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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 *)
(************************************************************************)
(** Universes. *)
type universe_level
type universe
module UniverseLSet : Set.S with type elt = universe_level
(** 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_universe_level : Names.dir_path * int -> universe_level
val make_universe : universe_level -> universe
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
val universe_level : universe -> universe_level option
val compare_levels : universe_level -> universe_level -> int
(** The type of a universe *)
val super : universe -> universe
(** The max of 2 universes *)
val sup : universe -> universe -> universe
(** {6 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
val is_initial_universes : universes -> bool
(** {6 Constraints. } *)
type constraints
val empty_constraint : constraints
val union_constraints : constraints -> constraints -> constraints
val is_empty_constraint : constraints -> bool
type constraint_function = universe -> universe -> constraints -> constraints
val enforce_geq : constraint_function
val enforce_eq : constraint_function
(** {6 ... } *)
(** 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 constraint_type = Lt | Le | Eq
exception UniverseInconsistency of constraint_type * universe * universe
val merge_constraints : constraints -> universes -> universes
val normalize_universes : universes -> universes
val sort_universes : universes -> universes
(** {6 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
(** {6 Pretty-printing of universes. } *)
val pr_uni_level : universe_level -> Pp.std_ppcmds
val pr_uni : universe -> Pp.std_ppcmds
val pr_universes : universes -> Pp.std_ppcmds
val pr_constraints : constraints -> Pp.std_ppcmds
(** {6 Dumping to a file } *)
val dump_universes :
(constraint_type -> string -> string -> unit) ->
universes -> unit
(** {6 Hash-consing } *)
val hcons_univlevel : universe_level -> universe_level
val hcons_univ : universe -> universe
val hcons_constraints : constraints -> constraints
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