module General = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

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

(* Lists. *)

let rec take n xs =
  match n, xs with
  | 0, _
  | _, [] ->
      []
  | _, (x :: xs as input) ->
     let xs' = take (n - 1) xs in
     if xs == xs' then
       input
     else
       x :: xs'

let rec drop n xs =
  match n, xs with
  | 0, _ ->
      xs
  | _, [] ->
      []
  | _, _ :: xs ->
      drop (n - 1) xs

let rec uniq1 cmp x ys =
  match ys with
  | [] ->
      []
  | y :: ys ->
      if cmp x y = 0 then
        uniq1 compare x ys
      else
        y :: uniq1 cmp y ys

let uniq cmp xs =
  match xs with
  | [] ->
      []
  | x :: xs ->
      x :: uniq1 cmp x xs

let weed cmp xs =
  uniq cmp (List.sort cmp xs)

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

(* Streams. *)

type 'a stream =
    'a head Lazy.t

and 'a head =
  | Nil
  | Cons of 'a * 'a stream

(* The length of a stream. *)

let rec length xs =
  match Lazy.force xs with
  | Nil ->
      0
  | Cons (_, xs) ->
      1 + length xs

(* Folding over a stream. *)

let rec foldr f xs accu =
  match Lazy.force xs with
  | Nil ->
      accu
  | Cons (x, xs) ->
      f x (foldr f xs accu)

end
module Convert = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* An ocamlyacc-style, or Menhir-style, parser requires access to
   the lexer, which must be parameterized with a lexing buffer, and
   to the lexing buffer itself, where it reads position information. *)

(* This traditional API is convenient when used with ocamllex, but
   inelegant when used with other lexer generators. *)

type ('token, 'semantic_value) traditional =
    (Lexing.lexbuf -> 'token) -> Lexing.lexbuf -> 'semantic_value

(* This revised API is independent of any lexer generator. Here, the
   parser only requires access to the lexer, and the lexer takes no
   parameters. The tokens returned by the lexer may contain position
   information. *)

type ('token, 'semantic_value) revised =
    (unit -> 'token) -> 'semantic_value

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

(* Converting a traditional parser, produced by ocamlyacc or Menhir,
   into a revised parser. *)

(* A token of the revised lexer is essentially a triple of a token
   of the traditional lexer (or raw token), a start position, and
   and end position. The three [get] functions are accessors. *)

(* We do not require the type ['token] to actually be a triple type.
   This enables complex applications where it is a record type with
   more than three fields. It also enables simple applications where
   positions are of no interest, so ['token] is just ['raw_token]
   and [get_startp] and [get_endp] return dummy positions. *)

let traditional2revised
  (get_raw_token : 'token -> 'raw_token)
  (get_startp    : 'token -> Lexing.position)
  (get_endp      : 'token -> Lexing.position)
  (parser : ('raw_token, 'semantic_value) traditional)
: ('token, 'semantic_value) revised =

  (* Accept a revised lexer. *)

  fun (lexer : unit -> 'token) ->

    (* Create a dummy lexing buffer. *)

    let lexbuf : Lexing.lexbuf =
      Lexing.from_string ""
    in

    (* Wrap the revised lexer as a traditional lexer. A traditional
       lexer returns a raw token and updates the fields of the lexing
       buffer with new positions, which will be read by the parser. *)

    let lexer (lexbuf : Lexing.lexbuf) : 'raw_token =
      let token : 'token = lexer() in
      lexbuf.Lexing.lex_start_p <- get_startp token;
      lexbuf.Lexing.lex_curr_p <- get_endp token;
      get_raw_token token
    in

    (* Invoke the traditional parser. *)

    parser lexer lexbuf

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

(* Converting a revised parser back to a traditional parser. *)

let revised2traditional
  (make_token : 'raw_token -> Lexing.position -> Lexing.position -> 'token)
  (parser : ('token, 'semantic_value) revised)
: ('raw_token, 'semantic_value) traditional =

  (* Accept a traditional lexer and a lexing buffer. *)

  fun (lexer : Lexing.lexbuf -> 'raw_token) (lexbuf : Lexing.lexbuf) ->

    (* Wrap the traditional lexer as a revised lexer. *)

    let lexer () : 'token =
      let token : 'raw_token = lexer lexbuf in
      make_token token lexbuf.Lexing.lex_start_p lexbuf.Lexing.lex_curr_p
    in

    (* Invoke the revised parser. *)

    parser lexer

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

(* Simplified versions of the above, where concrete triples are used. *)

module Simplified = struct

  let traditional2revised parser =
    traditional2revised
      (fun (token, _, _)  -> token)
      (fun (_, startp, _) -> startp)
      (fun (_, _, endp)   -> endp)
      parser

  let revised2traditional parser =
    revised2traditional
      (fun token startp endp -> (token, startp, endp))
      parser

end
end
module IncrementalEngine = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

open General

(* This signature describes the incremental LR engine. *)

(* In this mode, the user controls the lexer, and the parser suspends
   itself when it needs to read a new token. *)

module type INCREMENTAL_ENGINE = sig

  type token

  (* The type ['a checkpoint] represents an intermediate or final state of the
     parser. An intermediate checkpoint is a suspension: it records the parser's
     current state, and allows parsing to be resumed. The parameter ['a] is
     the type of the semantic value that will eventually be produced if the
     parser succeeds. *)

  (* [Accepted] and [Rejected] are final checkpoints. [Accepted] carries a
     semantic value. *)

  (* [InputNeeded] is an intermediate checkpoint. It means that the parser wishes
     to read one token before continuing. *)

  (* [Shifting] is an intermediate checkpoint. It means that the parser is taking
     a shift transition. It exposes the state of the parser before and after
     the transition. The Boolean parameter tells whether the parser intends to
     request a new token after this transition. (It always does, except when
     it is about to accept.) *)

  (* [AboutToReduce] is an intermediate checkpoint. It means that the parser is
     about to perform a reduction step. It exposes the parser's current
     state as well as the production that is about to be reduced. *)

  (* [HandlingError] is an intermediate checkpoint. It means that the parser has
     detected an error and is currently handling it, in several steps. *)

  type env

  type production

  type 'a checkpoint = private
    | InputNeeded of env
    | Shifting of env * env * bool
    | AboutToReduce of env * production
    | HandlingError of env
    | Accepted of 'a
    | Rejected

  (* [offer] allows the user to resume the parser after it has suspended
     itself with a checkpoint of the form [InputNeeded env]. [offer] expects the
     old checkpoint as well as a new token and produces a new checkpoint. It does not
     raise any exception. *)

  val offer:
    'a checkpoint ->
    token * Lexing.position * Lexing.position ->
    'a checkpoint

  (* [resume] allows the user to resume the parser after it has suspended
     itself with a checkpoint of the form [AboutToReduce (env, prod)] or
     [HandlingError env]. [resume] expects the old checkpoint and produces a new
     checkpoint. It does not raise any exception. *)

  val resume:
    'a checkpoint ->
    'a checkpoint

  (* A token supplier is a function of no arguments which delivers a new token
     (together with its start and end positions) every time it is called. *)

  type supplier =
    unit -> token * Lexing.position * Lexing.position

  (* A pair of a lexer and a lexing buffer can be easily turned into a supplier. *)

  val lexer_lexbuf_to_supplier:
    (Lexing.lexbuf -> token) ->
    Lexing.lexbuf ->
    supplier

  (* The functions [offer] and [resume] are sufficient to write a parser loop.
     One can imagine many variations (which is why we expose these functions
     in the first place!). Here, we expose a few variations of the main loop,
     ready for use. *)

  (* [loop supplier checkpoint] begins parsing from [checkpoint], reading
     tokens from [supplier]. It continues parsing until it reaches a
     checkpoint of the form [Accepted v] or [Rejected]. In the former case, it
     returns [v]. In the latter case, it raises the exception [Error]. *)

  val loop: supplier -> 'a checkpoint -> 'a

  (* [loop_handle succeed fail supplier checkpoint] begins parsing from
     [checkpoint], reading tokens from [supplier]. It continues parsing until
     it reaches a checkpoint of the form [Accepted v] or [HandlingError env]
     (or [Rejected], but that should not happen, as [HandlingError _] will be
     observed first). In the former case, it calls [succeed v]. In the latter
     case, it calls [fail] with this checkpoint. It cannot raise [Error].

     This means that Menhir's traditional error-handling procedure (which pops
     the stack until a state that can act on the [error] token is found) does
     not get a chance to run. Instead, the user can implement her own error
     handling code, in the [fail] continuation. *)

  val loop_handle:
    ('a -> 'answer) ->
    ('a checkpoint -> 'answer) ->
    supplier -> 'a checkpoint -> 'answer

  (* [loop_handle_undo] is analogous to [loop_handle], except it passes a pair
     of checkpoints to the failure continuation.

     The first (and oldest) checkpoint is the last [InputNeeded] checkpoint that
     was encountered before the error was detected. The second (and newest)
     checkpoint is where the error was detected, as in [loop_handle]. Going back
     to the first checkpoint can be thought of as undoing any reductions that
     were performed after seeing the problematic token. (These reductions must
     be default reductions or spurious reductions.)

