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open Ident

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type const =
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  | Integer of Intervals.V.t
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  | Atom of Atoms.V.t
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  | Char of Chars.V.t
  | Pair of const * const
  | Xml of const * const
  | Record of const label_map
  | String of U.uindex * U.uindex * U.t * const

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type service_params =
  | TProd of service_params * service_params
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  | TOption of service_params
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  | TList of string * service_params
  | TSet of service_params
  | TSum of service_params * service_params
  | TString of string
  | TInt of string
  | TInt32 of string
  | TInt64 of string
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  | TFloat of string
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  | TBool of string
  | TFile of string
      (* | TUserType of string * (string -> 'a) * ('a -> string) *)
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  | TCoord of string
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  | TCoordv of service_params * string
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  | TESuffix of string
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  | TESuffixs of string
      (*  | TESuffixu of (string * (string -> 'a) * ('a -> string)) *)
  | TSuffix of (bool * service_params)
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  | TUnit
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  | TAny
  | TConst of string;;
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module Const: Custom.T with type t = const
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(*
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module CompUnit : sig
  include Custom.T

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  val get_current: unit -> t
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  val mk: U.t -> t
  val value: t -> U.t
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  val print_qual: Format.formatter -> t -> unit
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  val enter: t -> unit
  val leave: unit -> unit
  val close_serialize: unit -> t list

  val pervasives: t

  module Tbl : Inttbl.S with type key = t
end
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*)
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module Abstracts : sig
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  module T : Custom.T with type t = string
  type abs = T.t
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  type t
  val any: t
  val atom: abs -> t
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  val compare: t -> t -> int
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  module V : sig type t = abs * Obj.t end
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  val contains: abs -> t -> bool
end

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(** Algebra **)

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module BoolAtoms : BoolVar.S with
  type s = Atoms.t and
  type elem = Atoms.t Var.pairvar
module BoolIntervals : BoolVar.S with
  type s = Intervals.t and
  type elem = Intervals.t Var.pairvar
module BoolChars : BoolVar.S with
  type s = Chars.t and
  type elem = Chars.t Var.pairvar
module BoolAbstracts: BoolVar.S with
  type s = Abstracts.t and
  type elem = Abstracts.t Var.pairvar

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include Custom.T
module Node : Custom.T
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module Pair : Bool.S with type elem = (Node.t * Node.t)
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module BoolPair : BoolVar.S with
  type s = Pair.t and
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  type elem = Pair.t Var.pairvar
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module Rec : Bool.S with type elem = bool * Node.t Ident.label_map
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module BoolRec : BoolVar.S with
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  type s = Rec.t and
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  type elem = Rec.t Var.pairvar
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type descr = t
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val make: unit -> Node.t
val define: Node.t -> t -> unit
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val cons: t -> Node.t
val internalize: Node.t -> Node.t
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val id: Node.t -> int
val descr: Node.t -> t
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(** Boolean connectives **)

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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
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val no_var  : t -> bool
val is_var  : t -> bool
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val has_tlv : t -> bool
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val is_closed : Var.Set.t -> t -> bool
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val any_node : Node.t
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val empty_node : Node.t
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val non_constructed : t
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val non_constructed_or_absent : t
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(** Constructors **)

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type pair_kind = [ `Normal | `XML ]

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val var      : Var.var -> t
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val interval : Intervals.t -> t
val atom     : Atoms.t -> t
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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
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  (** bool = true -> open record; bool = false -> closed record *)
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val record_fields : bool * Node.t label_map -> t
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val char     : Chars.t -> t
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val constant : const -> t
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val abstract : Abstracts.t -> t
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(** Helpers *)

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val all_vars : t -> Var.Set.t
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val tuple : Node.t list -> t

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val rec_of_list: bool -> (bool * Ns.Label.t * t) list -> t
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val empty_closed_record: t
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val empty_open_record: t
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(** Positive systems and least solutions **)

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module Positive : sig
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  type v
  val forward: unit -> v
  val define: v -> v -> unit
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  val ty: t -> v
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  val cup: v list -> v
  val times: v -> v -> v
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  val xml: v -> v -> v
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  val substitute : t -> (Var.var * t) -> t
  val substituterec : t -> Var.var -> t
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  val solve: v -> Node.t
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  val substitutefree : Var.Set.t -> t -> t
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  val clean_type : Var.Set.t -> t -> t
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end

