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353 lines
14 KiB
353 lines
14 KiB
4 years ago
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(**************************************************************************)
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(* *)
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(* OCaml *)
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(* *)
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(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
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(* *)
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(* Copyright 1996 Institut National de Recherche en Informatique et *)
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(* en Automatique. *)
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(* *)
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(* All rights reserved. This file is distributed under the terms of *)
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(* the GNU Lesser General Public License version 2.1, with the *)
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(* special exception on linking described in the file LICENSE. *)
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(* *)
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(**************************************************************************)
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(** Association tables over ordered types.
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This module implements applicative association tables, also known as
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finite maps or dictionaries, given a total ordering function
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over the keys.
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All operations over maps are purely applicative (no side-effects).
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The implementation uses balanced binary trees, and therefore searching
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and insertion take time logarithmic in the size of the map.
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For instance:
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{[
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module IntPairs =
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struct
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type t = int * int
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let compare (x0,y0) (x1,y1) =
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match Stdlib.compare x0 x1 with
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0 -> Stdlib.compare y0 y1
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| c -> c
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end
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module PairsMap = Map.Make(IntPairs)
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let m = PairsMap.(empty |> add (0,1) "hello" |> add (1,0) "world")
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]}
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This creates a new module [PairsMap], with a new type ['a PairsMap.t]
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of maps from [int * int] to ['a]. In this example, [m] contains [string]
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values so its type is [string PairsMap.t].
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*)
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module type OrderedType =
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sig
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type t
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(** The type of the map keys. *)
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val compare : t -> t -> int
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(** A total ordering function over the keys.
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This is a two-argument function [f] such that
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[f e1 e2] is zero if the keys [e1] and [e2] are equal,
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[f e1 e2] is strictly negative if [e1] is smaller than [e2],
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and [f e1 e2] is strictly positive if [e1] is greater than [e2].
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Example: a suitable ordering function is the generic structural
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comparison function {!Stdlib.compare}. *)
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end
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(** Input signature of the functor {!Map.Make}. *)
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module type S =
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sig
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type key
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(** The type of the map keys. *)
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type (+'a) t
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(** The type of maps from type [key] to type ['a]. *)
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val empty: 'a t
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(** The empty map. *)
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val is_empty: 'a t -> bool
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(** Test whether a map is empty or not. *)
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val mem: key -> 'a t -> bool
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(** [mem x m] returns [true] if [m] contains a binding for [x],
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and [false] otherwise. *)
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val add: key -> 'a -> 'a t -> 'a t
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(** [add x y m] returns a map containing the same bindings as
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[m], plus a binding of [x] to [y]. If [x] was already bound
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in [m] to a value that is physically equal to [y],
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[m] is returned unchanged (the result of the function is
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then physically equal to [m]). Otherwise, the previous binding
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of [x] in [m] disappears.
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@before 4.03 Physical equality was not ensured. *)
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val update: key -> ('a option -> 'a option) -> 'a t -> 'a t
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(** [update x f m] returns a map containing the same bindings as
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[m], except for the binding of [x]. Depending on the value of
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[y] where [y] is [f (find_opt x m)], the binding of [x] is
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added, removed or updated. If [y] is [None], the binding is
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removed if it exists; otherwise, if [y] is [Some z] then [x]
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is associated to [z] in the resulting map. If [x] was already
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bound in [m] to a value that is physically equal to [z], [m]
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is returned unchanged (the result of the function is then
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physically equal to [m]).
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@since 4.06.0
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*)
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val singleton: key -> 'a -> 'a t
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(** [singleton x y] returns the one-element map that contains a binding [y]
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for [x].
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@since 3.12.0
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*)
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val remove: key -> 'a t -> 'a t
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(** [remove x m] returns a map containing the same bindings as
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[m], except for [x] which is unbound in the returned map.
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If [x] was not in [m], [m] is returned unchanged
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(the result of the function is then physically equal to [m]).
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@before 4.03 Physical equality was not ensured. *)
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val merge:
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(key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t
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(** [merge f m1 m2] computes a map whose keys are a subset of the keys of
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[m1] and of [m2]. The presence of each such binding, and the
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corresponding value, is determined with the function [f].
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In terms of the [find_opt] operation, we have
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[find_opt x (merge f m1 m2) = f x (find_opt x m1) (find_opt x m2)]
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for any key [x], provided that [f x None None = None].
