Module Multiset.Make

Parameters

X : Map.OrderedType

Signature

type elt = X.t

Elements of the multiset

type t

A multiset of elements of type 'a

val size : t -> int

Number of distinct elements.

val cardinal : t -> Z.t

Number of unique occurrences of elements (the multiplicity of each element is considered)

val empty : t

Empty multiset

val is_empty : t -> bool

Is the multiset empty?

val mem : t -> elt -> bool

Is the element part of the multiset?

val find : t -> elt -> Z.t

Return the multiplicity of the element within the multiset. Will return Z.zero if the element is not part of the multiset

val singleton : elt -> t

val doubleton : elt -> elt -> t

val add : t -> elt -> t

Add one occurrence of the element

val add_coeff : t -> elt -> Z.t -> t

Add several occurrences of the element

val union : t -> t -> t

Union of multisets (max of multiplicies)

val intersection : t -> t -> t

Intersection of multisets (min of multiplicies)

val sum : t -> t -> t

Sum of multiplicies

val difference : t -> t -> t

Difference of multisets. If x has a bigger multiplicity in the second argument it won't appear in the result

val product : Z.t -> t -> t

Multiply all multiplicities with the given coefficient

val filter : (elt -> Z.t -> bool) -> t -> t

Filter out elements that don't satisfy the predicate

val map : (elt -> elt) -> t -> t

Apply a function to all elements

val map_coeff : (elt -> Z.t -> Z.t) -> t -> t

Apply a function to all coefficients.

val filter_map : (elt -> Z.t -> (elt * Z.t) option) -> t -> t

More powerful mapping

val flat_map : (elt -> t) -> t -> t

replace each element by a multiset in its own

val iter : (elt -> unit) -> t -> unit

Iterate on distinct occurrences of elements

val fold : ('a -> elt -> 'a) -> 'a -> t -> 'a

fold on occurrences of elements

val iter_coeffs : (elt -> Z.t -> unit) -> t -> unit

Iterate on elements with their multiplicity

val fold_coeffs : ('a -> elt -> Z.t -> 'a) -> 'a -> t -> 'a

Fold on elements with their multiplicity

val for_all : (elt -> bool) -> t -> bool

val exists : (elt -> bool) -> t -> bool

val choose : t -> elt

Chose one element, or

raises Not_found

if the multiset is empty

val of_list : elt list -> t

Multiset from list

val of_coeffs : (elt * Z.t) list -> t

From list of elements with multiplicities. Multiplicities lower than 0 will not count.

val of_iarray : elt IArray.t -> t

From immutable array

val of_array : elt array -> t

val to_list : t -> (elt * Z.t) list

List of elements with their coefficients

val equal : t -> t -> bool

Check equality of two multisets

val cancel : t -> t -> t * t

Remove common elements from the multisets. For instance, on {1,1,2} and {1,2,2,3}, cancel will return ({1}, {2,3})