     [loop_handle_undo] must initially be applied to an [InputNeeded] checkpoint.
     The parser's initial checkpoints satisfy this constraint. *)

  val loop_handle_undo:
    ('a -> 'answer) ->
    ('a checkpoint -> 'a checkpoint -> 'answer) ->
    supplier -> 'a checkpoint -> 'answer

  (* [loop_test f checkpoint accu] assumes that [checkpoint] has been obtained
     by submitting a token to the parser. It runs the parser from [checkpoint],
     through an arbitrary number of reductions, until the parser either accepts
     this token (i.e., shifts) or rejects it (i.e., signals an error). If the
     parser decides to shift, then the accumulator is updated by applying the
     user function [f] to the [env] just before shifting and to the old [accu].
     Otherwise, the accumulator is not updated, i.e., [accu] is returned. *)

  (* It is desirable that the semantic actions be side-effect free, or that
     their side-effects be harmless (replayable). *)

  val loop_test:
    (env -> 'accu -> 'accu) ->
    'a checkpoint -> 'accu -> 'accu

  (* The function [loop_test] can be used, after an error has been detected, to
     dynamically test which tokens would have been accepted at this point. We
     provide this test, ready for use. *)

  (* For completeness, one must undo any spurious reductions before carrying out
     this test -- that is, one must apply [acceptable] to the FIRST checkpoint
     that is passed by [loop_handle_undo] to its failure continuation. *)

  (* This test causes some semantic actions to be run! The semantic actions
     should be side-effect free, or their side-effects should be harmless. *)

  (* The position [pos] is used as the start and end positions of the
     hypothetical token, and may be picked up by the semantic actions. We
     suggest using the position where the error was detected. *)

  val acceptable: 'a checkpoint -> token -> Lexing.position -> bool

  (* The abstract type ['a lr1state] describes the non-initial states of the
     LR(1) automaton. The index ['a] represents the type of the semantic value
     associated with this state's incoming symbol. *)

  type 'a lr1state

  (* The states of the LR(1) automaton are numbered (from 0 and up). *)

  val number: _ lr1state -> int

  (* An element is a pair of a non-initial state [s] and a semantic value [v]
     associated with the incoming symbol of this state. The idea is, the value
     [v] was pushed onto the stack just before the state [s] was entered. Thus,
     for some type ['a], the state [s] has type ['a lr1state] and the value [v]
     has type ['a]. In other words, the type [element] is an existential type. *)

  type element =
    | Element: 'a lr1state * 'a * Lexing.position * Lexing.position -> element

  (* The parser's stack is (or, more precisely, can be viewed as) a stream of
     elements. The type [stream] is defined by the module [General]. *)

  type stack =
    element stream

  (* This is the parser's stack, a stream of elements. This stream is empty if
     the parser is in an initial state; otherwise, it is non-empty.  The LR(1)
     automaton's current state is the one found in the top element of the
     stack. *)

  val stack: env -> stack

  (* These are the start and end positions of the current lookahead token. If
     invoked in an initial state, this function returns a pair of twice the
     initial position. *)

  val positions: env -> Lexing.position * Lexing.position

  (* This tells whether the parser is about to perform a default reduction.
     In particular, when applied to an environment taken from a result of
     the form [AboutToReduce (env, prod)], this tells whether the reduction
     that is about to take place is a default reduction. *)

  val has_default_reduction: env -> bool

end

(* This signature is a fragment of the inspection API that is made available
   to the user when [--inspection] is used. This fragment contains type
   definitions for symbols. *)

module type SYMBOLS = sig

  (* The type ['a terminal] represents a terminal symbol. The type ['a
     nonterminal] represents a nonterminal symbol. In both cases, the index
     ['a] represents the type of the semantic values associated with this
     symbol. The concrete definitions of these types are generated. *)

  type 'a terminal
  type 'a nonterminal

  (* The type ['a symbol] represents a terminal or nonterminal symbol. It is
     the disjoint union of the types ['a terminal] and ['a nonterminal]. *)

  type 'a symbol =
    | T : 'a terminal -> 'a symbol
    | N : 'a nonterminal -> 'a symbol

  (* The type [xsymbol] is an existentially quantified version of the type
     ['a symbol]. This type is useful in situations where the index ['a]
     is not statically known. *)

  type xsymbol =
    | X : 'a symbol -> xsymbol

end

(* This signature describes the inspection API that is made available to the
   user when [--inspection] is used. *)

module type INSPECTION = sig

  (* The types of symbols are described above. *)

  include SYMBOLS

  (* The type ['a lr1state] is meant to be the same as in [INCREMENTAL_ENGINE]. *)

  type 'a lr1state

  (* The type [production] is meant to be the same as in [INCREMENTAL_ENGINE].
     It represents a production of the grammar. A production can be examined
     via the functions [lhs] and [rhs] below. *)

  type production

  (* An LR(0) item is a pair of a production [prod] and a valid index [i] into
     this production. That is, if the length of [rhs prod] is [n], then [i] is
     comprised between 0 and [n], inclusive. *)

  type item =
      production * int

  (* Ordering functions. *)

  val compare_terminals: _ terminal -> _ terminal -> int
  val compare_nonterminals: _ nonterminal -> _ nonterminal -> int
  val compare_symbols: xsymbol -> xsymbol -> int
  val compare_productions: production -> production -> int
  val compare_items: item -> item -> int

  (* [incoming_symbol s] is the incoming symbol of the state [s], that is,
     the symbol that the parser must recognize before (has recognized when)
     it enters the state [s]. This function gives access to the semantic
     value [v] stored in a stack element [Element (s, v, _, _)]. Indeed,
     by case analysis on the symbol [incoming_symbol s], one discovers the
     type ['a] of the value [v]. *)

  val incoming_symbol: 'a lr1state -> 'a symbol

  (* [items s] is the set of the LR(0) items in the LR(0) core of the LR(1)
     state [s]. This set is not epsilon-closed. This set is presented as a
     list, in an arbitrary order. *)

  val items: _ lr1state -> item list

  (* [lhs prod] is the left-hand side of the production [prod]. This is
     always a non-terminal symbol. *)

  val lhs: production -> xsymbol

  (* [rhs prod] is the right-hand side of the production [prod]. This is
     a (possibly empty) sequence of (terminal or nonterminal) symbols. *)

  val rhs: production -> xsymbol list

  (* [nullable nt] tells whether the non-terminal symbol [nt] is nullable.
     That is, it is true if and only if this symbol produces the empty
     word [epsilon]. *)

  val nullable: _ nonterminal -> bool

  (* [first nt t] tells whether the FIRST set of the nonterminal symbol [nt]
     contains the terminal symbol [t]. That is, it is true if and only if
     [nt] produces a word that begins with [t]. *)

  val first: _ nonterminal -> _ terminal -> bool

  (* [xfirst] is analogous to [first], but expects a first argument of type
     [xsymbol] instead of [_ terminal]. *)

  val xfirst: xsymbol -> _ terminal -> bool

  (* [foreach_terminal] enumerates the terminal symbols, including [error].
     [foreach_terminal_but_error] enumerates the terminal symbols, excluding
     [error]. *)

  val foreach_terminal:           (xsymbol -> 'a -> 'a) -> 'a -> 'a
  val foreach_terminal_but_error: (xsymbol -> 'a -> 'a) -> 'a -> 'a

end

(* This signature combines the incremental API and the inspection API. *)

module type EVERYTHING = sig

  include INCREMENTAL_ENGINE

  include INSPECTION
    with type 'a lr1state := 'a lr1state
    with type production := production

end

end
module EngineTypes = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* This file defines several types and module types that are used in the
   specification of module [Engine]. *)

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

(* It would be nice if we could keep the structure of stacks and environments
   hidden. However, stacks and environments must be accessible to semantic
   actions, so the following data structure definitions must be public. *)

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

(* A stack is a linked list of cells. A sentinel cell -- which is its own
   successor -- is used to mark the bottom of the stack. The sentinel cell
   itself is not significant -- it contains dummy values. *)

type ('state, 'semantic_value) stack = {

  (* The state that we should go back to if we pop this stack cell. *)

  (* This convention means that the state contained in the top stack cell is
     not the current state [env.current]. It also means that the state found
     within the sentinel is a dummy -- it is never consulted. This convention
     is the same as that adopted by the code-based back-end. *)

  state: 'state;

  (* The semantic value associated with the chunk of input that this cell
     represents. *)

  semv: 'semantic_value;

  (* The start and end positions of the chunk of input that this cell
     represents. *)

  startp: Lexing.position;
  endp: Lexing.position;

  (* The next cell down in the stack. If this is a self-pointer, then this
     cell is the sentinel, and the stack is conceptually empty. *)

  next: ('state, 'semantic_value) stack;

}

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

(* A parsing environment contains all of the parser's state (except for the
   current program point). *)

type ('state, 'semantic_value, 'token) env = {

  (* If this flag is true, then the first component of [env.triple] should
     be ignored, as it has been logically overwritten with the [error]
     pseudo-token. *)

  error: bool;

  (* The last token that was obtained from the lexer, together with its start
     and end positions. Warning: before the first call to the lexer has taken
     place, a dummy (and possibly invalid) token is stored here. *)

  triple: 'token * Lexing.position * Lexing.position;

  (* The stack. In [CodeBackend], it is passed around on its own,
     whereas, here, it is accessed via the environment. *)

  stack: ('state, 'semantic_value) stack;

  (* The current state. In [CodeBackend], it is passed around on its
     own, whereas, here, it is accessed via the environment. *)

  current: 'state;

}

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

(* This signature describes the parameters that must be supplied to the LR
   engine. *)

module type TABLE = sig

  (* The type of automaton states. *)

  type state

  (* States are numbered. *)

  val number: state -> int

  (* The type of tokens. These can be thought of as real tokens, that is,
     tokens returned by the lexer. They carry a semantic value. This type
     does not include the [error] pseudo-token. *)

  type token

  (* The type of terminal symbols. These can be thought of as integer codes.
     They do not carry a semantic value. This type does include the [error]
     pseudo-token. *)

  type terminal

  (* The type of semantic values. *)

  type semantic_value

  (* A token is conceptually a pair of a (non-[error]) terminal symbol and
     a semantic value. The following two functions are the pair projections. *)

  val token2terminal: token -> terminal
  val token2value: token -> semantic_value

  (* Even though the [error] pseudo-token is not a real token, it is a
     terminal symbol. Furthermore, for regularity, it must have a semantic
     value. *)

  val error_terminal: terminal
  val error_value: semantic_value

  (* The type of productions. *)

  type production

  (* If a state [s] has a default reduction on production [prod], then, upon
     entering [s], the automaton should reduce [prod] without consulting the
     lookahead token. The following function allows determining which states
     have default reductions. *)

  (* Instead of returning a value of a sum type -- either [DefRed prod], or
     [NoDefRed] -- it accepts two continuations, and invokes just one of
     them. This mechanism allows avoiding a memory allocation. *)

  val default_reduction:
    state ->
    ('env -> production -> 'answer) ->
    ('env -> 'answer) ->
    'env -> 'answer

  (* An LR automaton can normally take three kinds of actions: shift, reduce,
     or fail. (Acceptance is a particular case of reduction: it consists in
     reducing a start production.) *)

  (* There are two variants of the shift action. [shift/discard s] instructs
     the automaton to discard the current token, request a new one from the
     lexer, and move to state [s]. [shift/nodiscard s] instructs it to move to
     state [s] without requesting a new token. This instruction should be used
     when [s] has a default reduction on [#]. See [CodeBackend.gettoken] for
     details. *)

  (* This is the automaton's action table. It maps a pair of a state and a
     terminal symbol to an action. *)

  (* Instead of returning a value of a sum type -- one of shift/discard,
     shift/nodiscard, reduce, or fail -- this function accepts three
     continuations, and invokes just one them. This mechanism allows avoiding
     a memory allocation. *)

  (* In summary, the parameters to [action] are as follows:

     - the first two parameters, a state and a terminal symbol, are used to
       look up the action table;

     - the next parameter is the semantic value associated with the above
       terminal symbol; it is not used, only passed along to the shift
       continuation, as explained below;

     - the shift continuation expects an environment; a flag that tells
       whether to discard the current token; the terminal symbol that
       is being shifted; its semantic value; and the target state of
       the transition;

     - the reduce continuation expects an environment and a production;

     - the fail continuation expects an environment;

     - the last parameter is the environment; it is not used, only passed
       along to the selected continuation. *)

  val action:
    state ->
    terminal ->
    semantic_value ->
    ('env -> bool -> terminal -> semantic_value -> state -> 'answer) ->
    ('env -> production -> 'answer) ->
    ('env -> 'answer) ->
    'env -> 'answer

  (* This is the automaton's goto table. It maps a pair of a state and a
     production to a new state.

