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(************************************************************************)
(*         *   The Coq Proof Assistant / The Coq Development Team       *)
(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
(* <O___,, *       (see CREDITS file for the list of authors)           *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)

(** The modules defined below represent a {e local context}
    as defined by Chapter 4 in the Reference Manual:

    A {e local context} is an ordered list of of {e local declarations}
    of names that we call {e variables}.

    A {e local declaration} of some variable can be either:
    - a {e local assumption}, or
    - a {e local definition}.

    {e Local assumptions} are denoted in the Reference Manual as [(name : typ)] and
    {e local definitions} are there denoted as [(name := value : typ)].
*)

open Names

(** Representation of contexts that can capture anonymous as well as non-anonymous variables.
    Individual declarations are then designated by de Bruijn indexes. *)
module Rel :
sig
  module Declaration :
  sig
    (* local declaration *)
    type ('constr, 'types) pt =
    | LocalAssum of Name.t * 'types            (** name, type *)
    | LocalDef of Name.t * 'constr * 'types   (** name, value, type *)

    (** Return the name bound by a given declaration. *)
    val get_name : ('c, 't) pt -> Name.t

    (** Return [Some value] for local-declarations and [None] for local-assumptions. *)
    val get_value : ('c, 't) pt -> 'c option

    (** Return the type of the name bound by a given declaration. *)
    val get_type : ('c, 't) pt -> 't

    (** Set the name that is bound by a given declaration. *)
    val set_name : Name.t -> ('c, 't) pt -> ('c, 't) pt

    (** Set the type of the bound variable in a given declaration. *)
    val set_type : 't -> ('c, 't) pt -> ('c, 't) pt

    (** Return [true] iff a given declaration is a local assumption. *)
    val is_local_assum : ('c, 't) pt -> bool

    (** Return [true] iff a given declaration is a local definition. *)
    val is_local_def : ('c, 't) pt -> bool

    (** Check whether any term in a given declaration satisfies a given predicate. *)
    val exists : ('c -> bool) -> ('c, 'c) pt -> bool

    (** Check whether all terms in a given declaration satisfy a given predicate. *)
    val for_all : ('c -> bool) -> ('c, 'c) pt -> bool

    (** Check whether the two given declarations are equal. *)
    val equal : ('c -> 'c -> bool) -> ('c, 'c) pt -> ('c, 'c) pt -> bool

    (** Map the name bound by a given declaration. *)
    val map_name : (Name.t -> Name.t) -> ('c, 't) pt -> ('c, 't) pt

    (** For local assumptions, this function returns the original local assumptions.
        For local definitions, this function maps the value in the local definition. *)
    val map_value : ('c -> 'c) -> ('c, 't) pt -> ('c, 't) pt

    (** Map the type of the name bound by a given declaration. *)
    val map_type : ('t -> 't) -> ('c, 't) pt -> ('c, 't) pt

    (** Map all terms in a given declaration. *)
    val map_constr : ('c -> 'c) -> ('c, 'c) pt -> ('c, 'c) pt

    (** Perform a given action on all terms in a given declaration. *)
    val iter_constr : ('c -> unit) -> ('c, 'c) pt -> unit

    (** Reduce all terms in a given declaration to a single value. *)
    val fold_constr : ('c -> 'a -> 'a) -> ('c, 'c) pt -> 'a -> 'a

    val to_tuple : ('c, 't) pt -> Name.t * 'c option * 't

    (** Turn [LocalDef] into [LocalAssum], identity otherwise. *)
    val drop_body : ('c, 't) pt -> ('c, 't) pt
  end

  (** Rel-context is represented as a list of declarations.
      Inner-most declarations are at the beginning of the list.
      Outer-most declarations are at the end of the list. *)
  type ('constr, 'types) pt = ('constr, 'types) Declaration.pt list

  (** empty rel-context *)
  val empty : ('c, 't) pt

  (** Return a new rel-context enriched by with a given inner-most declaration. *)
  val add : ('c, 't) Declaration.pt -> ('c, 't) pt -> ('c, 't) pt

  (** Return the number of {e local declarations} in a given context. *)
  val length : ('c, 't) pt -> int

  (** Check whether given two rel-contexts are equal. *)
  val equal : ('c -> 'c -> bool) -> ('c, 'c) pt -> ('c, 'c) pt -> bool

  (** Return the number of {e local assumptions} in a given rel-context. *)
  val nhyps : ('c, 't) pt -> int

