception Not_found -> ()
    end
    else begin
      (* If [a] is [any], we query the table for every concrete [a].
         We can limit ourselves to symbols that do not cause an error
         in state [s]. Those that do certainly do not have an entry;
         see the assertion in [register] above. *)
      foreach_terminal_not_causing_an_error s (fun a ->
        query s nt a z f
      )
        (* TEMPORARY try a scheme that allows a more efficient iteration? *)
    end
690

691
  let verbose () =
692
    Printf.eprintf "E stores %d facts.\n%!" !count
693

694 695
end

POTTIER Francois's avatar
POTTIER Francois committed
696 697
(* ------------------------------------------------------------------------ *)

698
let new_edge s nt w z =
699
  assert (Terminal.real z);
700
  if E.register s nt w z then
701
    let sym = Symbol.N nt in
702
    T.query s (W.first w z) (fun fact ->
703
      assert (compatible fact.lookahead (W.first w z));
704 705
      match Trie.step sym fact.position with
      | position ->
706
          assert (not (is_solid (Trie.current position)));
707
          if not (causes_an_error (Trie.current position) z) then
708
            add {
709
              position;
710 711 712 713 714
              word = W.append fact.word w;
              lookahead = z
            }
      | exception Not_found ->
          ()
715
    )
716 717 718 719 720 721 722 723 724 725

(* [consequences fact] is invoked when we discover a new fact (i.e., one that
   was not previously known). It studies the consequences of this fact. These
   consequences are of two kinds:

   - As in Dijkstra's algorithm, the new fact can be viewed as a newly
   discovered vertex. We study its (currently known) outgoing edges,
   and enqueue new facts in the priority queue.

   - Sometimes, a fact can also be viewed as a newly discovered edge.
POTTIER Francois's avatar
POTTIER Francois committed
726 727
   This is the case when the word from [fact.source] to [fact.current]
   represents a production of the grammar and [fact.current] is willing
728 729 730 731 732 733 734 735
   to reduce this production. We record the existence of this edge,
   and re-inspect any previously discovered vertices which are
   interested in this outgoing edge.
*)
(**)

let consequences fact =

POTTIER Francois's avatar
POTTIER Francois committed
736
  let current = current fact in
737

POTTIER Francois's avatar
POTTIER Francois committed
738
  (* 1. View [fact] as a vertex. Examine the transitions out of [current]. *)
739
  
740
  SymbolMap.iter (fun sym s' ->
741
    match Trie.step sym fact.position, sym with
742
    | exception Not_found -> ()
743
    | position, Symbol.T t ->
744 745
        (* [t] cannot be the [error] token, because the trie does not have
           any edges labeled [error]. *)
746
        assert (non_error t);
747

POTTIER Francois's avatar
POTTIER Francois committed
748
        (* 1a. There is a transition labeled [t] out of [current]. If
749 750 751 752 753
           the lookahead assumption [fact.lookahead] is compatible with [t],
           then we derive a new fact, where one more edge has been taken. We
           enqueue this new fact for later examination. *)
        (**)

754
        if compatible fact.lookahead t then begin
755
          let word = W.append fact.word (W.singleton t) in
756 757 758 759 760 761 762 763
          (* assert (Lr1.Node.compare (Trie.current position) s' = 0); *)
          (* [s'] has a terminal incoming symbol. It is always entered
             without consideration for the next lookahead symbol. Thus,
             we use [any] as the lookahead assumption in the new fact
             that we produce. *)
          assert (is_solid (Trie.current position));
          add { position; word; lookahead = any }
        end
764

765
    | position, Symbol.N nt ->
766

POTTIER Francois's avatar
POTTIER Francois committed
767
        (* 1b. There is a transition labeled [nt] out of [current]. We
768 769 770 771 772 773
           need to know how this nonterminal edge can be taken. We query for a
           word [w] that allows us to take this edge. The answer depends on
           the terminal symbol [z] that comes *after* this word: we try all
           such symbols. Furthermore, we need the first symbol of [w.z] to
           satisfy the lookahead assumption [fact.lookahead], so the answer
           also depends on this assumption. *)
POTTIER Francois's avatar
POTTIER Francois committed
774 775
        (* TEMPORARY it could be that the answer does not depend on [z]...
           (default reduction) *)
776 777 778
        (**)

        foreach_terminal_not_causing_an_error s' (fun z ->
POTTIER Francois's avatar
POTTIER Francois committed
779
          E.query current nt fact.lookahead z (fun w ->
780 781
            assert (compatible fact.lookahead (W.first w z));
            assert (not (is_solid (Trie.current position)));
782
            add {
783
              position;
784 785 786 787 788
              word = W.append fact.word w;
              lookahead = z
            }
          )
        )
789

