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(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
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(*i $Id$ i*)

(* Universes. *)

type universe

(* The universes hierarchy: Type 0- = Prop <= Type 0 = Set <= Type 1 <= ... *)
(* Typing of universes: Type 0-, Type 0 : Type 1; Type i : Type (i+1) if i>0 *)

val type0m_univ : universe  (* image of Prop in the universes hierarchy *)
val type0_univ : universe  (* image of Set in the universes hierarchy *)
val type1_univ : universe  (* the universe of the type of Prop/Set *)

val make_univ : Names.dir_path * int -> universe

val is_type0_univ : universe -> bool
val is_type0m_univ : universe -> bool
val is_univ_variable : universe -> bool

(* The type of a universe *)
val super : universe -> universe

(* The max of 2 universes *)
val sup   : universe -> universe -> universe

(*s Graphs of universes. *)

type universes

type check_function = universes -> universe -> universe -> bool
val check_geq : check_function
val check_eq : check_function

(* The empty graph of universes *)
val initial_universes : universes

(*s Constraints. *)

module Constraint : Set.S

type constraints = Constraint.t

type constraint_function = universe -> universe -> constraints -> constraints

val enforce_geq : constraint_function
val enforce_eq : constraint_function

(*s Merge of constraints in a universes graph.
  The function [merge_constraints] merges a set of constraints in a given
  universes graph. It raises the exception [UniverseInconsistency] if the
  constraints are not satisfiable. *)

type order_request = Lt | Le | Eq

exception UniverseInconsistency of order_request * universe * universe

val merge_constraints : constraints -> universes -> universes

(*s Support for sort-polymorphic inductive types *)

val fresh_local_univ : unit -> universe

val solve_constraints_system : universe option array -> universe array ->
  universe array

val subst_large_constraint : universe -> universe -> universe -> universe

val subst_large_constraints :
  (universe * universe) list -> universe -> universe

val no_upper_constraints : universe -> constraints -> bool

(*s Pretty-printing of universes. *)

val pr_uni : universe -> Pp.std_ppcmds
val pr_universes : universes -> Pp.std_ppcmds
val pr_constraints : constraints -> Pp.std_ppcmds

(*s Dumping to a file *)

val dump_universes : out_channel -> universes -> unit

val hcons1_univ : universe -> universe