package coq

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Formal proof management system

Install 

dune-project
 Dependency

coq.inria.fr Edit opam file Versions (40)

Authors

  1. T
    The Coq development team, INRIA, CNRS, and contributors.

Maintainers

  1. C
    coqdev@inria.fr

Sources

coq-8.15.0.tar.gz
sha256=73466e61f229b23b4daffdd964be72bd7a110963b9d84bd4a86bb05c5dc19ef3

doc/coq-core.kernel/UGraph/index.html

Module UGraphSource

Sourcetype t

Graphs of universes.

Sourceval set_cumulative_sprop : bool -> t -> t

Makes the system incomplete.

Sourceval set_type_in_type : bool -> t -> t
Sourceval 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.

Sourcetype 'a check_function = t -> 'a -> 'a -> bool
Sourceval check_eq_level : Univ.Level.t check_function
Sourceval initial_universes : t

The initial graph of universes: Prop < Set

Sourceval initial_universes_with : t -> t

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

Sourceval 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.

Sourceval enforce_constraint : Univ.univ_constraint -> t -> t
Sourceval merge_constraints : Univ.Constraints.t -> t -> t
Sourceval check_constraint : t -> Univ.univ_constraint -> bool
Sourceval check_constraints : Univ.Constraints.t -> t -> bool

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

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

Sourceexception AlreadyDeclared
Sourcemodule Bound : sig ... end
Sourceval add_universe : Univ.Level.t -> lbound:Bound.t -> strict:bool -> t -> t
Sourceval add_universe_unconstrained : Univ.Level.t -> t -> t

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

Sourceexception UndeclaredLevel of Univ.Level.t

Check that the universe levels are declared. Otherwise

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

The empty graph of universes

Sourceval 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.

Sourceval 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.

Sourceval 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.

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

Known universes

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

Dumping
Sourcetype 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)

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

Debugging