     This convention is slightly different from the textbook approach. The
     goto table is usually indexed by a state and a non-terminal symbol. *)

  val goto: state -> production -> state

  (* [is_start prod] tells whether the production [prod] is a start production. *)

  val is_start: production -> bool

  (* By convention, a semantic action is responsible for:

     1. fetching whatever semantic values and positions it needs off the stack;

     2. popping an appropriate number of cells off the stack, as dictated
        by the length of the right-hand side of the production;

     3. computing a new semantic value, as well as new start and end positions;

     4. pushing a new stack cell, which contains the three values
        computed in step 3;

     5. returning the new stack computed in steps 2 and 4.

     Point 1 is essentially forced upon us: if semantic values were fetched
     off the stack by this interpreter, then the calling convention for
     semantic actions would be variadic: not all semantic actions would have
     the same number of arguments. The rest follows rather naturally. *)

  (* Semantic actions are allowed to raise [Error]. *)

  exception Error

  type semantic_action =
      (state, semantic_value, token) env -> (state, semantic_value) stack

  val semantic_action: production -> semantic_action

  (* The LR engine requires a number of hooks, which are used for logging. *)

  (* The comments below indicate the conventional messages that correspond
     to these hooks in the code-based back-end; see [CodeBackend]. *)

  (* If the flag [log] is false, then the logging functions are not called.
     If it is [true], then they are called. *)

  val log : bool

  module Log : sig

    (* State %d: *)

    val state: state -> unit

    (* Shifting (<terminal>) to state <state> *)

    val shift: terminal -> state -> unit

    (* Reducing a production should be logged either as a reduction
       event (for regular productions) or as an acceptance event (for
       start productions). *)

    (* Reducing production <production> / Accepting *)

    val reduce_or_accept: production -> unit

    (* Lookahead token is now <terminal> (<pos>-<pos>) *)

    val lookahead_token: terminal -> Lexing.position -> Lexing.position -> unit

    (* Initiating error handling *)

    val initiating_error_handling: unit -> unit

    (* Resuming error handling *)

    val resuming_error_handling: unit -> unit

    (* Handling error in state <state> *)

    val handling_error: state -> unit

  end

end

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

(* This signature describes the monolithic (traditional) LR engine. *)

(* In this interface, the parser controls the lexer. *)

module type MONOLITHIC_ENGINE = sig

  type state

  type token

  type semantic_value

  (* An entry point to the engine requires a start state, a lexer, and a lexing
     buffer. It either succeeds and produces a semantic value, or fails and
     raises [Error]. *)

  exception Error

  val entry:
    state ->
    (Lexing.lexbuf -> token) ->
    Lexing.lexbuf ->
    semantic_value

end

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

(* The following signatures describe the incremental LR engine. *)

(* First, see [INCREMENTAL_ENGINE] in the file [IncrementalEngine.ml]. *)

(* The [start] function is set apart because we do not wish to publish
   it as part of the generated [parser.mli] file. Instead, the table
   back-end will publish specialized versions of it, with a suitable
   type cast. *)

module type INCREMENTAL_ENGINE_START = sig

  (* [start] is an entry point. It requires a start state and a start position
     and begins the parsing process. If the lexer is based on an OCaml lexing
     buffer, the start position should be [lexbuf.lex_curr_p]. [start] produces
     a checkpoint, which usually will be an [InputNeeded] checkpoint. (It could
     be [Accepted] if this starting state accepts only the empty word. It could
     be [Rejected] if this starting state accepts no word at all.) It does not
     raise any exception. *)

  (* [start s pos] should really produce a checkpoint of type ['a checkpoint],
     for a fixed ['a] that depends on the state [s]. We cannot express this, so
     we use [semantic_value checkpoint], which is safe. The table back-end uses
     [Obj.magic] to produce safe specialized versions of [start]. *)

  type state
  type semantic_value
  type 'a checkpoint

  val start:
    state ->
    Lexing.position ->
    semantic_value checkpoint

end

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

(* This signature describes the LR engine, which combines the monolithic
   and incremental interfaces. *)

module type ENGINE = sig

  include MONOLITHIC_ENGINE

  include IncrementalEngine.INCREMENTAL_ENGINE
    with type token := token
     and type 'a lr1state = state (* useful for us; hidden from the end user *)

  include INCREMENTAL_ENGINE_START
    with type state := state
     and type semantic_value := semantic_value
     and type 'a checkpoint := 'a checkpoint

end

end
module Engine = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

open EngineTypes

(* The LR parsing engine. *)

(* This module is used:

   - at compile time, if so requested by the user, via the --interpret options;
   - at run time, in the table-based back-end. *)

module Make (T : TABLE) = struct

  (* This propagates type and exception definitions. *)

  include T

  type env =
      (state, semantic_value, token) EngineTypes.env

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

  (* The type [checkpoint] represents an intermediate or final result of the
     parser. See [EngineTypes]. *)

  (* The type [checkpoint] is presented to the user as a private type (see
     [IncrementalEngine]). This prevents the user from manufacturing checkpoints
     (i.e., continuations) that do not make sense. (Such continuations could
     potentially violate the LR invariant and lead to crashes.) *)

  type 'a checkpoint =
    | InputNeeded of env
    | Shifting of env * env * bool
    | AboutToReduce of env * production
    | HandlingError of env
    | Accepted of 'a
    | Rejected

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

  (* In the code-based back-end, the [run] function is sometimes responsible
     for pushing a new cell on the stack. This is motivated by code sharing
     concerns. In this interpreter, there is no such concern; [run]'s caller
     is always responsible for updating the stack. *)

  (* In the code-based back-end, there is a [run] function for each state
     [s]. This function can behave in two slightly different ways, depending
     on when it is invoked, or (equivalently) depending on [s].

     If [run] is invoked after shifting a terminal symbol (or, equivalently,
     if [s] has a terminal incoming symbol), then [run] discards a token,
     unless [s] has a default reduction on [#]. (Indeed, in that case,
     requesting the next token might drive the lexer off the end of the input
     stream.)

     If, on the other hand, [run] is invoked after performing a goto transition,
     or invoked directly by an entry point, then there is nothing to discard.

     These two cases are reflected in [CodeBackend.gettoken].

     Here, the code is structured in a slightly different way. It is up to the
     caller of [run] to indicate whether to discard a token, via the parameter
     [please_discard]. This flag is set when [s] is being entered by shifting
     a terminal symbol and [s] does not have a default reduction on [#]. *)

  (* The following recursive group of functions are tail recursive, produce a
     checkpoint of type [semantic_value checkpoint], and cannot raise an
     exception. A semantic action can raise [Error], but this exception is
     immediately caught within [reduce]. *)

  let rec run env please_discard : semantic_value checkpoint =

    (* Log the fact that we just entered this state. *)

    if log then
      Log.state env.current;

    (* If [please_discard] is set, we discard the current lookahead token and
       fetch the next one. In order to request a token from the user, we
       return an [InputNeeded] continuation, which, when invoked by the user,
       will take us to [discard]. If [please_discard] is not set, we skip this
       step and jump directly to [check_for_default_reduction]. *)

    if please_discard then
      InputNeeded env
    else
      check_for_default_reduction env

  (* [discard env triple] stores [triple] into [env], overwriting the previous
     token. It is invoked by [offer], which itself is invoked by the user in
     response to an [InputNeeded] checkpoint. *)

  and discard env triple =
    if log then begin
      let (token, startp, endp) = triple in
      Log.lookahead_token (T.token2terminal token) startp endp
    end;
    let env = { env with error = false; triple } in
    check_for_default_reduction env

  and check_for_default_reduction env =

    (* Examine what situation we are in. This case analysis is analogous to
       that performed in [CodeBackend.gettoken], in the sub-case where we do
       not have a terminal incoming symbol. *)

    T.default_reduction
      env.current
      announce_reduce       (* there is a default reduction; perform it *)
      check_for_error_token (* there is none; continue below *)
      env

  and check_for_error_token env =

    (* There is no default reduction. Consult the current lookahead token
       so as to determine which action should be taken. *)

    (* Peeking at the first input token, without taking it off the input
       stream, is done by reading [env.triple]. We are careful to first
       check [env.error]. *)

    (* Note that, if [please_discard] was true, then we have just called
       [discard], so the lookahead token cannot be [error]. *)

    (* Returning [HandlingError env] is equivalent to calling [error env]
       directly, except it allows the user to regain control. *)

    if env.error then begin
      if log then
        Log.resuming_error_handling();
      HandlingError env
    end
    else
      let (token, _, _) = env.triple in

      (* We consult the two-dimensional action table, indexed by the
         current state and the current lookahead token, in order to
         determine which action should be taken. *)

      T.action
        env.current                    (* determines a row *)
        (T.token2terminal token)       (* determines a column *)
        (T.token2value token)
        shift                          (* shift continuation *)
        announce_reduce                (* reduce continuation *)
        initiate                       (* failure continuation *)
        env

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

  (* This function takes care of shift transitions along a terminal symbol.
     (Goto transitions are taken care of within [reduce] below.) The symbol
     can be either an actual token or the [error] pseudo-token. *)

  (* Here, the lookahead token CAN be [error]. *)

  and shift env
      (please_discard : bool)
      (terminal : terminal)
      (value : semantic_value)
      (s' : state) =

    (* Log the transition. *)

    if log then
      Log.shift terminal s';

