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Datei:
natural.pvs
Sprache: PVS
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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) *)
(************************************************************************)
(** {5 Purely functional streams}
Contrarily to OCaml module [Stream], these are meant to be used purely
functionally. This implies in particular that accessing an element does not
discard it. *)
type +'a t
(** Type of pure streams. *)
type ('a,'r) u =
| Nil
| Cons of 'a * 'r
(** View type to decompose and build streams. *)
(** {6 Constructors} *)
val empty : 'a t
(** The empty stream. *)
val cons : 'a -> 'a t -> 'a t
(** Append an element in front of a stream. *)
val thunk : (unit -> ('a,'a t) u) -> 'a t
(** Internalize the laziness of a stream. *)
val make : ('a -> ('b, 'a) u) -> 'a -> 'b t
(** Coiteration constructor. *)
(** {6 Destructors} *)
val is_empty : 'a t -> bool
(** Whethere a stream is empty. *)
val peek : 'a t -> ('a , 'a t) u
(** Return the head and the tail of a stream, if any. *)
(** {6 Standard operations}
All stream-returning functions are lazy. The other ones are eager. *)
val app : 'a t -> 'a t -> 'a t
(** Append two streams. Not tail-rec. *)
val map : ('a -> 'b) -> 'a t -> 'b t
(** Mapping of streams. Not tail-rec. *)
val iter : ('a -> unit) -> 'a t -> unit
(** Iteration over streams. *)
val fold : ('a -> 'b -> 'a) -> 'a -> 'b t -> 'a
(** Fold over streams. *)
val concat : 'a t t -> 'a t
(** Appends recursively a stream of streams. *)
val map_filter : ('a -> 'b option) -> 'a t -> 'b t
(** Mixing [map] and [filter]. Not tail-rec. *)
val concat_map : ('a -> 'b t) -> 'a t -> 'b t
(** [concat_map f l] is the same as [concat (map f l)]. *)
(** {6 Conversions} *)
val of_list : 'a list -> 'a t
(** Convert a list into a stream. *)
val to_list : 'a t -> 'a list
(** Convert a stream into a list. *)
(** {6 Other}*)
val force : 'a t -> 'a t
(** Forces the whole stream. *)
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