(* This file is free software, part of Libzipperposition. See file "license" for more details. *)
module type S = sig
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
val of_seq : t -> elt Sequence.t -> t
val to_seq : t -> elt Sequence.t
val of_coeffs : t -> (elt * Z.t) Sequence.t -> t
val to_coeffs : t -> (elt * Z.t) Sequence.t
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 @raise 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 eq : 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 |
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) Sequence.t2
(** 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 *) |
val pp : elt CCFormat.printer -> t CCFormat.printer
end