The type of a witness registry.

The type of elements stored in the registry.

The type of a witness in the registry.

A function to produce an empty witness registry. Registries use mutable data structures to cache results, so each empty registry must be created separately.

Obtains a witness for the provided value. If the value already has a witness, it is returned; otherwise, a new witness is created and returned. If the same element is added to two different registries, it will not be given the same witness for each.

Obtains a value for the provided witness. Raises Not_found if no such witness is stored in the provided registry.

Determines if two witnesses are equal. Two witnesses are equal only if they witness the same value.

Compares two witnesses. This comparison operation is arbitrary; although the element type must be comparable, there is no guarantee of a connection between the comparison of elements and the comparison of their witnesses.