package coq

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package coq
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type t

Graphs of universes.

val set_cumulative_sprop : bool -> t -> t

Makes the system incomplete.

val set_type_in_type : bool -> t -> t
val type_in_type : t -> bool

When type_in_type, functions adding constraints do not fail and may instead ignore inconsistent constraints.

Checking functions such as check_leq always return true.

type 'a check_function = t -> 'a -> 'a -> bool
val check_eq_level : Univ.Level.t check_function
val initial_universes : t

The initial graph of universes: Prop < Set

val initial_universes_with : t -> t

Initial universes, but keeping options such as type in type from the argument.

val check_eq_instances : Univ.Instance.t check_function

Check equality of instances w.r.t. a universe graph

...

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.univ_constraint -> t -> t
val merge_constraints : Univ.Constraints.t -> t -> t
val check_constraint : t -> Univ.univ_constraint -> bool
val check_constraints : Univ.Constraints.t -> t -> bool
val enforce_leq_alg : Univ.Universe.t -> Univ.Universe.t -> t -> Univ.Constraints.t * t

Picks an arbitrary set of constraints sufficient to ensure u <= v.

Adds a universe to the graph, ensuring it is >= or > Set.

exception AlreadyDeclared
module Bound : sig ... end
val add_universe : Univ.Level.t -> lbound:Bound.t -> strict:bool -> t -> t
val add_universe_unconstrained : Univ.Level.t -> t -> t

Add a universe without (Prop,Set) <= u

exception UndeclaredLevel of Univ.Level.t

Check that the universe levels are declared. Otherwise

val check_declared_universes : t -> Univ.Level.Set.t -> unit
val empty_universes : t

The empty graph of universes

val constraints_of_universes : t -> Univ.Constraints.t * Univ.Level.Set.t list

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 choose : (Univ.Level.t -> bool) -> t -> Univ.Level.t -> Univ.Level.t option

choose p g u picks a universe verifying p and equal to u in g.

val constraints_for : kept:Univ.Level.Set.t -> t -> Univ.Constraints.t

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 domain : t -> Univ.Level.Set.t

Known universes

val check_subtype : lbound:Bound.t -> Univ.AbstractContext.t check_function

check_subtype univ ctx1 ctx2 checks whether ctx2 is an instance of ctx1.

Dumping
type node =
  1. | Alias of Univ.Level.t
  2. | Node of bool Univ.Level.Map.t
    (*

    Nodes v s.t. u < v (true) or u <= v (false)

    *)
val repr : t -> node Univ.Level.Map.t
Pretty-printing of universes.
val pr_universes : (Univ.Level.t -> Pp.t) -> node Univ.Level.Map.t -> Pp.t
val check_universes_invariants : t -> unit

Debugging