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@since 3.12.0
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*)
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val union: (key -> 'a -> 'a -> 'a option) -> 'a t -> 'a t -> 'a t
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(** [union f m1 m2] computes a map whose keys are a subset of the keys
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of [m1] and of [m2]. When the same binding is defined in both
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arguments, the function [f] is used to combine them.
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This is a special case of [merge]: [union f m1 m2] is equivalent
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to [merge f' m1 m2], where
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- [f' _key None None = None]
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- [f' _key (Some v) None = Some v]
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- [f' _key None (Some v) = Some v]
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- [f' key (Some v1) (Some v2) = f key v1 v2]
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@since 4.03.0
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*)
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val compare: ('a -> 'a -> int) -> 'a t -> 'a t -> int
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(** Total ordering between maps. The first argument is a total ordering
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used to compare data associated with equal keys in the two maps. *)
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val equal: ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
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(** [equal cmp m1 m2] tests whether the maps [m1] and [m2] are
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equal, that is, contain equal keys and associate them with
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equal data. [cmp] is the equality predicate used to compare
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the data associated with the keys. *)
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val iter: (key -> 'a -> unit) -> 'a t -> unit
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(** [iter f m] applies [f] to all bindings in map [m].
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[f] receives the key as first argument, and the associated value
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as second argument. The bindings are passed to [f] in increasing
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order with respect to the ordering over the type of the keys. *)
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val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
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(** [fold f m a] computes [(f kN dN ... (f k1 d1 a)...)],
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where [k1 ... kN] are the keys of all bindings in [m]
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(in increasing order), and [d1 ... dN] are the associated data. *)
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val for_all: (key -> 'a -> bool) -> 'a t -> bool
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(** [for_all p m] checks if all the bindings of the map
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satisfy the predicate [p].
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@since 3.12.0
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*)
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val exists: (key -> 'a -> bool) -> 'a t -> bool
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(** [exists p m] checks if at least one binding of the map
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satisfies the predicate [p].
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@since 3.12.0
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*)
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val filter: (key -> 'a -> bool) -> 'a t -> 'a t
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(** [filter p m] returns the map with all the bindings in [m]
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that satisfy predicate [p]. If every binding in [m] satisfies [p],
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[m] is returned unchanged (the result of the function is then
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physically equal to [m])
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@since 3.12.0
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@before 4.03 Physical equality was not ensured.
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*)
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val filter_map: (key -> 'a -> 'b option) -> 'a t -> 'b t
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(** [filter_map f m] applies the function [f] to every binding of
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[m], and builds a map from the results. For each binding
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[(k, v)] in the input map:
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- if [f k v] is [None] then [k] is not in the result,
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- if [f k v] is [Some v'] then the binding [(k, v')]
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is in the output map.
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For example, the following function on maps whose values are lists
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{[
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filter_map
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(fun _k li -> match li with [] -> None | _::tl -> Some tl)
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m
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]}
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drops all bindings of [m] whose value is an empty list, and pops
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the first element of each value that is non-empty.
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@since 4.11.0
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*)
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val partition: (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
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(** [partition p m] returns a pair of maps [(m1, m2)], where
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[m1] contains all the bindings of [m] that satisfy the
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predicate [p], and [m2] is the map with all the bindings of
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[m] that do not satisfy [p].
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@since 3.12.0
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*)
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val cardinal: 'a t -> int
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(** Return the number of bindings of a map.
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@since 3.12.0
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*)
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val bindings: 'a t -> (key * 'a) list
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(** Return the list of all bindings of the given map.
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The returned list is sorted in increasing order of keys with respect
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to the ordering [Ord.compare], where [Ord] is the argument
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given to {!Map.Make}.
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@since 3.12.0
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*)
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val min_binding: 'a t -> (key * 'a)
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(** Return the binding with the smallest key in a given map
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(with respect to the [Ord.compare] ordering), or raise
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[Not_found] if the map is empty.
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@since 3.12.0
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*)
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val min_binding_opt: 'a t -> (key * 'a) option
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(** Return the binding with the smallest key in the given map
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(with respect to the [Ord.compare] ordering), or [None]
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if the map is empty.
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@since 4.05
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*)
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val max_binding: 'a t -> (key * 'a)
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(** Same as {!Map.S.min_binding}, but returns the binding with
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the largest key in the given map.