(** Normalization **)

module Product : sig
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  val any : t
  val any_xml : t
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  val any_of: pair_kind -> t
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  val other : ?kind:pair_kind -> t -> t
  val is_product : ?kind:pair_kind -> t -> bool
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  (* List of non-empty rectangles *)
  type t = (descr * descr) list
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  val is_empty: t -> bool
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  val get: ?kind:pair_kind -> descr -> t
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  val pi1: t -> descr
  val pi2: t -> descr
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  val pi2_restricted: descr -> t -> descr
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  (* 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
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  val normal: ?kind:pair_kind -> descr -> normal
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  val constraint_on_2: normal -> descr -> descr
    (* constraint_on_2 n t1:  maximal t2 such that (t1,t2) <= n *)
    (* Assumption: t1 <= pi1(n) *)

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  val need_second: t -> bool
    (* Is there more than a single rectangle ? *)
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  val clean_normal: t -> t
    (* Merge rectangles with same second component *)
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end

module Record : sig
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  val any : t
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  val absent : t
  val absent_node : Node.t
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  val or_absent: t -> t
  val any_or_absent: t
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  val any_or_absent_node : Node.t
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  val has_absent: t -> bool
  val has_record: t -> bool
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  val split : t -> label -> Product.t
  val split_normal : t -> label -> Product.normal
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  val pi : label -> t -> t
    (* May contain absent *)

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

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  val condition : t -> label -> t -> t
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    (* condition t1 l t2 : What must follow if field l hash type t2 *)
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  val project_opt : t -> label -> t
  val has_empty_record: t -> bool
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  val first_label: t -> label
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  val all_labels: t -> LabelSet.t
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  val empty_cases: t -> bool * bool
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  val merge: t -> t -> t
  val remove_field: t -> label -> t
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  val get: t -> ((bool * t) label_map * bool * bool) list
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  type t
  val focus: descr -> label -> t
  val get_this: t -> descr
  val need_others: t -> bool
  val constraint_on_others: t -> descr -> descr
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end

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module Arrow : sig
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  val any : t
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  val sample: t -> t
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  (** [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.
  *)
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  val check_strenghten: t -> t -> t
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  val check_iface: (t * t) list -> t -> bool
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  type t = descr * (descr * descr) list list
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  val is_empty: t -> bool
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  val get: descr -> t
    (* Always succeed; no check <= Arrow.any *)
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  val domain: t -> descr
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  (* Always succeed; no check on the domain *)
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  val apply: t -> descr -> descr
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  (** True if the type of the argument is needed to obtain
     the type of the result (must use [apply]; otherwise,
     [apply_noarg] is enough *)
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  val need_arg : t -> bool
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  val apply_noarg : t -> descr
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end
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module Int : sig
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  val has_int : t -> Intervals.V.t -> bool
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  val get: t -> BoolIntervals.t
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  val any : t
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end

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

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

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module Abstract : sig
  val has_abstract : t -> Abstracts.T.t -> bool
  val get: t -> BoolAbstracts.t
  val any : t
end
(*
val get_abstract: t -> Abstracts.t
*)
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val normalize : t -> t
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(** Subtyping  **)
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val is_empty : t -> bool
val non_empty: t -> bool
val subtype  : t -> t -> bool
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val disjoint : t -> t -> bool
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val equiv : t -> t -> bool
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(** Tools for compilation of PM **)

val cond_partition: t -> (t * t) list -> t list
  (* The second argument is a list of pair of types (ti,si)
     interpreted as the question "member of ti under the assumption si".
     The result is a partition of the first argument which is precise enough
     to answer all the questions. *)

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module Print :
sig
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  val register_global : string -> Ns.QName.t -> t -> unit
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  val pp_const : Format.formatter -> const -> unit
  val pp_type: Format.formatter -> t -> unit
  val pp_node: Format.formatter -> Node.t -> unit
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  (* Don't try to find a global name at toplevel *)
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  val pp_noname: Format.formatter -> t -> unit
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  val string_of_type: t -> string
  val string_of_node: Node.t -> string
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  val printf : t -> unit
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end
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module Service :
sig
  val to_service_params: t -> service_params
  val to_string: service_params -> string
end