    (* Push a new cell onto the stack, containing the identity of the
       state that we are leaving. *)

    let (_, startp, endp) = env.triple in
    let stack = {
      state = env.current;
      semv = value;
      startp;
      endp;
      next = env.stack;
    } in

    (* Switch to state [s']. *)

    let new_env = { env with stack; current = s' } in

    (* Expose the transition to the user. (In principle, we have a choice
       between exposing the transition before we take it, after we take
       it, or at some point in between. This affects the number and type
       of the parameters carried by [Shifting]. Here, we choose to expose
       the transition after we take it; this allows [Shifting] to carry
       only three parameters, whose meaning is simple.) *)

    Shifting (env, new_env, please_discard)

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

  (* The function [announce_reduce] stops the parser and returns a checkpoint
     which allows the parser to be resumed by calling [reduce]. *)

  (* Only ordinary productions are exposed to the user. Start productions
     are not exposed to the user. Reducing a start production simply leads
     to the successful termination of the parser. *)

  and announce_reduce env (prod : production) =
    if T.is_start prod then
      accept env prod
    else
      AboutToReduce (env, prod)

  (* The function [reduce] takes care of reductions. It is invoked by
     [resume] after an [AboutToReduce] event has been produced. *)

  (* Here, the lookahead token CAN be [error]. *)

  (* The production [prod] CANNOT be a start production. *)

  and reduce env (prod : production) =

    (* Log a reduction event. *)

    if log then
      Log.reduce_or_accept prod;

    (* Invoke the semantic action. The semantic action is responsible for
       truncating the stack and pushing a new cell onto the stack, which
       contains a new semantic value. It can raise [Error]. *)

    (* If the semantic action terminates normally, it returns a new stack,
       which becomes the current stack. *)

    (* If the semantic action raises [Error], we catch it and initiate error
       handling. *)

    (* This [match/with/exception] construct requires OCaml 4.02. *)

    match T.semantic_action prod env with
    | stack ->

        (* By our convention, the semantic action has produced an updated
           stack. The state now found in the top stack cell is the return
           state. *)

        (* Perform a goto transition. The target state is determined
           by consulting the goto table at the return state and at
           production [prod]. *)

        let current = T.goto stack.state prod in
        let env = { env with stack; current } in
        run env false

    | exception Error ->
        initiate env

  and accept env prod =
    (* Log an accept event. *)
    if log then
      Log.reduce_or_accept prod;
    (* Extract the semantic value out of the stack. *)
    let v = env.stack.semv in
    (* Finish. *)
    Accepted v

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

  (* The following functions deal with errors. *)

  (* [initiate] initiates or resumes error handling. *)

  (* Here, the lookahead token CAN be [error]. *)

  and initiate env =
    if log then
      Log.initiating_error_handling();
    let env = { env with error = true } in
    HandlingError env

  (* [error] handles errors. *)

  and error env =
    assert env.error;

    (* Consult the column associated with the [error] pseudo-token in the
       action table. *)

    T.action
      env.current                    (* determines a row *)
      T.error_terminal               (* determines a column *)
      T.error_value
      error_shift                    (* shift continuation *)
      error_reduce                   (* reduce continuation *)
      error_fail                     (* failure continuation *)
      env

  and error_shift env please_discard terminal value s' =

    (* Here, [terminal] is [T.error_terminal], and [value] is [T.error_value]. *)

    assert (terminal = T.error_terminal && value = T.error_value);

    (* This state is capable of shifting the [error] token. *)

    if log then
      Log.handling_error env.current;
    shift env please_discard terminal value s'

  and error_reduce env prod =

    (* This state is capable of performing a reduction on [error]. *)

    if log then
      Log.handling_error env.current;
    reduce env prod
      (* Intentionally calling [reduce] instead of [announce_reduce].
         It does not seem very useful, and it could be confusing, to
         expose the reduction steps taken during error handling. *)

  and error_fail env =

    (* This state is unable to handle errors. Attempt to pop a stack
       cell. *)

    let cell = env.stack in
    let next = cell.next in
    if next == cell then

      (* The stack is empty. Die. *)

      Rejected

    else begin

      (* The stack is nonempty. Pop a cell, updating the current state
         with that found in the popped cell, and try again. *)

      let env = { env with
        stack = next;
        current = cell.state
      } in
      HandlingError env

    end

  (* End of the nest of tail recursive functions. *)

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

  (* The incremental interface. See [EngineTypes]. *)

  (* [start s] begins the parsing process. *)

  let start (s : state) (initial : Lexing.position) : semantic_value checkpoint =

    (* Build an empty stack. This is a dummy cell, which is its own successor.
       Its [next] field WILL be accessed by [error_fail] if an error occurs and
       is propagated all the way until the stack is empty. Its [endp] field WILL
       be accessed (by a semantic action) if an epsilon production is reduced
       when the stack is empty. *)

    let rec empty = {
      state = s;                          (* dummy *)
      semv = T.error_value;               (* dummy *)
      startp = initial;                   (* dummy *)
      endp = initial;
      next = empty;
    } in

    (* Build an initial environment. *)

    (* Unfortunately, there is no type-safe way of constructing a
       dummy token. Tokens carry semantic values, which in general
       we cannot manufacture. This instance of [Obj.magic] could
       be avoided by adopting a different representation (e.g., no
       [env.error] field, and an option in the first component of
       [env.triple]), but I like this representation better. *)

    let dummy_token = Obj.magic () in
    let env = {
      error = false;
      triple = (dummy_token, initial, initial); (* dummy *)
      stack = empty;
      current = s;
    } in

    (* Begin parsing. *)

    (* The parameter [please_discard] here is [true], which means we know
       that we must read at least one token. This claim relies on the fact
       that we have ruled out the two special cases where a start symbol
       recognizes the empty language or the singleton language {epsilon}. *)

    run env true

  (* [offer checkpoint triple] is invoked by the user in response to a
     checkpoint of the form [InputNeeded env]. It checks that [checkpoint] is
     indeed of this form, and invokes [discard]. *)

  (* [resume checkpoint] is invoked by the user in response to a checkpoint of
     the form [AboutToReduce (env, prod)] or [HandlingError env]. It checks
     that [checkpoint] is indeed of this form, and invokes [reduce] or
     [error], as appropriate. *)

  (* In reality, [offer] and [resume] accept an argument of type
     [semantic_value checkpoint] and produce a checkpoint of the same type.
     The choice of [semantic_value] is forced by the fact that this is the
     parameter of the checkpoint [Accepted]. *)

  (* We change this as follows. *)

  (* We change the argument and result type of [offer] and [resume] from
     [semantic_value checkpoint] to ['a checkpoint]. This is safe, in this
     case, because we give the user access to values of type [t checkpoint]
     only if [t] is indeed the type of the eventual semantic value for this
     run. (More precisely, by examining the signatures [INCREMENTAL_ENGINE]
     and [INCREMENTAL_ENGINE_START], one finds that the user can build a value
     of type ['a checkpoint] only if ['a] is [semantic_value]. The table
     back-end goes further than this and produces versions of [start] composed
     with a suitable cast, which give the user access to a value of type
     [t checkpoint] where [t] is the type of the start symbol.) *)

  let offer : 'a . 'a checkpoint ->
                   token * Lexing.position * Lexing.position ->
                   'a checkpoint
  = function
    | InputNeeded env ->
        Obj.magic discard env
    | _ ->
        raise (Invalid_argument "offer expects InputNeeded")

  let resume : 'a . 'a checkpoint -> 'a checkpoint = function
    | HandlingError env ->
        Obj.magic error env
    | Shifting (_, env, please_discard) ->
        Obj.magic run env please_discard
    | AboutToReduce (env, prod) ->
        Obj.magic reduce env prod
    | _ ->
        raise (Invalid_argument "resume expects HandlingError | AboutToReduce")

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

  (* The traditional interface. See [EngineTypes]. *)

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

  (* Wrapping a lexer and lexbuf as a token supplier. *)

  type supplier =
    unit -> token * Lexing.position * Lexing.position

  let lexer_lexbuf_to_supplier
      (lexer : Lexing.lexbuf -> token)
      (lexbuf : Lexing.lexbuf)
  : supplier =
    fun () ->
      let token = lexer lexbuf in
      let startp = lexbuf.Lexing.lex_start_p
      and endp = lexbuf.Lexing.lex_curr_p in
      token, startp, endp

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

  (* The main loop repeatedly handles intermediate checkpoints, until a final
     checkpoint is obtained. This allows implementing the monolithic interface
     ([entry]) in terms of the incremental interface ([start], [offer],
     [handle], [reduce]). *)

  (* By convention, acceptance is reported by returning a semantic value, whereas
     rejection is reported by raising [Error]. *)

  (* [loop] is polymorphic in ['a]. No cheating is involved in achieving this.
     All of the cheating resides in the types assigned to [offer] and [handle]
     above. *)

  let rec loop : 'a . supplier -> 'a checkpoint -> 'a =
    fun read checkpoint ->
    match checkpoint with
    | InputNeeded _ ->
        (* The parser needs a token. Request one from the lexer,
           and offer it to the parser, which will produce a new
           checkpoint. Then, repeat. *)
        let triple = read() in
        let checkpoint = offer checkpoint triple in
        loop read checkpoint
    | Shifting _
    | AboutToReduce _
    | HandlingError _ ->
        (* The parser has suspended itself, but does not need
           new input. Just resume the parser. Then, repeat. *)
        let checkpoint = resume checkpoint in
        loop read checkpoint
    | Accepted v ->
        (* The parser has succeeded and produced a semantic value.
           Return this semantic value to the user. *)
        v
    | Rejected ->
        (* The parser rejects this input. Raise an exception. *)
        raise Error

  let entry (s : state) lexer lexbuf : semantic_value =
    let initial = lexbuf.Lexing.lex_curr_p in
    loop (lexer_lexbuf_to_supplier lexer lexbuf) (start s initial)

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

  (* [loop_handle] stops if it encounters an error, and at this point, invokes
     its failure continuation, without letting Menhir do its own traditional
     error-handling (which involves popping the stack, etc.). *)

  let rec loop_handle succeed fail read checkpoint =
    match checkpoint with
    | InputNeeded _ ->
        let triple = read() in
        let checkpoint = offer checkpoint triple in
        loop_handle succeed fail read checkpoint
    | Shifting _
    | AboutToReduce _ ->
        let checkpoint = resume checkpoint in
        loop_handle succeed fail read checkpoint
    | HandlingError _
    | Rejected ->
        (* The parser has detected an error. Invoke the failure continuation. *)
        fail checkpoint
    | Accepted v ->
        (* The parser has succeeded and produced a semantic value. Invoke the
           success continuation. *)
        succeed v

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

  (* [loop_handle_undo] is analogous to [loop_handle], except it passes a pair
     of checkpoints to the failure continuation.