POTTIER Francois's avatar
POTTIER Francois committed
790
  ) (Lr1.transitions current);
791 792

  (* 2. View [fact] as a possible edge. This is possible if the path from
POTTIER Francois's avatar
POTTIER Francois committed
793 794
     [fact.source] to [current] represents a production [prod] and
     [current] is willing to reduce this production. We check that
795
     [fact.position] accepts [epsilon]. This guarantees that reducing [prod]
796 797 798 799
     takes us all the way back to [fact.source]. Thus, this production gives
     rise to an edge labeled [nt] -- the left-hand side of [prod] -- out of
     [fact.source]. This edge is subject to the lookahead assumption
     [fact.lookahead], so we record that. *)
800 801
  (**)

802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819
  if fact.lookahead <> any then begin
    match has_reduction current fact.lookahead with
    | Some prod when Trie.accepts prod fact.position ->
        new_edge (source fact) (Production.nt prod) fact.word fact.lookahead
    | _ ->
        ()
  end
  else begin
    (* Every reduction must be considered. *)
    match Invariant.has_default_reduction current with
    | Some (prod, _) ->
        if Trie.accepts prod fact.position then
          (* TEMPORARY for now, avoid sending [any] into [new_edge] *)
          foreach_terminal (fun z ->
            new_edge (source fact) (Production.nt prod) (fact.word) z
          )
    | None ->
       TerminalMap.iter (fun z prods ->
820
         if non_error z then
821 822 823 824 825
           let prod = Misc.single prods in
           if Trie.accepts prod fact.position then
             new_edge (source fact) (Production.nt prod) (fact.word) z
       ) (Lr1.reductions current)
  end
826

827
let level = ref 0
828

POTTIER Francois's avatar
POTTIER Francois committed
829 830 831
let extracted, considered =
  ref 0, ref 0

POTTIER Francois's avatar
POTTIER Francois committed
832
let done_with_level () =
833 834 835 836 837 838 839 840
  Printf.eprintf "Done with level %d.\n" !level;
  if X.verbose then begin
    W.verbose();
    T.verbose();
    E.verbose()
  end;
  Printf.eprintf "Q stores %d facts.\n" (Q.cardinal q);
  Printf.eprintf "%d facts extracted out of Q, of which %d considered.\n%!"
POTTIER Francois's avatar
POTTIER Francois committed
841
    !extracted !considered
POTTIER Francois's avatar
POTTIER Francois committed
842

843
let discover fact =
POTTIER Francois's avatar
POTTIER Francois committed
844
  incr extracted;
845
  if T.register fact then begin
846
    if W.length fact.word > ! level then begin
POTTIER Francois's avatar
POTTIER Francois committed
847
      done_with_level();
848 849
      level := W.length fact.word;
    end;
POTTIER Francois's avatar
POTTIER Francois committed
850
    incr considered;
851
    consequences fact
852
  end
853

POTTIER Francois's avatar
POTTIER Francois committed
854
let () =
855 856
  if X.verbose then
    Trie.verbose();
857
  Q.repeat q discover;
858
  Time.tick "Running LRijkstra";
POTTIER Francois's avatar
POTTIER Francois committed
859
  done_with_level()
860

861 862
(* ------------------------------------------------------------------------ *)

863 864 865 866 867
(* The following code validates the fact that an error can be triggered in
   state [s'] by beginning in the initial state [s] and reading the
   sequence of terminal symbols [w]. We use this for debugging purposes. *)

let fail msg =
868
  Printf.eprintf "coverage: internal error: %s.\n%!" msg;
869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892
  false

open ReferenceInterpreter

let validate s s' w : bool =
  match
    ReferenceInterpreter.check_error_path (Lr1.nt_of_entry s) (W.elements w)
  with
  | OInputReadPastEnd ->
      fail "input was read past its end"
  | OInputNotFullyConsumed ->
      fail "input was not fully consumed"
  | OUnexpectedAccept ->
      fail "input was unexpectedly accepted"
  | OK state ->
      Lr1.Node.compare state s' = 0 ||
      fail (
        Printf.sprintf "error occurred in state %d instead of %d"
          (Lr1.number state)
          (Lr1.number s')
      )