  (** Return a declaration designated by a given de Bruijn index.
      @raise Not_found if the designated de Bruijn index outside the range. *)
  val lookup : int -> ('c, 't) pt -> ('c, 't) Declaration.pt

  (** Map all terms in a given rel-context. *)
  val map : ('c -> 'c) -> ('c, 'c) pt -> ('c, 'c) pt

  (** Perform a given action on every declaration in a given rel-context. *)
  val iter : ('c -> unit) -> ('c, 'c) pt -> unit

  (** Reduce all terms in a given rel-context to a single value.
      Innermost declarations are processed first. *)
  val fold_inside : ('a -> ('c, 't) Declaration.pt -> 'a) -> init:'a -> ('c, 't) pt -> 'a

  (** Reduce all terms in a given rel-context to a single value.
      Outermost declarations are processed first. *)
  val fold_outside : (('c, 't) Declaration.pt -> 'a -> 'a) -> ('c, 't) pt -> init:'a -> 'a

  (** Map a given rel-context to a list where each {e local assumption} is mapped to [true]
      and each {e local definition} is mapped to [false]. *)
  val to_tags : ('c, 't) pt -> bool list

  (** Turn all [LocalDef] into [LocalAssum], leave [LocalAssum] unchanged. *)
  val drop_bodies : ('c, 't) pt -> ('c, 't) pt

  (** [extended_list mk n Γ] builds an instance [args] such that [Γ,Δ ⊢ args:Γ]
      with n = |Δ| and with the {e local definitions} of [Γ] skipped in
      [args] where [mk] is used to build the corresponding variables.
      Example: for [x:T, y:=c, z:U] and [n]=2, it gives [mk 5, mk 3]. *)
  val to_extended_list : (int -> 'r) -> int -> ('c, 't) pt -> 'r list

  (** [extended_vect n Γ] does the same, returning instead an array. *)
  val to_extended_vect : (int -> 'r) -> int -> ('c, 't) pt -> 'r array
end

(** This module represents contexts that can capture non-anonymous variables.
    Individual declarations are then designated by the identifiers they bind. *)
module Named :
sig
  (** Representation of {e local declarations}. *)
  module Declaration :
  sig
    type ('constr, 'types) pt =
      | LocalAssum of Id.t * 'types             (** identifier, type *)
      | LocalDef of Id.t * 'constr * 'types    (** identifier, value, type *)

    (** Return the identifier bound by a given declaration. *)
    val get_id : ('c, 't) pt -> Id.t

    (** Return [Some value] for local-declarations and [None] for local-assumptions. *)
    val get_value : ('c, 't) pt -> 'c option

    (** Return the type of the name bound by a given declaration. *)
    val get_type : ('c, 't) pt -> 't

    (** Set the identifier that is bound by a given declaration. *)
    val set_id : Id.t -> ('c, 't) pt -> ('c, 't) pt

    (** Set the type of the bound variable in a given declaration. *)
    val set_type : 't -> ('c, 't) pt -> ('c, 't) pt

    (** Return [true] iff a given declaration is a local assumption. *)
    val is_local_assum : ('c, 't) pt -> bool

    (** Return [true] iff a given declaration is a local definition. *)
    val is_local_def : ('c, 't) pt -> bool

    (** Check whether any term in a given declaration satisfies a given predicate. *)
    val exists : ('c -> bool) -> ('c, 'c) pt -> bool

    (** Check whether all terms in a given declaration satisfy a given predicate. *)
    val for_all : ('c -> bool) -> ('c, 'c) pt -> bool

    (** Check whether the two given declarations are equal. *)
    val equal : ('c -> 'c -> bool) -> ('c, 'c) pt -> ('c, 'c) pt -> bool

    (** Map the identifier bound by a given declaration. *)
    val map_id : (Id.t -> Id.t) -> ('c, 't) pt -> ('c, 't) pt

    (** For local assumptions, this function returns the original local assumptions.
        For local definitions, this function maps the value in the local definition. *)
    val map_value : ('c -> 'c) -> ('c, 't) pt -> ('c, 't) pt

    (** Map the type of the name bound by a given declaration. *)
    val map_type : ('t -> 't) -> ('c, 't) pt -> ('c, 't) pt

    (** Map all terms in a given declaration. *)
    val map_constr : ('c -> 'c) -> ('c, 'c) pt -> ('c, 'c) pt