     The first (and oldest) checkpoint is the last [InputNeeded] checkpoint that
     was encountered before the error was detected. The second (and newest)
     checkpoint is where the error was detected, as in [loop_handle]. Going back
     to the first checkpoint can be thought of as undoing any reductions that
     were performed after seeing the problematic token. (These reductions must
     be default reductions or spurious reductions.) *)

  let rec loop_handle_undo succeed fail read (inputneeded, checkpoint) =
    match checkpoint with
    | InputNeeded _ ->
        (* Update the last recorded [InputNeeded] checkpoint. *)
        let inputneeded = checkpoint in
        let triple = read() in
        let checkpoint = offer checkpoint triple in
        loop_handle_undo succeed fail read (inputneeded, checkpoint)
    | Shifting _
    | AboutToReduce _ ->
        let checkpoint = resume checkpoint in
        loop_handle_undo succeed fail read (inputneeded, checkpoint)
    | HandlingError _
    | Rejected ->
        fail inputneeded checkpoint
    | Accepted v ->
        succeed v

  (* For simplicity, we publish a version of [loop_handle_undo] that takes a
     single checkpoint as an argument, instead of a pair of checkpoints. We
     check that the argument is [InputNeeded _], and duplicate it. *)

  (* The parser cannot accept or reject before it asks for the very first
     character of input. (Indeed, we statically reject a symbol that
     generates the empty language or the singleton language {epsilon}.)
     So, the [start] checkpoint must match [InputNeeded _]. Hence, it is
     permitted to call [loop_handle_undo] with a [start] checkpoint. *)

  let loop_handle_undo succeed fail read checkpoint =
    assert (match checkpoint with InputNeeded _ -> true | _ -> false);
    loop_handle_undo succeed fail read (checkpoint, checkpoint)

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

  (* [loop_test f checkpoint accu] assumes that [checkpoint] has been obtained
     by submitting a token to the parser. It runs the parser from [checkpoint],
     through an arbitrary number of reductions, until the parser either accepts
     this token (i.e., shifts) or rejects it (i.e., signals an error). If the
     parser decides to shift, then the accumulator is updated by applying the
     user function [f] to the [env] just before shifting and to the old [accu].
     Otherwise, the accumulator is not updated, i.e., [accu] is returned. *)

  (* This test causes some semantic actions to be run! The semantic actions
     should be side-effect free, or their side-effects should be harmless. *)

  let rec loop_test f checkpoint accu =
    match checkpoint with
    | Shifting (env, _, _) ->
        (* The parser is about to shift, which means it is willing to
           consume the terminal symbol that we have fed it. Update the
           accumulator with the state just before this transition. *)
        f env accu
    | AboutToReduce _ ->
        (* The parser wishes to reduce. Just follow. *)
        loop_test f (resume checkpoint) accu
    | HandlingError _ ->
        (* The parser fails, which means it rejects the terminal symbol
           that we have fed it. Do not update the accumulator. *)
        accu
    | InputNeeded _
    | Accepted _
    | Rejected ->
        (* None of these cases can arise. Indeed, after a token is submitted
           to it, the parser must shift, reduce, or signal an error, before
           it can request another token or terminate. *)
        assert false

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

  (* The function [loop_test] can be used, after an error has been detected, to
     dynamically test which tokens would have been accepted at this point. We
     provide this test, ready for use. *)

  (* For completeness, one must undo any spurious reductions before carrying out
     this test -- that is, one must apply [acceptable] to the FIRST checkpoint
     that is passed by [loop_handle_undo] to its failure continuation. *)

  (* This test causes some semantic actions to be run! The semantic actions
     should be side-effect free, or their side-effects should be harmless. *)

  (* The position [pos] is used as the start and end positions of the
     hypothetical token, and may be picked up by the semantic actions. We
     suggest using the position where the error was detected. *)

  let acceptable checkpoint token pos =
    let triple = (token, pos, pos) in
    let checkpoint = offer checkpoint triple in
    loop_test (fun _env _accu -> true) checkpoint false

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

  (* The type ['a lr1state] describes the (non-initial) states of the LR(1)
     automaton. The index ['a] represents the type of the semantic value
     associated with the state's incoming symbol. *)

  (* The type ['a lr1state] is defined as an alias for [state], which itself
     is usually defined as [int] (see [TableInterpreter]). So, ['a lr1state]
     is technically a phantom type, but should really be thought of as a GADT
     whose data constructors happen to be represented as integers. It is
     presented to the user as an abstract type (see [IncrementalEngine]). *)

  type 'a lr1state =
      state

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

  (* Stack inspection. *)

  (* We offer a read-only view of the parser's state as a stream of elements.
     Each element contains a pair of a (non-initial) state and a semantic
     value associated with (the incoming symbol of) this state. Note that the
     type [element] is an existential type. *)

  type element =
    | Element: 'a lr1state * 'a * Lexing.position * Lexing.position -> element

  open General

  type stack =
    element stream

  (* If [current] is the current state and [cell] is the top stack cell,
     then [stack cell current] is a view of the parser's state as a stream
     of elements. *)

  let rec stack cell current : element stream =
    lazy (
      (* The stack is empty iff the top stack cell is its own successor. In
         that case, the current state [current] should be an initial state
         (which has no incoming symbol).
         We do not allow the user to inspect this state. *)
      let next = cell.next in
      if next == cell then
        Nil
      else
        (* Construct an element containing the current state [current] as well
           as the semantic value contained in the top stack cell. This semantic
           value is associated with the incoming symbol of this state, so it
           makes sense to pair them together. The state has type ['a state] and
           the semantic value has type ['a], for some type ['a]. Here, the OCaml
           type-checker thinks ['a] is [semantic_value] and considers this code
           well-typed. Outside, we will use magic to provide the user with a way
           of inspecting states and recovering the value of ['a]. *)
        let element = Element (
          current,
          cell.semv,
          cell.startp,
          cell.endp
        ) in
        Cons (element, stack next cell.state)
    )

  let stack env : element stream =
    stack env.stack env.current

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

  (* Access to the position of the lookahead token. *)

  let positions { triple = (_, startp, endp); _ } =
    startp, endp

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

  (* Access to information about default reductions. *)

  (* We can make this a function of states, or a function of environments. For
     now, the latter appears simpler. *)

  let has_default_reduction env : bool =
    T.default_reduction
      env.current
      (fun _env _prod -> true)
      (fun _env -> false)
      env

end

end
module Printers = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

module Make
  (I : IncrementalEngine.EVERYTHING)
  (User : sig
    val print: string -> unit
    val print_symbol: I.xsymbol -> unit
    val print_element: (I.element -> unit) option
  end)
= struct

  let arrow = " -> "
  let dot = "."
  let space = " "
  let newline = "\n"

  open User
  open I

  (* Printing a list of symbols. An optional dot is printed at offset
     [i] into the list [symbols], if this offset lies between [0] and
     the length of the list (included). *)

  let rec print_symbols i symbols =
    if i = 0 then begin
      print dot;
      print space;
      print_symbols (-1) symbols
    end
    else begin
      match symbols with
      | [] ->
          ()
      | symbol :: symbols ->
          print_symbol symbol;
          print space;
          print_symbols (i - 1) symbols
    end

  (* Printing an element as a symbol. *)

  let print_element_as_symbol element =
    match element with
    | Element (s, _, _, _) ->
        print_symbol (X (incoming_symbol s))

  (* Some of the functions that follow need an element printer. They use
     [print_element] if provided by the user; otherwise they use
     [print_element_as_symbol]. *)

  let print_element =
    match print_element with
    | Some print_element ->
        print_element
    | None ->
        print_element_as_symbol

  (* Printing a stack as a list of symbols. *)

  let print_stack stack =
    General.foldr (fun element () ->
      print_element element;
      print space
    ) stack ();
    print newline

  (* Printing an item. *)

  let print_item (prod, i) =
    print_symbol (lhs prod);
    print arrow;
    print_symbols i (rhs prod);
    print newline

  (* Printing a list of symbols (public version). *)

  let print_symbols symbols =
    print_symbols (-1) symbols

  (* Printing a production (without a dot). *)

  let print_production prod =
    print_item (prod, -1)

  (* Printing the current LR(1) state. *)

  let print_current_state env =
    print "Current LR(1) state: ";
    match Lazy.force (stack env) with
    | General.Nil ->
        print "<some initial state>";
        print newline
    | General.Cons (Element (current, _, _, _), _) ->
        print (string_of_int (Obj.magic current)); (* TEMPORARY safe conversion needed *)
        print newline;
        List.iter print_item (items current)

  let print_env env =
    print_stack (stack env);
    print_current_state env;
    print newline

end

end
module InfiniteArray = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(** This module implements infinite arrays, that is, arrays that grow
    transparently upon demand. *)

type 'a t = {
    default: 'a;
    mutable table: 'a array;
    mutable extent: int; (* the index of the greatest [set] ever, plus one *)
  }

let default_size =
  16384 (* must be non-zero *)

let make x = {
  default = x;
  table = Array.make default_size x;
  extent = 0;
}

let rec new_length length i =
  if i < length then
    length
  else
    new_length (2 * length) i

let ensure a i =
  assert (0 <= i);
  let table = a.table in
  let length = Array.length table in
  if i >= length then begin
    let table' = Array.make (new_length (2 * length) i) a.default in
    Array.blit table 0 table' 0 length;
    a.table <- table'
  end

let get a i =
  ensure a i;
  Array.unsafe_get a.table (i)

let set a i x =
  ensure a i;
  Array.unsafe_set a.table (i) x;
  if a.extent <= i then
    a.extent <- i + 1

let extent a =
  a.extent

let domain a =
  Array.sub a.table 0 a.extent

end
module PackedIntArray = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* A packed integer array is represented as a pair of an integer [k] and
   a string [s]. The integer [k] is the number of bits per integer that we
   use. The string [s] is just an array of bits, which is read in 8-bit
   chunks. *)

