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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(** 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 t = LocalAssum of Name.t * Constr.t (** name, type *)
| LocalDef of Name.t * Constr.t * Constr.t (** name, value, type *)
(** Return the name bound by a given declaration. *)
val get_name : t -> Name.t
(** Return [Some value] for local-declarations and [None] for local-assumptions. *)
val get_value : t -> Constr.t option
(** Return the type of the name bound by a given declaration. *)
val get_type : t -> Constr.t
(** Set the name that is bound by a given declaration. *)
val set_name : Name.t -> t -> t
(** Set the type of the bound variable in a given declaration. *)
val set_type : Constr.t -> t -> t
(** Return [true] iff a given declaration is a local assumption. *)
val is_local_assum : t -> bool
(** Return [true] iff a given declaration is a local definition. *)
val is_local_def : t -> bool
(** Check whether any term in a given declaration satisfies a given predicate. *)
val exists : (Constr.t -> bool) -> t -> bool
(** Check whether all terms in a given declaration satisfy a given predicate. *)
val for_all : (Constr.t -> bool) -> t -> bool
(** Check whether the two given declarations are equal. *)
val equal : t -> t -> bool
(** Map the name bound by a given declaration. *)
val map_name : (Name.t -> Name.t) -> t -> t
(** 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 : (Constr.t -> Constr.t) -> t -> t
(** Map the type of the name bound by a given declaration. *)
val map_type : (Constr.t -> Constr.t) -> t -> t
(** Map all terms in a given declaration. *)
val map_constr : (Constr.t -> Constr.t) -> t -> t
(** Perform a given action on all terms in a given declaration. *)
val iter_constr : (Constr.t -> unit) -> t -> unit
(** Reduce all terms in a given declaration to a single value. *)
val fold : (Constr.t -> 'a -> 'a) -> t -> 'a -> 'a
val to_tuple : t -> Name.t * Constr.t option * Constr.t
val of_tuple : Name.t * Constr.t option * Constr.t -> t
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 t = Declaration.t list
(** empty rel-context *)
val empty : t
(** Return a new rel-context enriched by with a given inner-most declaration. *)
val add : Declaration.t -> t -> t
(** Return the number of {e local declarations} in a given context. *)
val length : t -> int
(** Check whether given two rel-contexts are equal. *)
val equal : t -> t -> bool
(** Return the number of {e local assumptions} in a given rel-context. *)
val nhyps : t -> 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 -> t -> Declaration.t
(** Map all terms in a given rel-context. *)
val map : (Constr.t -> Constr.t) -> t -> t
(** Perform a given action on every declaration in a given rel-context. *)
val iter : (Constr.t -> unit) -> t -> unit
(** Reduce all terms in a given rel-context to a single value.
Innermost declarations are processed first. *)
val fold_inside : ('a -> Declaration.t -> 'a) -> init:'a -> t -> 'a
(** Reduce all terms in a given rel-context to a single value.
Outermost declarations are processed first. *)
val fold_outside : (Declaration.t -> 'a -> 'a) -> t -> 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 : t -> bool list
(** [extended_list 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]. Example: for [x:T, y:=c, z:U] and [n]=2, it gives [Rel 5, Rel 3]. *)
val to_extended_list : int -> t -> Constr.t list
(** [extended_vect n Γ] does the same, returning instead an array. *)
val to_extended_vect : int -> t -> Constr.t 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 t = LocalAssum of Id.t * Constr.t (** identifier, type *)
| LocalDef of Id.t * Constr.t * Constr.t (** identifier, value, type *)
(** Return the identifier bound by a given declaration. *)
val get_id : t -> Id.t
(** Return [Some value] for local-declarations and [None] for local-assumptions. *)
val get_value : t -> Constr.t option
(** Return the type of the name bound by a given declaration. *)
val get_type : t -> Constr.t
(** Set the identifier that is bound by a given declaration. *)
val set_id : Id.t -> t -> t
(** Set the type of the bound variable in a given declaration. *)
val set_type : Constr.t -> t -> t
(** Return [true] iff a given declaration is a local assumption. *)
val is_local_assum : t -> bool
(** Return [true] iff a given declaration is a local definition. *)
val is_local_def : t -> bool
(** Check whether any term in a given declaration satisfies a given predicate. *)
val exists : (Constr.t -> bool) -> t -> bool
(** Check whether all terms in a given declaration satisfy a given predicate. *)
val for_all : (Constr.t -> bool) -> t -> bool
(** Check whether the two given declarations are equal. *)
val equal : t -> t -> bool
(** Map the identifier bound by a given declaration. *)
val map_id : (Id.t -> Id.t) -> t -> t
(** 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 : (Constr.t -> Constr.t) -> t -> t
(** Map the type of the name bound by a given declaration. *)
val map_type : (Constr.t -> Constr.t) -> t -> t
(** Map all terms in a given declaration. *)
val map_constr : (Constr.t -> Constr.t) -> t -> t
(** Perform a given action on all terms in a given declaration. *)
val iter_constr : (Constr.t -> unit) -> t -> unit
(** Reduce all terms in a given declaration to a single value. *)
val fold : (Constr.t -> 'a -> 'a) -> t -> 'a -> 'a
val to_tuple : t -> Id.t * Constr.t option * Constr.t
val of_tuple : Id.t * Constr.t option * Constr.t -> t
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 t = Declaration.t list
(** empty named-context *)
val empty : t
(** Return a new rel-context enriched by with a given inner-most declaration. *)
val add : Declaration.t -> t -> t
(** Return the number of {e local declarations} in a given named-context. *)
val length : t -> 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 -> t -> Declaration.t
(** Check whether given two rel-contexts are equal. *)
val equal : t -> t -> bool
(** Map all terms in a given named-context. *)
val map : (Constr.t -> Constr.t) -> t -> t
(** Perform a given action on every declaration in a given named-context. *)
val iter : (Constr.t -> unit) -> t -> unit
(** Reduce all terms in a given named-context to a single value.
Innermost declarations are processed first. *)
val fold_inside : ('a -> Declaration.t -> 'a) -> init:'a -> t -> 'a
(** Reduce all terms in a given named-context to a single value.
Outermost declarations are processed first. *)
val fold_outside : (Declaration.t -> 'a -> 'a) -> t -> init:'a -> 'a
(** Return the set of all identifiers bound in a given named-context. *)
val to_vars : t -> Id.Set.t
(** [instance_from_named_context 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 : t -> Constr.t list
end
module NamedList :
sig
module Declaration :
sig
type t = Id.t list * Constr.t option * Constr.t
val map_constr : (Constr.t -> Constr.t) -> t -> t
end
type t = Declaration.t list
val fold : (Declaration.t -> 'a -> 'a) -> t -> init:'a -> 'a
end
type section_context = Named.t
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