    (** Perform a given action on all terms in a given declaration. *)
    val iter_constr : ('c -> unit) -> ('c, 'c) pt -> unit

    (** Reduce all terms in a given declaration to a single value. *)
    val fold_constr : ('c -> 'a -> 'a) -> ('c, 'c) pt -> 'a -> 'a

    val to_tuple : ('c, 't) pt -> Id.t * 'c option * 't
    val of_tuple : Id.t * 'c option * 't -> ('c, 't) pt

    (** Turn [LocalDef] into [LocalAssum], identity otherwise. *)
    val drop_body : ('c, 't) pt -> ('c, 't) pt

    (** Convert [Rel.Declaration.t] value to the corresponding [Named.Declaration.t] value.
        The function provided as the first parameter determines how to translate "names" to "ids". *)
    val of_rel_decl : (Name.t -> Id.t) -> ('c, 't) Rel.Declaration.pt -> ('c, 't) pt

    (** Convert [Named.Declaration.t] value to the corresponding [Rel.Declaration.t] value. *)
    (* TODO: Move this function to [Rel.Declaration] module and rename it to [of_named]. *)
    val to_rel_decl : ('c, 't) pt -> ('c, 't) Rel.Declaration.pt
  end

  (** Named-context is represented as a list of declarations.
      Inner-most declarations are at the beginning of the list.
      Outer-most declarations are at the end of the list. *)
  type ('constr, 'types) pt = ('constr, 'types) Declaration.pt list

  (** empty named-context *)
  val empty : ('c, 't) pt

  (** Return a new named-context enriched by with a given inner-most declaration. *)
  val add : ('c, 't) Declaration.pt -> ('c, 't) pt -> ('c, 't) pt

  (** Return the number of {e local declarations} in a given named-context. *)
  val length : ('c, 't) pt -> int

  (** Return a declaration designated by an identifier of the variable bound in that declaration.
      @raise Not_found if the designated identifier is not bound in a given named-context. *)
  val lookup : Id.t -> ('c, 't) pt -> ('c, 't) Declaration.pt

  (** Check whether given two named-contexts are equal. *)
  val equal : ('c -> 'c -> bool) -> ('c, 'c) pt -> ('c, 'c) pt -> bool

  (** Map all terms in a given named-context. *)
  val map : ('c -> 'c) -> ('c, 'c) pt -> ('c, 'c) pt

  (** Perform a given action on every declaration in a given named-context. *)
  val iter : ('c -> unit) -> ('c, 'c) pt -> unit

  (** Reduce all terms in a given named-context to a single value.
      Innermost declarations are processed first. *)
  val fold_inside : ('a -> ('c, 't) Declaration.pt -> 'a) -> init:'a -> ('c, 't) pt -> 'a

  (** Reduce all terms in a given named-context to a single value.
      Outermost declarations are processed first. *)
  val fold_outside : (('c, 't) Declaration.pt -> 'a -> 'a) -> ('c, 't) pt -> init:'a -> 'a

  (** Return the set of all identifiers bound in a given named-context. *)
  val to_vars : ('c, 't) pt -> Id.Set.t

  (** Turn all [LocalDef] into [LocalAssum], leave [LocalAssum] unchanged. *)
  val drop_bodies : ('c, 't) pt -> ('c, 't) pt

  (** [to_instance Ω] builds an instance [args] such
      that [Ω ⊢ args:Ω] where [Ω] is a named-context and with the local
      definitions of [Ω] skipped. Example: for [id1:T,id2:=c,id3:U], it
      gives [Var id1, Var id3]. All [idj] are supposed distinct. *)
  val to_instance : (Id.t -> 'r) -> ('c, 't) pt -> 'r list
end

module Compacted :
sig
  module Declaration :
  sig
    type ('constr, 'types) pt =
      | LocalAssum of Id.t list * 'types
      | LocalDef of Id.t list * 'constr * 'types

    val map_constr : ('c -> 'c) -> ('c, 'c) pt -> ('c, 'c) pt
    val of_named_decl : ('c, 't) Named.Declaration.pt -> ('c, 't) pt
    val to_named_context : ('c, 't) pt -> ('c, 't) Named.pt
  end

  type ('constr, 'types) pt = ('constr, 'types) Declaration.pt list

  val fold : (('c, 't) Declaration.pt -> 'a -> 'a) -> ('c, 't) pt -> init:'a -> 'a
end