(* The ocaml programming language treats string literals and array literals
   in slightly different ways: the former are statically allocated, while
   the latter are dynamically allocated. (This is rather arbitrary.) In the
   context of Menhir's table-based back-end, where compact, immutable
   integer arrays are needed, ocaml strings are preferable to ocaml arrays. *)

type t =
  int * string

(* The magnitude [k] of an integer [v] is the number of bits required
   to represent [v]. It is rounded up to the nearest power of two, so
   that [k] divides [Sys.word_size]. *)

let magnitude (v : int) =
  if v < 0 then
    Sys.word_size
  else
    let rec check k max = (* [max] equals [2^k] *)
      if (max <= 0) || (v < max) then
        k
          (* if [max] just overflew, then [v] requires a full ocaml
             integer, and [k] is the number of bits in an ocaml integer
             plus one, that is, [Sys.word_size]. *)
      else
        check (2 * k) (max * max)
    in
    check 1 2

(* [pack a] turns an array of integers into a packed integer array. *)

(* Because the sign bit is the most significant bit, the magnitude of
   any negative number is the word size. In other words, [pack] does
   not achieve any space savings as soon as [a] contains any negative
   numbers, even if they are ``small''. *)

let pack (a : int array) : t =

  let m = Array.length a in

  (* Compute the maximum magnitude of the array elements. This tells
     us how many bits per element we are going to use. *)

  let k =
    Array.fold_left (fun k v ->
      max k (magnitude v)
    ) 1 a
  in

  (* Because access to ocaml strings is performed on an 8-bit basis,
     two cases arise. If [k] is less than 8, then we can pack multiple
     array entries into a single character. If [k] is greater than 8,
     then we must use multiple characters to represent a single array
     entry. *)

  if k <= 8 then begin

    (* [w] is the number of array entries that we pack in a character. *)

    assert (8 mod k = 0);
    let w = 8 / k in

    (* [n] is the length of the string that we allocate. *)

    let n =
      if m mod w = 0 then
        m / w
      else
        m / w + 1
    in

    let s =
      Bytes.create n
    in

    (* Define a reader for the source array. The reader might run off
       the end if [w] does not divide [m]. *)

    let i = ref 0 in
    let next () =
      let ii = !i in
      if ii = m then
        0 (* ran off the end, pad with zeroes *)
      else
        let v = a.(ii) in
        i := ii + 1;
        v
    in

    (* Fill up the string. *)

    for j = 0 to n - 1 do
      let c = ref 0 in
      for _x = 1 to w do
        c := (!c lsl k) lor next()
      done;
      Bytes.set s j (Char.chr !c)
    done;

    (* Done. *)

    k, Bytes.unsafe_to_string s

  end
  else begin (* k > 8 *)

    (* [w] is the number of characters that we use to encode an array entry. *)

    assert (k mod 8 = 0);
    let w = k / 8 in

    (* [n] is the length of the string that we allocate. *)

    let n =
      m * w
    in

    let s =
      Bytes.create n
    in

    (* Fill up the string. *)

    for i = 0 to m - 1 do
      let v = ref a.(i) in
      for x = 1 to w do
        Bytes.set s ((i + 1) * w - x) (Char.chr (!v land 255));
        v := !v lsr 8
      done
    done;

    (* Done. *)

    k, Bytes.unsafe_to_string s

  end

(* Access to a string. *)

let read (s : string) (i : int) : int =
  Char.code (String.unsafe_get s i)

(* [get1 t i] returns the integer stored in the packed array [t] at index [i].
   It assumes (and does not check) that the array's bit width is [1]. The
   parameter [t] is just a string. *)

let get1 (s : string) (i : int) : int =
  let c = read s (i lsr 3) in
  let c = c lsr ((lnot i) land 0b111) in
  let c = c land 0b1 in
  c

(* [get t i] returns the integer stored in the packed array [t] at index [i]. *)

(* Together, [pack] and [get] satisfy the following property: if the index [i]
   is within bounds, then [get (pack a) i] equals [a.(i)]. *)

let get ((k, s) : t) (i : int) : int =
  match k with
  | 1 ->
      get1 s i
  | 2 ->
      let c = read s (i lsr 2) in
      let c = c lsr (2 * ((lnot i) land 0b11)) in
      let c = c land 0b11 in
      c
  | 4 ->
      let c = read s (i lsr 1) in
      let c = c lsr (4 * ((lnot i) land 0b1)) in
      let c = c land 0b1111 in
      c
  | 8 ->
      read s i
  | 16 ->
      let j = 2 * i in
      (read s j) lsl 8 + read s (j + 1)
  | _ ->
      assert (k = 32); (* 64 bits unlikely, not supported *)
      let j = 4 * i in
      (((read s j lsl 8) + read s (j + 1)) lsl 8 + read s (j + 2)) lsl 8 + read s (j + 3)

(* [unflatten1 (n, data) i j] accesses the two-dimensional bitmap
   represented by [(n, data)] at indices [i] and [j]. The integer
   [n] is the width of the bitmap; the string [data] is the second
   component of the packed array obtained by encoding the table as
   a one-dimensional array. *)

let unflatten1 (n, data) i j =
   get1 data (n * i + j)

end
module RowDisplacement = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* This module compresses a two-dimensional table, where some values
   are considered insignificant, via row displacement. *)

(* This idea reportedly appears in Aho and Ullman's ``Principles
   of Compiler Design'' (1977). It is evaluated in Tarjan and Yao's
   ``Storing a Sparse Table'' (1979) and in Dencker, D�rre, and Heuft's
   ``Optimization of Parser Tables for Portable Compilers'' (1984). *)

(* A compressed table is represented as a pair of arrays. The
   displacement array is an array of offsets into the data array. *)

type 'a table =
    int array * (* displacement *)
     'a array   (* data *)

(* In a natural version of this algorithm, displacements would be greater
   than (or equal to) [-n]. However, in the particular setting of Menhir,
   both arrays are intended to be compressed with [PackedIntArray], which
   does not efficiently support negative numbers. For this reason, we are
   careful not to produce negative displacements. *)

(* In order to avoid producing negative displacements, we simply use the
   least significant bit as the sign bit. This is implemented by [encode]
   and [decode] below. *)

(* One could also think, say, of adding [n] to every displacement, so as
   to ensure that all displacements are nonnegative. This would work, but
   would require [n] to be published, for use by the decoder. *)

let encode (displacement : int) : int =
  if displacement >= 0 then
    displacement lsl 1
  else
    (-displacement) lsl 1 + 1

let decode (displacement : int) : int =
  if displacement land 1 = 0 then
    displacement lsr 1
  else
    -(displacement lsr 1)

(* It is reasonable to assume that, as matrices grow large, their
   density becomes low, i.e., they have many insignificant entries.
   As a result, it is important to work with a sparse data structure
   for rows. We internally represent a row as a list of its
   significant entries, where each entry is a pair of a [j] index and
   an element. *)

type 'a row =
    (int * 'a) list

(* [compress equal insignificant dummy m n t] turns the two-dimensional table
   [t] into a compressed table. The parameter [equal] is equality of data
   values. The parameter [wildcard] tells which data values are insignificant,
   and can thus be overwritten with other values. The parameter [dummy] is
   used to fill holes in the data array. [m] and [n] are the integer
   dimensions of the table [t]. *)

let compress
    (equal : 'a -> 'a -> bool)
    (insignificant : 'a -> bool)
    (dummy : 'a)
    (m : int) (n : int)
    (t : 'a array array)
    : 'a table =

  (* Be defensive. *)

  assert (Array.length t = m);
  assert begin
    for i = 0 to m - 1 do
      assert (Array.length t.(i) = n)
    done;
    true
  end;

  (* This turns a row-as-array into a row-as-sparse-list. The row is
     accompanied by its index [i] and by its rank (the number of its
     significant entries, that is, the length of the row-as-a-list. *)

  let sparse (i : int) (line : 'a array) : int * int * 'a row (* index, rank, row *) =

    let rec loop (j : int) (rank : int) (row : 'a row) =
      if j < 0 then
        i, rank, row
      else
        let x = line.(j) in
        if insignificant x then
          loop (j - 1) rank row
        else
          loop (j - 1) (1 + rank) ((j, x) :: row)
    in

    loop (n - 1) 0 []

  in

  (* Construct an array of all rows, together with their index and rank. *)

  let rows : (int * int * 'a row) array = (* index, rank, row *)
    Array.mapi sparse t
  in

  (* Sort this array by decreasing rank. This does not have any impact
     on correctness, but reportedly improves compression. The
     intuitive idea is that rows with few significant elements are
     easy to fit, so they should be inserted last, after the problem
     has become quite constrained by fitting the heavier rows. This
     heuristic is attributed to Ziegler. *)

  Array.fast_sort (fun (_, rank1, _) (_, rank2, _) ->
    compare rank2 rank1
  ) rows;

  (* Allocate a one-dimensional array of displacements. *)

  let displacement : int array =
    Array.make m 0
  in

  (* Allocate a one-dimensional, infinite array of values. Indices
     into this array are written [k]. *)

  let data : 'a InfiniteArray.t =
    InfiniteArray.make dummy
  in

  (* Determine whether [row] fits at offset [k] within the current [data]
     array, up to extension of this array. *)

  (* Note that this check always succeeds when [k] equals the length of
     the [data] array. Indeed, the loop is then skipped. This property
     guarantees the termination of the recursive function [fit] below. *)

  let fits k (row : 'a row) : bool =

    let d = InfiniteArray.extent data in

    let rec loop = function
      | [] ->
          true
      | (j, x) :: row ->

          (* [x] is a significant element. *)

          (* By hypothesis, [k + j] is nonnegative. If it is greater than or
             equal to the current length of the data array, stop -- the row
             fits. *)

          assert (k + j >= 0);

          if k + j >= d then
            true

          (* We now know that [k + j] is within bounds of the data
             array. Check whether it is compatible with the element [y] found
             there. If it is, continue. If it isn't, stop -- the row does not
             fit. *)

          else
            let y = InfiniteArray.get data (k + j) in
            if insignificant y || equal x y then
              loop row
            else
              false

    in
    loop row

  in

  (* Find the leftmost position where a row fits. *)

  (* If the leftmost significant element in this row is at offset [j],
     then we can hope to fit as far left as [-j] -- so this element
     lands at offset [0] in the data array. *)

  (* Note that displacements may be negative. This means that, for
     insignificant elements, accesses to the data array could fail: they could
     be out of bounds, either towards the left or towards the right. This is
     not a problem, as long as [get] is invoked only at significant
     elements. *)

  let rec fit k row : int =
    if fits k row then
      k
    else
      fit (k + 1) row
  in

  let fit row =
    match row with
    | [] ->
        0 (* irrelevant *)
    | (j, _) :: _ ->
        fit (-j) row
  in