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module Witness : sig
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  type witness
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  val pp: Format.formatter -> witness -> unit
  val printf : witness -> unit
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end
val witness: t -> Witness.witness
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module Cache : sig
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  type 'a cache
  val emp: 'a cache
  val find: (t -> 'a) -> t -> 'a cache -> 'a cache * 'a

  val memo: (t -> 'a) -> (t -> 'a)
end
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module Tallying : sig
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  type constr =
  |Pos of (Var.var * t) (** alpha <= t | alpha \in P *)
  |Neg of (t * Var.var) (** t <= alpha | alpha \in N *)
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  exception UnSatConstr of string
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  exception Step1Fail
  exception Step2Fail
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  module CS : sig
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    module M : sig
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      type key = Var.var
      type t
      val compare  : t -> t -> int
      val empty : t
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      val add : Var.Set.t -> key -> descr*descr -> t -> t
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      val singleton : key -> descr*descr -> t
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      val pp : Format.formatter -> t -> unit
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      val inter : Var.Set.t -> t -> t -> t
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    end
    module E : sig
      include Map.S with type key = Var.var
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      val pp : Format.formatter -> descr t -> unit
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    end
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    module ES : sig
      include Set.S with type elt = descr E.t
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      val pp : Format.formatter -> t -> unit
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    end
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    module S : sig
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      type t = M.t list
      val empty : t
      val add : M.t -> t -> t
      val singleton : M.t -> t
      val union : t -> t -> t
      val elements : t -> M.t list
      val fold : (M.t -> 'b -> 'b) -> M.t list -> 'b -> 'b
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      val pp : Format.formatter -> t -> unit
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    end

    type s = S.t
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    type m =  M.t
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    type es = ES.t
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    type sigma = t E.t
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    type sl = sigma list
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    val pp_s  : Format.formatter -> s -> unit
    val pp_m  : Format.formatter -> m -> unit
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    val pp_e  : Format.formatter -> sigma -> unit
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    val pp_sl : Format.formatter -> sl -> unit
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    (* val merge : m -> m -> m *)
    val singleton : Var.Set.t -> constr -> s
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    val sat : s
    val unsat : s
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    val union : s -> s -> s
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    val prod : Var.Set.t -> s -> s -> s
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  end

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  val norm : Var.Set.t -> t -> CS.s
  val merge : Var.Set.t -> CS.m -> CS.s
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  val solve : CS.s -> CS.es
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  val unify : CS.sigma -> CS.sigma
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  (* [s1 ... sn] . si is a solution for tallying problem
     if si # delta and for all (s,t) in C si @ s < si @ t *)
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  val tallying : Var.Set.t -> (t * t) list -> CS.sl
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  val ($$) : t -> CS.sigma -> t

  (** Symbolic Substitution Set *)
  type symsubst =
    |I (** Identity *)
    |S of CS.sigma (** Substitution *)
    |A of (symsubst * symsubst) (** Composition si (sj t) *)

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  (** Cartesian Product of two symbolic substitution sets *)
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  val ( ++ ) : symsubst list -> symsubst list -> symsubst list

  (** Evaluation of a substitution *)
  val (@@) : t -> symsubst -> t

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  val domain : CS.sl -> Var.Set.t
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  val codomain : CS.sl -> Var.Set.t
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  val is_identity : CS.sl -> bool
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  val identity : CS.sl
  val filter : (Var.t -> bool) -> CS.sl -> CS.sl
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end

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(** Square Subtype relation. [squaresubtype delta s t] .
    True if there exists a substitution such that s < t only
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    considering variables that are not in delta *)
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val squaresubtype : Var.Set.t -> t -> t -> Tallying.CS.sl
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val is_squaresubtype : Var.Set.t -> t -> t -> bool
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(** apply_raw s t returns the 4-tuple (subst,ss, tt, res) where
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   subst is the set of substitution that make the application succeed,
   ss and tt are the expansions of s and t corresponding to that substitution
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   and res is the type of the result of the application *)
val apply_full : Var.Set.t -> t -> t -> t

val apply_raw : Var.Set.t -> t -> t -> Tallying.CS.sl * t * t * t

val squareapply : Var.Set.t -> t -> t -> (Tallying.CS.sl * t)