Module `Id.Pred`

Predicates over identifiers.

type elt = t: The type of the elements in the set.

type t: The type of sets.

val empty : t: The empty set.

val full : t: The set of all elements (of type elm).

val is_empty : t -> bool: Test whether a set is empty or not.

val is_full : t -> bool: Test whether a set contains the whole type or not.

val mem : elt -> t -> bool: mem x s tests whether x belongs to the set s.

val singleton : elt -> t: singleton x returns the one-element set containing only x.

val add : elt -> t -> t: add x s returns a set containing all elements of s, plus x. If x was already in s, then s is returned unchanged.

val remove : elt -> t -> t: remove x s returns a set containing all elements of s, except x. If x was not in s, then s is returned unchanged.

val union : t -> t -> t: Set union.

val inter : t -> t -> t: Set intersection.

val diff : t -> t -> t: Set difference.

val complement : t -> t: Set complement.

val equal : t -> t -> bool: equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

val subset : t -> t -> bool: subset s1 s2 tests whether the set s1 is a subset of the set s2.

val elements : t -> bool * elt list: Gives a finite representation of the predicate: if the boolean is false, then the predicate is given in extension. if it is true, then the complement is given

val is_finite : t -> bool: true if the predicate can be given as a finite set (if elt is a finite type, we can have is_finite x = false yet x is finite, but we don't know how to list its elements)