  (* Write [row] at (compatible) offset [k]. *)

  let rec write k = function
    | [] ->
        ()
    | (j, x) :: row ->
        InfiniteArray.set data (k + j) x;
        write k row
  in

  (* Iterate over the sorted array of rows. Fit and write each row at
     the leftmost compatible offset. Update the displacement table. *)

  Array.iter (fun (i, _, row) ->
    let k = fit row in (* if [row] has leading insignificant elements, then [k] can be negative *)
    write k row;
    displacement.(i) <- encode k
  ) rows;

  (* Return the compressed tables. *)

  displacement, InfiniteArray.domain data

(* [get ct i j] returns the value found at indices [i] and [j] in the
   compressed table [ct]. This function call is permitted only if the
   value found at indices [i] and [j] in the original table is
   significant -- otherwise, it could fail abruptly. *)

(* Together, [compress] and [get] have the property that, if the value
   found at indices [i] and [j] in an uncompressed table [t] is
   significant, then [get (compress t) i j] is equal to that value. *)

let get (displacement, data) i j =
  assert (0 <= i && i < Array.length displacement);
  let k = decode displacement.(i) in
  assert (0 <= k + j && k + j < Array.length data);
    (* failure of this assertion indicates an attempt to access an
       insignificant element that happens to be mapped out of the bounds
       of the [data] array. *)
  data.(k + j)

(* [getget] is a variant of [get] which only requires read access,
   via accessors, to the two components of the table. *)

let getget get_displacement get_data (displacement, data) i j =
  let k = decode (get_displacement displacement i) in
  get_data data (k + j)

end
module LinearizedArray = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* The [entry] array contains offsets into the [data] array. It has [n+1]
   elements if the original (unencoded) array has [n] elements. The value
   of [entry.(n)] is the length of the [data] array. This convention is
   natural and allows avoiding a special case. *)

type 'a t =
  (* data: *)   'a array *
  (* entry: *) int array

let make (a : 'a array array) : 'a t =
  let n = Array.length a in
  (* Build the entry array. *)
  let size = ref 0 in
  let entry = Array.init (n + 1) (fun i ->
    let s = !size in
    if i < n then
      size := s + Array.length a.(i);
    s
  ) in
  assert (entry.(n) = !size);
  (* Build the data array. *)
  let i = ref 0
  and j = ref 0 in
  let data = Array.init !size (fun _ ->
    while !j = Array.length a.(!i) do
      i := !i + 1;
      j := 0;
    done;
    let x = a.(!i).(!j) in
    j := !j + 1;
    x
  ) in
  data, entry

let length ((_, entry) : 'a t) : int =
  Array.length entry

let row_length ((_, entry) : 'a t) i : int =
  entry.(i + 1) - entry.(i)

let row_length_via get_entry i =
  get_entry (i + 1) - get_entry i

let read ((data, entry) as la : 'a t) i j : 'a =
  assert (0 <= j && j < row_length la i);
  data.(entry.(i) + j)

let read_via get_data get_entry i j =
  assert (0 <= j && j < row_length_via get_entry i);
  get_data (get_entry i + j)

let write ((data, entry) as la : 'a t) i j (v : 'a) : unit =
  assert (0 <= j && j < row_length la i);
  data.(entry.(i) + j) <- v

let rec read_interval_via get_data i j =
  if i = j then
    []
  else
    get_data i :: read_interval_via get_data (i + 1) j

let read_row_via get_data get_entry i =
  read_interval_via get_data (get_entry i) (get_entry (i + 1))

let read_row ((data, entry) : 'a t) i : 'a list =
  read_row_via (Array.get data) (Array.get entry) i

end
module TableFormat = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* This signature defines the format of the parse tables. It is used as
   an argument to [TableInterpreter.Make]. *)

module type TABLES = sig

  (* This is the parser's type of tokens. *)

  type token

  (* This maps a token to its internal (generation-time) integer code. *)

  val token2terminal: token -> int

  (* This is the integer code for the error pseudo-token. *)

  val error_terminal: int

  (* This maps a token to its semantic value. *)

  val token2value: token -> Obj.t

  (* Traditionally, an LR automaton is described by two tables, namely, an
     action table and a goto table. See, for instance, the Dragon book.

     The action table is a two-dimensional matrix that maps a state and a
     lookahead token to an action. An action is one of: shift to a certain
     state, reduce a certain production, accept, or fail.

     The goto table is a two-dimensional matrix that maps a state and a
     non-terminal symbol to either a state or undefined. By construction, this
     table is sparse: its undefined entries are never looked up. A compression
     technique is free to overlap them with other entries.

     In Menhir, things are slightly different. If a state has a default
     reduction on token [#], then that reduction must be performed without
     consulting the lookahead token. As a result, we must first determine
     whether that is the case, before we can obtain a lookahead token and use it
     as an index in the action table.

     Thus, Menhir's tables are as follows.

     A one-dimensional default reduction table maps a state to either ``no
     default reduction'' (encoded as: 0) or ``by default, reduce prod''
     (encoded as: 1 + prod). The action table is looked up only when there
     is no default reduction. *)

  val default_reduction: PackedIntArray.t

  (* Menhir follows Dencker, D�rre and Heuft, who point out that, although the
     action table is not sparse by nature (i.e., the error entries are
     significant), it can be made sparse by first factoring out a binary error
     matrix, then replacing the error entries in the action table with undefined
     entries. Thus:

     A two-dimensional error bitmap maps a state and a terminal to either
     ``fail'' (encoded as: 0) or ``do not fail'' (encoded as: 1). The action
     table, which is now sparse, is looked up only in the latter case. *)

  (* The error bitmap is flattened into a one-dimensional table; its width is
     recorded so as to allow indexing. The table is then compressed via
     [PackedIntArray]. The bit width of the resulting packed array must be
     [1], so it is not explicitly recorded. *)

  (* The error bitmap does not contain a column for the [#] pseudo-terminal.
     Thus, its width is [Terminal.n - 1]. We exploit the fact that the integer
     code assigned to [#] is greatest: the fact that the right-most column
     in the bitmap is missing does not affect the code for accessing it. *)

  val error: int (* width of the bitmap *) * string (* second component of [PackedIntArray.t] *)

  (* A two-dimensional action table maps a state and a terminal to one of
     ``shift to state s and discard the current token'' (encoded as: s | 10),
     ``shift to state s without discarding the current token'' (encoded as: s |
     11), or ``reduce prod'' (encoded as: prod | 01). *)

  (* The action table is first compressed via [RowDisplacement], then packed
     via [PackedIntArray]. *)

  (* Like the error bitmap, the action table does not contain a column for the
     [#] pseudo-terminal. *)

  val action: PackedIntArray.t * PackedIntArray.t

  (* A one-dimensional lhs table maps a production to its left-hand side (a
     non-terminal symbol). *)

  val lhs: PackedIntArray.t

  (* A two-dimensional goto table maps a state and a non-terminal symbol to
     either undefined (encoded as: 0) or a new state s (encoded as: 1 + s). *)

  (* The goto table is first compressed via [RowDisplacement], then packed
     via [PackedIntArray]. *)

  val goto: PackedIntArray.t * PackedIntArray.t

  (* The number of start productions. A production [prod] is a start
     production if and only if [prod < start] holds. This is also the
     number of start symbols. A nonterminal symbol [nt] is a start
     symbol if and only if [nt < start] holds. *)

  val start: int

  (* A one-dimensional semantic action table maps productions to semantic
     actions. The calling convention for semantic actions is described in
     [EngineTypes]. This table contains ONLY NON-START PRODUCTIONS, so the
     indexing is off by [start]. Be careful. *)

  val semantic_action: ((int, Obj.t, token) EngineTypes.env ->
                        (int, Obj.t)        EngineTypes.stack) array

  (* The parser defines its own [Error] exception. This exception can be
     raised by semantic actions and caught by the engine, and raised by the
     engine towards the final user. *)

  exception Error

  (* The parser indicates whether to generate a trace. Generating a
     trace requires two extra tables, which respectively map a
     terminal symbol and a production to a string. *)

  val trace: (string array * string array) option

end

end
module InspectionTableFormat = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

(* This signature defines the format of the tables that are produced (in
   addition to the tables described in [TableFormat]) when the command line
   switch [--inspection] is enabled. It is used as an argument to
   [InspectionTableInterpreter.Make]. *)

module type TABLES = sig

  (* The types of symbols. *)

  include IncrementalEngine.SYMBOLS

  (* The type ['a lr1state] describes an LR(1) state. The generated parser defines
     it internally as [int]. *)

  type 'a lr1state

  (* Some of the tables that follow use encodings of (terminal and
     nonterminal) symbols as integers. So, we need functions that
     map the integer encoding of a symbol to its algebraic encoding. *)

  val    terminal: int -> xsymbol
  val nonterminal: int -> xsymbol

  (* The left-hand side of every production already appears in the
     signature [TableFormat.TABLES], so we need not repeat it here. *)

  (* The right-hand side of every production. This a linearized array
     of arrays of integers, whose [data] and [entry] components have
     been packed. The encoding of symbols as integers in described in
     [TableBackend]. *)

  val rhs: PackedIntArray.t * PackedIntArray.t

  (* A mapping of every (non-initial) state to its LR(0) core. *)

  val lr0_core: PackedIntArray.t

  (* A mapping of every LR(0) state to its set of LR(0) items. Each item is
     represented in its packed form (see [Item]) as an integer. Thus the
     mapping is an array of arrays of integers, which is linearized and
     packed, like [rhs]. *)

  val lr0_items: PackedIntArray.t * PackedIntArray.t

  (* A mapping of every LR(0) state to its incoming symbol, if it has one. *)

  val lr0_incoming: PackedIntArray.t

  (* A table that tells which non-terminal symbols are nullable. *)

  val nullable: string
    (* This is a packed int array of bit width 1. It can be read
       using [PackedIntArray.get1]. *)

  (* A two-table dimensional table, indexed by a nonterminal symbol and
     by a terminal symbol (other than [#]), encodes the FIRST sets. *)

  val first: int (* width of the bitmap *) * string (* second component of [PackedIntArray.t] *)

end

end
module InspectionTableInterpreter = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

