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(***********************************************************************
v * The Coq Proof Assistant / The Coq Development Team
<O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud
\VV/ *************************************************************
// * This file is distributed under the terms of the
* GNU Lesser General Public License Version 2.1
***********************************************************************)
(** 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
(** {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
(** {6 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
(** {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 order_request = Lt | Le | Eq
exception UniverseInconsistency of order_request * universe * universe
val merge_constraints : constraints -> 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 : 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 : out_channel -> universes -> unit
val hcons1_univ : universe -> universe
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