Module UState

This file defines universe unification states which are part of evarmaps. Most of the API below is reexported in Evd. Consider using higher-level primitives when needed.

type universes_entry =
| Monomorphic_entry of Univ.ContextSet.t
| Polymorphic_entry of Univ.UContext.t
exception UniversesDiffer
type t

Type of universe unification states. They allow the incremental building of universe constraints during an interactive proof.

Constructors
val empty : t
val make : lbound:UGraph.Bound.t -> UGraph.t -> t
val make_with_initial_binders : lbound:UGraph.Bound.t -> UGraph.t -> Names.lident list -> t
val from_env : ?⁠binders:Names.lident list -> Environ.env -> t

Main entry point at the beginning of a declaration declaring the binding names as rigid universes.

val of_binders : UnivNames.universe_binders -> t

Main entry point when only names matter, e.g. for printing.

val of_context_set : Univ.ContextSet.t -> t

Main entry point when starting from the instance of a global reference, e.g. when building a scheme.

val is_empty : t -> bool
val union : t -> t -> t
Projections and other destructors
val context_set : t -> Univ.ContextSet.t

The local context of the state, i.e. a set of bound variables together with their associated constraints.

type universe_opt_subst = UnivSubst.universe_opt_subst
val subst : t -> UnivSubst.universe_opt_subst

The local universes that are unification variables

val nf_universes : t -> Constr.t -> Constr.t

Apply the local substitution subst

val ugraph : t -> UGraph.t

The current graph extended with the local constraints

val initial_graph : t -> UGraph.t

The initial graph with just the declarations of new universes.

val algebraics : t -> Univ.Level.Set.t

The subset of unification variables that can be instantiated with algebraic universes as they appear in inferred types only.

val constraints : t -> Univ.Constraints.t

Shorthand for context_set composed with ContextSet.constraints.

val context : t -> Univ.UContext.t

Shorthand for context_set with Context_set.to_context.

type named_universes_entry = universes_entry * UnivNames.universe_binders
val univ_entry : poly:bool -> t -> named_universes_entry

Pick from context or context_set based on poly.

val universe_binders : t -> UnivNames.universe_binders

Return local names of universes.

Constraints handling
val add_constraints : t -> Univ.Constraints.t -> t
raises UniversesDiffer

when universes differ

val add_universe_constraints : t -> UnivProblem.Set.t -> t
raises UniversesDiffer

when universes differ

Names
val universe_of_name : t -> Names.Id.t -> Univ.Level.t

Retrieve the universe associated to the name.

Unification
val restrict_universe_context : lbound:UGraph.Bound.t -> Univ.ContextSet.t -> Univ.Level.Set.t -> Univ.ContextSet.t

restrict_universe_context lbound (univs,csts) keep restricts univs to the universes in keep. The constraints csts are adjusted so that transitive constraints between remaining universes (those in keep and those not in univs) are preserved.

val restrict : t -> Univ.Level.Set.t -> t

restrict uctx ctx restricts the local universes of uctx to ctx extended by local named universes and side effect universes (from demote_seff_univs). Transitive constraints between retained universes are preserved.

type rigid =
| UnivRigid
| UnivFlexible of bool

Is substitution by an algebraic ok?

val univ_rigid : rigid
val univ_flexible : rigid
val univ_flexible_alg : rigid
val merge : ?⁠loc:Loc.t -> sideff:bool -> rigid -> t -> Univ.ContextSet.t -> t
val merge_subst : t -> UnivSubst.universe_opt_subst -> t
val emit_side_effects : Safe_typing.private_constants -> t -> t
val demote_global_univs : Environ.env -> t -> t

Removes from the uctx_local part of the UState the universes and constraints that are present in the universe graph in the input env (supposedly the global ones)

val demote_seff_univs : Univ.Level.Set.t -> t -> t

Mark the universes as not local any more, because they have been globally declared by some side effect. You should be using emit_side_effects instead.

val new_univ_variable : ?⁠loc:Loc.t -> rigid -> Names.Id.t option -> t -> t * Univ.Level.t

Declare a new local universe; use rigid if a global or bound universe; use flexible for a universe existential variable; use univ_flexible_alg for a universe existential variable allowed to be instantiated with an algebraic universe

val add_global_univ : t -> Univ.Level.t -> t
val make_flexible_variable : t -> algebraic:bool -> Univ.Level.t -> t

make_flexible_variable g algebraic l

Turn the variable l flexible, and algebraic if algebraic is true and l can be. That is if there are no strict upper constraints on l and and it does not appear in the instance of any non-algebraic universe. Otherwise the variable is just made flexible.

If l is already algebraic it will remain so even with algebraic:false.

val make_nonalgebraic_variable : t -> Univ.Level.t -> t

Make the level non algebraic. Undefined behaviour on already-defined algebraics.

val make_flexible_nonalgebraic : t -> t

Turn all undefined flexible algebraic variables into simply flexible ones. Can be used in case the variables might appear in universe instances (typically for polymorphic program obligations).

val is_sort_variable : t -> Sorts.t -> Univ.Level.t option
val normalize_variables : t -> t
val constrain_variables : Univ.Level.Set.t -> t -> t
val abstract_undefined_variables : t -> t
val fix_undefined_variables : t -> t
val minimize : t -> t

Universe minimization

type ('a, 'b) gen_universe_decl = {
univdecl_instance : 'a;
univdecl_extensible_instance : bool;
univdecl_constraints : 'b;
univdecl_extensible_constraints : bool;
}
type universe_decl = (Names.lident list, Univ.Constraints.t) gen_universe_decl
val default_univ_decl : universe_decl
val check_univ_decl : poly:bool -> t -> universe_decl -> named_universes_entry

check_univ_decl ctx decl

If non extensible in decl, check that the local universes (resp. universe constraints) in ctx are implied by decl.

Return a universes_entry containing the local universes of ctx and their constraints.

When polymorphic, the universes corresponding to decl.univdecl_instance come first in the order defined by that list.

val check_mono_univ_decl : t -> universe_decl -> Univ.ContextSet.t
TODO: Document me
val update_sigma_univs : t -> UGraph.t -> t
Pretty-printing
val pr_uctx_level : t -> Univ.Level.t -> Pp.t
val qualid_of_level : t -> Univ.Level.t -> Libnames.qualid option
val id_of_level : t -> Univ.Level.t -> Names.Id.t option

Only looks in the local names, not in the nametab.

val pr_weak : (Univ.Level.t -> Pp.t) -> t -> Pp.t
val pr_universe_opt_subst : universe_opt_subst -> Pp.t