open Ident

type const = | Integer of Intervals.V.t
	     | Atom of Atoms.V.t 
	     | Char of Chars.V.t

val compare_const: const -> const -> int
val hash_const: const -> int
val equal_const: const -> const -> bool

(** Algebra **)

include Custom.T
module Node : Custom.T
type descr = t

val make: unit -> Node.t
val define: Node.t -> t -> unit

val cons: t -> Node.t
val internalize: Node.t -> Node.t

val id: Node.t -> int
val descr: Node.t -> t

(** Boolean connectives **)

val cup    : t -> t -> t
val cap    : t -> t -> t
val diff   : t -> t -> t
val neg    : t -> t
val empty  : t
val any    : t

val any_node : Node.t

val non_constructed : t

(** Constructors **)

type pair_kind = [ `Normal | `XML ]

val interval : Intervals.t -> t
val atom     : Atoms.t -> t
val times    : Node.t -> Node.t -> t
val xml      : Node.t -> Node.t -> t
val arrow    : Node.t -> Node.t -> t
val record   : label -> Node.t -> t
  (* bool = true -> open record; bool = false -> closed record *)
val record'  : bool * Node.t label_map -> t
val char     : Chars.t -> t
val constant : const -> t

(** Helpers *)

  (** given a list of descrs create an OR type including all descrs *)
val choice_of_list: t list -> t

  (** do it yourself: create an Xml type from three types (tag type, attribute
  type, content type) *)
val xml': t -> t -> t -> t

  (** Build a record from a list of <name,t> pairs. Open defaults to true.
  All specified fields are required. *)
val rec_of_list: ?opened:bool -> (string * t) list -> t

  (** Similiar to rec_of_list, the additional boolean value specify whether the
  specified field is optional (true) or not (false. *)
val rec_of_list': ?opened:bool -> (bool * string * t) list -> t

val empty_closed_record: t
val empty_opened_record: t

(** Positive systems and least solutions **)

module Positive :
sig
  type v
  val forward: unit -> v
  val define: v -> v -> unit
  val ty: t -> v
  val cup: v list -> v
  val times: v -> v -> v
  val xml: v -> v -> v

  val solve: v -> Node.t
end

(** Normalization **)

module Product : sig
  val any : t
  val any_xml : t
  val other : ?kind:pair_kind -> t -> t
  val is_product : ?kind:pair_kind -> t -> bool

  (* List of non-empty rectangles *)
  type t = (descr * descr) list
  val is_empty: t -> bool
  val get: ?kind:pair_kind -> descr -> t
  val pi1: t -> descr
  val pi2: t -> descr
  val pi2_restricted: descr -> t -> descr
    
  (* Intersection with (pi1,Any) *)
  val restrict_1: t -> descr -> t

  (* List of non-empty rectangles whose first projection
     are pair-wise disjunct *)
  type normal = t
  val normal: ?kind:pair_kind -> descr -> normal

  val constraint_on_2: normal -> descr -> descr
    (* constraint_on_2 n t1:  maximal t2 such that (t1,t2) <= n *)
    (* Assumption: t1 <= pi1(n) *)

  val need_second: t -> bool
    (* Is there more than a single rectangle ? *)
end

module Record : sig
  val any : t
  val or_absent: t -> t
  val any_or_absent: t

  val has_absent: t -> bool
  val has_record: t -> bool

  val split : t -> label -> Product.t
  val split_normal : t -> label -> Product.normal

  val project : t -> label -> t
    (* Raise Not_found if label is not necessarily present *)

  val condition : t -> label -> t -> t
    (* condition t1 l t2 : What must follow if field l hash type t2 *)
  val project_opt : t -> label -> t
  val has_empty_record: t -> bool


  val first_label: t -> label

  val empty_cases: t -> bool * bool

  val merge: t -> t -> t
  val remove_field: t -> label -> t

  val get: t -> ((bool * t) label_map * bool * bool) list
end

module Arrow : sig
  val any : t

  val sample: t -> t

  val check_strenghten: t -> t -> t
    (* [check_strenghten t s]
       Assume that [t] is an intersection of arrow types
       representing the interface of an abstraction;
       check that this abstraction has type [s] (otherwise raise Not_found)
       and returns a refined type for this abstraction.
    *)

  val check_iface: (t * t) list -> t -> bool

  type t
  val is_empty: t -> bool
  val get: descr -> t
    (* Always succeed; no check <= Arrow.any *)

  val domain: t -> descr
  val apply: t -> descr -> descr
    (* Always succeed; no check on the domain *)

  val need_arg : t -> bool
    (* True if the type of the argument is needed to obtain
       the type of the result (must use [apply]; otherwise,
       [apply_noarg] is enough *)
  val apply_noarg : t -> descr
end


module Int : sig
  val has_int : t -> Intervals.V.t -> bool
  val get: t -> Intervals.t
  val any : t
end

module Atom : sig
  val has_atom : t -> Atoms.V.t -> bool
  val get: t -> Atoms.t
  val any : t
end

module Char : sig
  val has_char : t -> Chars.V.t -> bool
  val is_empty : t -> bool
  val get: t -> Chars.t
  val any : t
end

val normalize : t -> t

(** Subtyping  **)

val is_empty : t -> bool
val non_empty: t -> bool
val subtype  : t -> t -> bool

module Print :
sig
  val register_global : U.t -> t -> unit
  val print_const : Format.formatter -> const -> unit
  val print: Format.formatter -> t -> unit
end