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

(* The type functor. *)

module Symbols (T : sig

  type 'a terminal
  type 'a nonterminal

end) = struct

  open T

  (* This should be the only place in the whole library (and generator!)
     where these types are defined. *)

  type 'a symbol =
    | T : 'a terminal -> 'a symbol
    | N : 'a nonterminal -> 'a symbol

  type xsymbol =
    | X : 'a symbol -> xsymbol

end

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

(* The code functor. *)

module Make
  (B : TableFormat.TABLES)
  (T : InspectionTableFormat.TABLES
       with type 'a lr1state = int)
= struct

  (* Including [T] is an easy way of inheriting the definitions of the types
     [symbol] and [xsymbol]. *)

  include T

  (* This auxiliary function decodes a packed linearized array, as created by
     [TableBackend.linearize_and_marshal1]. Here, we read a row all at once. *)

  let read_packed_linearized ((data, entry) : PackedIntArray.t * PackedIntArray.t) (i : int) : int list =
    LinearizedArray.read_row_via
      (PackedIntArray.get data)
      (PackedIntArray.get entry)
      i

  (* This auxiliary function decodes a symbol. The encoding was done by
     [encode_symbol] or [encode_symbol_option] in the table back-end. *)

  let decode_symbol (symbol : int) : T.xsymbol =
    (* If [symbol] is 0, then we have no symbol. This could mean e.g.
       that the function [incoming_symbol] has been applied to an
       initial state. In principle, this cannot happen. *)
    assert (symbol > 0);
    (* The low-order bit distinguishes terminal and nonterminal symbols. *)
    let kind = symbol land 1 in
    let symbol = symbol lsr 1 in
    if kind = 0 then
      T.terminal (symbol - 1)
    else
      T.nonterminal symbol

  (* These auxiliary functions convert a symbol to its integer code. For speed
     and for convenience, we use an unsafe type cast. This relies on the fact
     that the data constructors of the [terminal] and [nonterminal] GADTs are
     declared in an order that reflects their internal code. In the case of
     nonterminal symbols, we add [start] to account for the presence of the
     start symbols. *)

  let n2i (nt : 'a T.nonterminal) : int =
    let answer = B.start + Obj.magic nt in
    assert (T.nonterminal answer = X (N nt)); (* TEMPORARY roundtrip *)
    answer

  let t2i (t : 'a T.terminal) : int =
    let answer = Obj.magic t in
    assert (T.terminal answer = X (T t)); (* TEMPORARY roundtrip *)
    answer

  (* Ordering functions. *)

  let compare_terminals t1 t2 =
    (* Subtraction is safe because overflow is impossible. *)
    t2i t1 - t2i t2

  let compare_nonterminals nt1 nt2 =
    (* Subtraction is safe because overflow is impossible. *)
    n2i nt1 - n2i nt2

  let compare_symbols symbol1 symbol2 =
    match symbol1, symbol2 with
    | X (T _), X (N _) ->
        -1
    | X (N _), X (T _) ->
        1
    | X (T t1), X (T t2) ->
        compare_terminals t1 t2
    | X (N nt1), X (N nt2) ->
        compare_nonterminals nt1 nt2

  let compare_productions prod1 prod2 =
    (* Subtraction is safe because overflow is impossible. *)
    prod1 - prod2

  let compare_items (prod1, index1) (prod2, index2) =
    let c = compare_productions prod1 prod2 in
    (* Subtraction is safe because overflow is impossible. *)
    if c <> 0 then c else index1 - index2

  (* The function [incoming_symbol] goes through the tables [T.lr0_core] and
     [T.lr0_incoming]. This yields a representation of type [xsymbol], out of
     which we strip the [X] quantifier, so as to get a naked symbol. This last
     step is ill-typed and potentially dangerous. It is safe only because this
     function is used at type ['a lr1state -> 'a symbol], which forces an
     appropriate choice of ['a]. *)

  let incoming_symbol (s : 'a T.lr1state) : 'a T.symbol =
    let core = PackedIntArray.get T.lr0_core s in
    let symbol = decode_symbol (PackedIntArray.get T.lr0_incoming core) in
    match symbol with
    | T.X symbol ->
        Obj.magic symbol

  (* The function [lhs] reads the table [B.lhs] and uses [T.nonterminal]
     to decode the symbol. *)

  let lhs prod =
    T.nonterminal (PackedIntArray.get B.lhs prod)

  (* The function [rhs] reads the table [T.rhs] and uses [decode_symbol]
     to decode the symbol. *)

  let rhs prod =
    List.map decode_symbol (read_packed_linearized T.rhs prod)

  (* The function [items] maps the LR(1) state [s] to its LR(0) core,
     then uses [core] as an index into the table [T.lr0_items]. The
     items are then decoded by the function [export] below, which is
     essentially a copy of [Item.export]. *)

  type item =
      int * int

  let export t : item =
    (t lsr 7, t mod 128)

  let items s =
    (* Map [s] to its LR(0) core. *)
    let core = PackedIntArray.get T.lr0_core s in
    (* Now use [core] to look up the table [T.lr0_items]. *)
    List.map export (read_packed_linearized T.lr0_items core)

  (* The function [nullable] maps the nonterminal symbol [nt] to its
     integer code, which it uses to look up the array [T.nullable].
     This yields 0 or 1, which we map back to a Boolean result. *)

  let decode_bool i =
    assert (i = 0 || i = 1);
    i = 1

  let nullable nt =
    decode_bool (PackedIntArray.get1 T.nullable (n2i nt))

  (* The function [first] maps the symbols [nt] and [t] to their integer
     codes, which it uses to look up the matrix [T.first]. *)

  let first nt t =
    decode_bool (PackedIntArray.unflatten1 T.first (n2i nt) (t2i t))

  let xfirst symbol t =
    match symbol with
    | X (T t') ->
        compare_terminals t t' = 0
    | X (N nt) ->
        first nt t

  (* The function [foreach_terminal] exploits the fact that the
     first component of [B.error] is [Terminal.n - 1], i.e., the
     number of terminal symbols, including [error] but not [#]. *)

  let rec foldij i j f accu =
    if i = j then
      accu
    else
      foldij (i + 1) j f (f i accu)

  let foreach_terminal f accu =
    let n, _ = B.error in
    foldij 0 n (fun i accu ->
      f (T.terminal i) accu
    ) accu

  let foreach_terminal_but_error f accu =
    let n, _ = B.error in
    foldij 0 n (fun i accu ->
      if i = B.error_terminal then
        accu
      else
        f (T.terminal i) accu
    ) accu

end
end
module TableInterpreter = struct
(**************************************************************************)
(*                                                                        *)
(*  Menhir                                                                *)
(*                                                                        *)
(*  François Pottier, INRIA Paris-Rocquencourt                            *)
(*  Yann Régis-Gianas, PPS, Université Paris Diderot                      *)
(*                                                                        *)
(*  Copyright 2005-2015 Institut National de Recherche en Informatique    *)
(*  et en Automatique. All rights reserved. This file is distributed      *)
(*  under the terms of the GNU Library General Public License, with the   *)
(*  special exception on linking described in file LICENSE.               *)
(*                                                                        *)
(**************************************************************************)

module Make (T : TableFormat.TABLES)

= Engine.Make (struct

  type state =
      int

  let number s = s

  type token =
      T.token

  type terminal =
      int

  type semantic_value =
      Obj.t

  let token2terminal =
    T.token2terminal

  let token2value =
    T.token2value

  let error_terminal =
    T.error_terminal

  let error_value =
    Obj.repr ()

  type production =
      int

  let default_reduction state defred nodefred env =
    let code = PackedIntArray.get T.default_reduction state in
    if code = 0 then
      nodefred env
    else
      defred env (code - 1)

  let is_start prod =
    prod < T.start

  (* This auxiliary function helps access a compressed, two-dimensional
     matrix, like the action and goto tables. *)

  let unmarshal2 table i j =
    RowDisplacement.getget
      PackedIntArray.get
      PackedIntArray.get
      table
      i j

  (* This auxiliary function helps access a flattened, two-dimensional
     matrix, like the error bitmap. *)

  let action state terminal value shift reduce fail env =
    match PackedIntArray.unflatten1 T.error state terminal with
    | 1 ->
        let action = unmarshal2 T.action state terminal in
        let opcode = action land 0b11
        and param = action lsr 2 in
        if opcode >= 0b10 then
          (* 0b10 : shift/discard *)
          (* 0b11 : shift/nodiscard *)
          let please_discard = (opcode = 0b10) in
          shift env please_discard terminal value param
        else
          (* 0b01 : reduce *)
          (* 0b00 : cannot happen *)
          reduce env param
    | c ->
        assert (c = 0);
        fail env

  let goto state prod =
    let code = unmarshal2 T.goto state (PackedIntArray.get T.lhs prod) in
    (* code = 1 + state *)
    code - 1

  exception Error =
        T.Error

  type semantic_action =
      (state, semantic_value, token) EngineTypes.env ->
      (state, semantic_value)        EngineTypes.stack

  let semantic_action prod =
    (* Indexing into the array [T.semantic_action] is off by [T.start],
       because the start productions do not have entries in this array. *)
    T.semantic_action.(prod - T.start)

  (* If [T.trace] is [None], then the logging functions do nothing. *)

  let log =
    match T.trace with Some _ -> true | None -> false

  module Log = struct

    open Printf

    let state state =
      match T.trace with
      | Some _ ->
          fprintf stderr "State %d:\n%!" state
      | None ->
          ()

    let shift terminal state =
      match T.trace with
      | Some (terminals, _) ->
          fprintf stderr "Shifting (%s) to state %d\n%!" terminals.(terminal) state
      | None ->
          ()

    let reduce_or_accept prod =
      match T.trace with
      | Some (_, productions) ->
          fprintf stderr "%s\n%!" productions.(prod)
      | None ->
          ()

    let lookahead_token token startp endp =
      match T.trace with
      | Some (terminals, _) ->
          fprintf stderr "Lookahead token is now %s (%d-%d)\n%!"
            terminals.(token)
            startp.Lexing.pos_cnum
            endp.Lexing.pos_cnum
      | None ->
          ()

    let initiating_error_handling () =
      match T.trace with
      | Some _ ->
          fprintf stderr "Initiating error handling\n%!"
      | None ->
          ()

    let resuming_error_handling () =
      match T.trace with
      | Some _ ->
          fprintf stderr "Resuming error handling\n%!"
      | None ->
          ()

    let handling_error state =
      match T.trace with
      | Some _ ->
          fprintf stderr "Handling error in state %d\n%!" state
      | None ->
          ()

  end

end)

end
module StaticVersion = struct
let require_20170101 = ()
end
