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19.26 Module Set: sets over ordered types


This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance.
module type OrderedType =
  sig
    type t
    val compare: t -> t -> int
  end
The input signature of the functor Set.Make. t is the type of the set elements. compare is a total ordering function over the set elements. This is a two-argument function f such that f e1 e2 is zero if the elements e1 and e2 are equal, f e1 e2 is strictly negative if e1 is smaller than e2, and f e1 e2 is strictly positive if e1 is greater than e2. Example: a suitable ordering function is the generic structural comparison function compare.
module type S =
  sig
    type elt
The type of the set elements.
    type t
The type of sets.
    val empty: t
The empty set.
    val is_empty: t -> bool
Test whether a set is empty or not.
    val mem: elt -> t -> bool
mem x s tests whether x belongs to the set s.
    val add: elt -> t -> t
add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged.
    val singleton: elt -> t
singleton x returns the one-element set containing only x.
    val remove: elt -> t -> t
remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged.
    val union: t -> t -> t
    val inter: t -> t -> t
    val diff: t -> t -> t
Union, intersection and set difference.
    val compare: t -> t -> int
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
    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 iter: (elt -> unit) -> t -> unit