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(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open Univ
(** {6 Graphs of universes. } *)
type t
val make_sprop_cumulative : t -> t
(** Don't use this in the kernel, it makes the system incomplete. *)
type 'a check_function = t -> 'a -> 'a -> bool
val check_leq : Universe.t check_function
val check_eq : Universe.t check_function
val check_eq_level : Level.t check_function
(** The initial graph of universes: Prop < Set *)
val initial_universes : t
(** Check equality of instances w.r.t. a universe graph *)
val check_eq_instances : Instance.t check_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. *)
val enforce_constraint : univ_constraint -> t -> t
val merge_constraints : Constraint.t -> t -> t
val check_constraint : t -> univ_constraint -> bool
val check_constraints : Constraint.t -> t -> bool
(** Picks an arbitrary set of constraints sufficient to ensure [u <= v]. *)
val enforce_leq_alg : Universe.t -> Universe.t -> t -> Constraint.t * t
(** Adds a universe to the graph, ensuring it is >= or > Set.
@raise AlreadyDeclared if the level is already declared in the graph. *)
exception AlreadyDeclared
val add_universe : Level.t -> lbound:Level.t -> strict:bool -> t -> t
(** Add a universe without (Prop,Set) <= u *)
val add_universe_unconstrained : Level.t -> t -> t
(** Check that the universe levels are declared. Otherwise
@raise UndeclaredLevel l for the first undeclared level found. *)
exception UndeclaredLevel of Univ.Level.t
val check_declared_universes : t -> Univ.LSet.t -> unit
(** {6 Pretty-printing of universes. } *)
val pr_universes : (Level.t -> Pp.t) -> t -> Pp.t
(** The empty graph of universes *)
val empty_universes : t
val sort_universes : t -> t
(** [constraints_of_universes g] returns [csts] and [partition] where
[csts] are the non-Eq constraints and [partition] is the partition
of the universes into equivalence classes. *)
val constraints_of_universes : t -> Constraint.t * LSet.t list
val choose : (Level.t -> bool) -> t -> Level.t -> Level.t option
(** [choose p g u] picks a universe verifying [p] and equal
to [u] in [g]. *)
(** [constraints_for ~kept g] returns the constraints about the
universes [kept] in [g] up to transitivity.
eg if [g] is [a <= b <= c] then [constraints_for ~kept:{a, c} g] is [a <= c]. *)
val constraints_for : kept:LSet.t -> t -> Constraint.t
val domain : t -> LSet.t
(** Known universes *)
val check_subtype : lbound:Level.t -> AUContext.t check_function
(** [check_subtype univ ctx1 ctx2] checks whether [ctx2] is an instance of
[ctx1]. *)
(** {6 Dumping to a file } *)
val dump_universes :
(constraint_type -> Level.t -> Level.t -> unit) -> t -> unit
(** {6 Debugging} *)
val check_universes_invariants : t -> unit
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