logtk

Core types and algorithms for logic
IN THIS PACKAGE
Module type Logtk . Multiset_intf . S
type elt

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

module Seq : sig ... end
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})

Comparisons

In the following, the comparison function must be equality-compatible with E.compare. In other words, if E.compare x y = 0 then f x y = Comparison.Eq must hold.

val compare : t -> t -> int

Compare two multisets with the multiset extension of E.compare

val compare_partial : ( elt -> elt -> Comparison.t ) -> t -> t -> Comparison.t

Compare two multisets with the multiset extension of the given ordering. This ordering is total iff the element ordering is.

val is_max : ( elt -> elt -> Comparison.t ) -> elt -> t -> bool

Is the given element maximal (ie not dominated by any other element) within the multiset?

val max : ( elt -> elt -> Comparison.t ) -> t -> t

Maximal elements of the multiset, w.r.t the given ordering.

val max_seq : ( elt -> elt -> Comparison.t ) -> t -> (elt * Z.t) Iter.t

Fold on maximal elements

val max_l : ( elt -> elt -> Comparison.t ) -> elt list -> elt list

Maximal elements of a list

val compare_partial_l : ( elt -> elt -> Comparison.t ) -> elt list -> elt list -> Comparison.t

Compare two multisets represented as list of elements