Module Univ

module UGlobal : sig ... end

Qualified global universe level

module Level : sig ... end

Universes.

module Universe : sig ... end

univ_level_mem l u Is l is mentioned in u ?

val univ_level_mem : Level.t -> Universe.t -> bool

univ_level_rem u v min removes u from v, resulting in min if v was exactly u.

val univ_level_rem : Level.t -> Universe.t -> Universe.t -> Universe.t
Constraints.
type constraint_type = AcyclicGraph.constraint_type =
| Lt
| Le
| Eq
type univ_constraint = Level.t * constraint_type * Level.t
module Constraints : sig ... end
type 'a constrained = 'a * Constraints.t

A value with universe Constraints.t.

val constraints_of : 'a constrained -> Constraints.t

Constrained

type 'a constraint_function = 'a -> 'a -> Constraints.t -> Constraints.t

Enforcing Constraints.t.

val enforce_eq_level : Level.t constraint_function
val enforce_leq_level : Level.t constraint_function
Support for universe polymorphism
module Variance : sig ... end
Universe instances
module Instance : sig ... end
val enforce_eq_instances : Instance.t constraint_function
val enforce_eq_variance_instances : Variance.t array -> Instance.t constraint_function
val enforce_leq_variance_instances : Variance.t array -> Instance.t constraint_function
type 'a puniverses = 'a * Instance.t
val out_punivs : 'a puniverses -> 'a
val in_punivs : 'a -> 'a puniverses
val eq_puniverses : ( 'a -> 'a -> bool ) -> 'a puniverses -> 'a puniverses -> bool

A vector of universe levels with universe Constraints.t, representing local universe variables and associated Constraints.t; the names are user-facing names for printing

module UContext : sig ... end
module AbstractContext : sig ... end
type 'a univ_abstracted = {
univ_abstracted_value : 'a;
univ_abstracted_binder : AbstractContext.t;
}

A value with bound universe levels.

val map_univ_abstracted : ( 'a -> 'b ) -> 'a univ_abstracted -> 'b univ_abstracted

Universe contexts (as sets)

A set of universes with universe Constraints.t. We linearize the set to a list after typechecking. Beware, representation could change.

module ContextSet : sig ... end
type 'a in_universe_context = 'a * UContext.t

A value in a universe context (resp. context set).

type 'a in_universe_context_set = 'a * ContextSet.t
val extend_in_context_set : 'a in_universe_context_set -> ContextSet.t -> 'a in_universe_context_set
Substitution
type universe_level_subst = Level.t Level.Map.t
val empty_level_subst : universe_level_subst
val is_empty_level_subst : universe_level_subst -> bool
val subst_univs_level_level : universe_level_subst -> Level.t -> Level.t

Substitution of universes.

val subst_univs_level_universe : universe_level_subst -> Universe.t -> Universe.t
val subst_univs_level_constraints : universe_level_subst -> Constraints.t -> Constraints.t
val subst_univs_level_abstract_universe_context : universe_level_subst -> AbstractContext.t -> AbstractContext.t
val subst_univs_level_instance : universe_level_subst -> Instance.t -> Instance.t

Level to universe substitutions.

val subst_instance_instance : Instance.t -> Instance.t -> Instance.t

Substitution of instances

val subst_instance_universe : Instance.t -> Universe.t -> Universe.t
val make_instance_subst : Instance.t -> universe_level_subst

Creates u(0) ↦ 0; ...; u(n-1) ↦ n - 1 out of u(0); ...; u(n - 1)

val abstract_universes : UContext.t -> Instance.t * AbstractContext.t

TODO: move universe abstraction out of the kernel

val make_abstract_instance : AbstractContext.t -> Instance.t
val compact_univ : Universe.t -> Universe.t * int list

compact_univ u remaps local variables in u such that their indices become consecutive. It returns the new universe and the mapping. Example: compact_univ (Var 0, i); (Prop, 0); (Var 2; j)) = (Var 0,i); (Prop, 0); (Var 1; j), 0; 2

Pretty-printing of universes.
val pr_constraint_type : constraint_type -> Pp.t
val pr_constraints : ( Level.t -> Pp.t ) -> Constraints.t -> Pp.t
val pr_universe_context : ( Level.t -> Pp.t ) -> ?variance:Variance.t array -> UContext.t -> Pp.t
val pr_abstract_universe_context : ( Level.t -> Pp.t ) -> ?variance:Variance.t array -> AbstractContext.t -> Pp.t
val pr_universe_context_set : ( Level.t -> Pp.t ) -> ContextSet.t -> Pp.t
val pr_universe_level_subst : universe_level_subst -> Pp.t
Hash-consing
val hcons_univ : Universe.t -> Universe.t
val hcons_constraints : Constraints.t -> Constraints.t
val hcons_universe_set : Level.Set.t -> Level.Set.t
val hcons_universe_context : UContext.t -> UContext.t
val hcons_abstract_universe_context : AbstractContext.t -> AbstractContext.t
val hcons_universe_context_set : ContextSet.t -> ContextSet.t