(* ------------------------------------------------------------------------ *)

893 894 895 896 897 898 899
(* We now wish to determine, given a state [s'] and a terminal symbol [z], a
   minimal path that takes us from some entry state to state [s'] with [z] as
   the next (unconsumed) symbol. *)

(* This can be formulated as a search for a shortest path in a graph. The
   graph is not just the automaton, though. It is a (much) larger graph whose
   vertices are pairs [s, z] and whose edges are obtained by querying the
900
   module [E] above. *)
901

902
let forward () =
903

904
  let module A = Astar.Make(struct
905

906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926
    (* A vertex is a pair [s, z].
       [z] cannot be the [error] token. *)
    type node =
        Lr1.node * Terminal.t

    let equal (s'1, z1) (s'2, z2) =
      Lr1.Node.compare s'1 s'2 = 0 && Terminal.compare z1 z2 = 0

    let hash (s, z) =
      Hashtbl.hash (Lr1.number s, z)

    (* An edge is labeled with a word. *)
    type label =
      W.word

    (* Forward search from every [s, z], where [s] is an initial state. *)
    let sources f =
      foreach_terminal (fun z ->
        ProductionMap.iter (fun _ s ->
          f (s, z)
        ) Lr1.entry
927 928
      )

929
    let successors (s, z) edge =
930
      assert (Terminal.real z);
931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953
      SymbolMap.iter (fun sym s' ->
        match sym with
        | Symbol.T t ->
            if Terminal.equal z t then
              let w = W.singleton t in
              foreach_terminal (fun z ->
                edge w 1 (s', z)
              )
        | Symbol.N nt ->
           foreach_terminal (fun z' ->
             E.query s nt z z' (fun w ->
               edge w (W.length w) (s', z')
             )
           )
      ) (Lr1.transitions s)

    let estimate _ =
      0

  end) in

  (* Search forward. *)

954
  Printf.eprintf "Forward search:\n%!";
955
  let seen = ref Lr1.NodeSet.empty in
956
  let _, _ = A.search (fun ((s', z), path) ->
957 958 959 960 961 962
    if causes_an_error s' z && not (Lr1.NodeSet.mem s' !seen) then begin
      seen := Lr1.NodeSet.add s' !seen;
      (* An error can be triggered in state [s'] by beginning in the initial
         state [s] and reading the sequence of terminal symbols [w]. *)
      let (s, _), ws = A.reverse path in
      let w = List.fold_right W.append ws (W.singleton z) in
963
      Printf.eprintf
964 965 966
        "An error can be reached from state %d to state %d:\n%!"
        (Lr1.number s)
        (Lr1.number s');
967
      Printf.eprintf "%s\n%!" (W.print w);
968 969 970
      assert (validate s s' w)
    end
  ) in
971
  Printf.eprintf "Reachable (forward): %d states\n%!"
972 973
    (Lr1.NodeSet.cardinal !seen);
  !seen
974 975

let () =
976 977
  let f = forward() in
  Time.tick "Forward search";
POTTIER Francois's avatar
POTTIER Francois committed
978
  let stat = Gc.quick_stat() in
979
  Printf.eprintf
POTTIER Francois's avatar
POTTIER Francois committed
980 981
    "Maximum size reached by the major heap: %dM\n"
    (stat.Gc.top_heap_words * (Sys.word_size / 8) / 1024 / 1024);
982
  ignore f
983 984

(* TODO:
POTTIER Francois's avatar
POTTIER Francois committed
985
  can we store fewer facts when we hit a default reduction?
986
  remove CompletedNatWitness?, revert Fix
987
  collect performance data, correlated with star size and alphabet size; draw a graph
POTTIER Francois's avatar
POTTIER Francois committed
988
  count the unreachable states and see if they are numerous in practice
POTTIER Francois's avatar
POTTIER Francois committed
989 990
  optionally report several ways of reaching an error in state s
    (with different lookahead tokens) (report all of them?)
991
  warn if --list-errors is set AND the grammar uses [error]
992
  control verbose output
POTTIER Francois's avatar
POTTIER Francois committed
993
  measure the cost of assertions
994 995
  remove $syntaxerror?
  how do we maintain the list of error messages when the grammar evolves?
996 997
  implement a naive semi-algorithm that enumerates all input sentences,
    and evaluate how well (or how badly) it scales
998
*)
POTTIER Francois's avatar
POTTIER Francois committed
999

1000
end