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121 lines
3.4 KiB
121 lines
3.4 KiB
(*
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* Copyright (c) Facebook, Inc. and its affiliates.
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*
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* This source code is licensed under the MIT license found in the
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* LICENSE file in the root directory of this source tree.
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*)
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(** Multiset - Set with (signed) rational multiplicity for each element *)
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open! NS0
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module type MULTIPLICITY = sig
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type t [@@deriving compare, equal, hash, sexp]
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val zero : t
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val add : t -> t -> t
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val sub : t -> t -> t
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val neg : t -> t
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end
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module type S = sig
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type mul
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type elt
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type t
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val compare : t -> t -> int
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val equal : t -> t -> bool
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val hash_fold_t : elt Hash.folder -> t Hash.folder
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val sexp_of_t : t -> Sexp.t
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val t_of_sexp : (Sexp.t -> elt) -> Sexp.t -> t
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val pp : (unit, unit) fmt -> (elt * mul) pp -> t pp
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(* constructors *)
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val empty : t
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(** The empty multiset over the provided order. *)
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val of_ : elt -> mul -> t
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val add : elt -> mul -> t -> t
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(** Add to multiplicity of single element. [O(log n)] *)
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val remove : elt -> t -> t
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(** Set the multiplicity of an element to zero. [O(log n)] *)
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val union : t -> t -> t
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(** Add multiplicities pointwise. [O(n + m)] *)
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val diff : t -> t -> t
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(** Subtract multiplicities pointwise. [O(n + m)] *)
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val map : t -> f:(elt -> mul -> elt * mul) -> t
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(** Map over the elements in ascending order. Preserves physical equality
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if [f] does. *)
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val map_counts : t -> f:(mul -> mul) -> t
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(** Map over the multiplicities of the elements in ascending order. *)
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val mapi_counts : t -> f:(elt -> mul -> mul) -> t
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(** Map over the multiplicities of the elements in ascending order. *)
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val flat_map : t -> f:(elt -> mul -> t) -> t
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(** Flat map over the elements in ascending order. Preserves physical
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equality if [f e m] is a singleton [(e', m')] with [e == e'] and
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[Mul.equal m m'] for all elements. *)
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val partition : t -> f:(elt -> mul -> bool) -> t * t
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(* queries *)
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val is_empty : t -> bool
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val is_singleton : t -> bool
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val length : t -> int
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(** Number of elements with non-zero multiplicity. [O(1)]. *)
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val count : elt -> t -> mul
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(** Multiplicity of an element. [O(log n)]. *)
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val only_elt : t -> (elt * mul) option
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(** The only element of a singleton multiset. [O(1)]. *)
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val choose_exn : t -> elt * mul
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(** Find an unspecified element. [O(1)]. *)
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val choose : t -> (elt * mul) option
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(** Find an unspecified element. [O(1)]. *)
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val pop : t -> (elt * mul * t) option
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(** Find and remove an unspecified element. [O(1)]. *)
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val min_elt : t -> (elt * mul) option
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(** Minimum element. [O(log n)]. *)
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val pop_min_elt : t -> (elt * mul * t) option
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(** Find and remove minimum element. [O(log n)]. *)
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val classify : t -> [`Zero | `One of elt * mul | `Many]
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(** Classify a set as either empty, singleton, or otherwise. *)
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val find_and_remove : elt -> t -> (mul * t) option
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(** Find and remove an element. *)
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val to_iter : t -> (elt * mul) iter
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(** Enumerate elements in ascending order. *)
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(* traversals *)
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val iter : t -> f:(elt -> mul -> unit) -> unit
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(** Iterate over the elements in ascending order. *)
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val exists : t -> f:(elt -> mul -> bool) -> bool
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(** Search for an element satisfying a predicate. *)
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val for_all : t -> f:(elt -> mul -> bool) -> bool
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(** Test whether all elements satisfy a predicate. *)
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val fold : t -> 's -> f:(elt -> mul -> 's -> 's) -> 's
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(** Fold over the elements in ascending order. *)
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end
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