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@since 3.12.0
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*)
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val max_binding_opt: 'a t -> (key * 'a) option
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(** Same as {!Map.S.min_binding_opt}, but returns the binding with
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the largest key in the given map.
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@since 4.05
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*)
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val choose: 'a t -> (key * 'a)
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(** Return one binding of the given map, or raise [Not_found] if
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the map is empty. Which binding is chosen is unspecified,
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but equal bindings will be chosen for equal maps.
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@since 3.12.0
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*)
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val choose_opt: 'a t -> (key * 'a) option
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(** Return one binding of the given map, or [None] if
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the map is empty. Which binding is chosen is unspecified,
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but equal bindings will be chosen for equal maps.
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@since 4.05
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*)
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val split: key -> 'a t -> 'a t * 'a option * 'a t
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(** [split x m] returns a triple [(l, data, r)], where
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[l] is the map with all the bindings of [m] whose key
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is strictly less than [x];
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[r] is the map with all the bindings of [m] whose key
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is strictly greater than [x];
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[data] is [None] if [m] contains no binding for [x],
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or [Some v] if [m] binds [v] to [x].
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@since 3.12.0
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*)
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val find: key -> 'a t -> 'a
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(** [find x m] returns the current value of [x] in [m],
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or raises [Not_found] if no binding for [x] exists. *)
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val find_opt: key -> 'a t -> 'a option
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(** [find_opt x m] returns [Some v] if the current value of [x]
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in [m] is [v], or [None] if no binding for [x] exists.
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@since 4.05
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*)
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val find_first: (key -> bool) -> 'a t -> key * 'a
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(** [find_first f m], where [f] is a monotonically increasing function,
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returns the binding of [m] with the lowest key [k] such that [f k],
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or raises [Not_found] if no such key exists.
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For example, [find_first (fun k -> Ord.compare k x >= 0) m] will return
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the first binding [k, v] of [m] where [Ord.compare k x >= 0]
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(intuitively: [k >= x]), or raise [Not_found] if [x] is greater than any
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element of [m].
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@since 4.05
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*)
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val find_first_opt: (key -> bool) -> 'a t -> (key * 'a) option
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(** [find_first_opt f m], where [f] is a monotonically increasing function,
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returns an option containing the binding of [m] with the lowest key [k]
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such that [f k], or [None] if no such key exists.
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@since 4.05
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*)
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val find_last: (key -> bool) -> 'a t -> key * 'a
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(** [find_last f m], where [f] is a monotonically decreasing function,
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returns the binding of [m] with the highest key [k] such that [f k],
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or raises [Not_found] if no such key exists.
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@since 4.05
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*)
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val find_last_opt: (key -> bool) -> 'a t -> (key * 'a) option
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(** [find_last_opt f m], where [f] is a monotonically decreasing function,
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returns an option containing the binding of [m] with the highest key [k]
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such that [f k], or [None] if no such key exists.
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@since 4.05
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*)
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val map: ('a -> 'b) -> 'a t -> 'b t
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(** [map f m] returns a map with same domain as [m], where the
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associated value [a] of all bindings of [m] has been
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replaced by the result of the application of [f] to [a].
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The bindings are passed to [f] in increasing order
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with respect to the ordering over the type of the keys. *)
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val mapi: (key -> 'a -> 'b) -> 'a t -> 'b t
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(** Same as {!Map.S.map}, but the function receives as arguments both the
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key and the associated value for each binding of the map. *)
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(** {1 Iterators} *)
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val to_seq : 'a t -> (key * 'a) Seq.t
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(** Iterate on the whole map, in ascending order of keys
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@since 4.07 *)
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val to_seq_from : key -> 'a t -> (key * 'a) Seq.t
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(** [to_seq_from k m] iterates on a subset of the bindings of [m],
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in ascending order of keys, from key [k] or above.
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@since 4.07 *)
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val add_seq : (key * 'a) Seq.t -> 'a t -> 'a t
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(** Add the given bindings to the map, in order.
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@since 4.07 *)
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val of_seq : (key * 'a) Seq.t -> 'a t
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(** Build a map from the given bindings
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@since 4.07 *)
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end
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(** Output signature of the functor {!Map.Make}. *)
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module Make (Ord : OrderedType) : S with type key = Ord.t
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(** Functor building an implementation of the map structure
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given a totally ordered type. *)
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