(*
Cours "Sémantique et Application à la Vérification de programmes"
Antoine Miné 2014
Ecole normale supérieure, Paris, France / CNRS / INRIA
*)
(*
This file is derived from the mapi.ml file from the OCaml distribution.
Changes are marked with the [AM] symbol.
Based on rev. 10632 2010-07-24 14:16:58Z.
Original copyright follows.
*)
(***********************************************************************)
(* *)
(* Objective Caml *)
(* *)
(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *)
(* *)
(* Copyright 1996 Institut National de Recherche en Informatique et *)
(* en Automatique. All rights reserved. This file is distributed *)
(* under the terms of the GNU Library General Public License, with *)
(* the special exception on linking described in file ../LICENSE. *)
(* *)
(***********************************************************************)
(* $Id: mapext.mli,v 1.1 2014-02-24 16:25:06 mine Exp $ *)
(** Association tables over ordered types.
This module implements applicative association tables, also known as
finite maps or dictionaries, given a total ordering function
over the keys.
All operations over maps are purely applicative (no side-effects).
The implementation uses balanced binary trees, and therefore searching
and insertion take time logarithmic in the size of the map.
*)
module type OrderedType =
sig
type t
(** The type of the map keys. *)
val compare : t -> t -> int
(** A total ordering function over the keys.
This is a two-argument function [f] such that
[f e1 e2] is zero if the keys [e1] and [e2] are equal,
[f e1 e2] is strictly negative if [e1] is smaller than [e2],
and [f e1 e2] is strictly positive if [e1] is greater than [e2].
Example: a suitable ordering function is the generic structural
comparison function {!Pervasives.compare}. *)
end
(** Input signature of the functor {!Map.Make}. *)
module type S =
sig
type key
(** The type of the map keys. *)
type (+'a) t
(** The type of maps from type [key] to type ['a]. *)
val empty: 'a t
(** The empty map. *)
val is_empty: 'a t -> bool
(** Test whether a map is empty or not. *)
val mem: key -> 'a t -> bool
(** [mem x m] returns [true] if [m] contains a binding for [x],
and [false] otherwise. *)
val add: key -> 'a -> 'a t -> 'a t
(** [add x y m] returns a map containing the same bindings as
[m], plus a binding of [x] to [y]. If [x] was already bound
in [m], its previous binding disappears. *)
val singleton: key -> 'a -> 'a t
(** [singleton x y] returns the one-element map that contains a binding [y]
for [x].
@since 3.12.0
*)
val remove: key -> 'a t -> 'a t
(** [remove x m] returns a map containing the same bindings as
[m], except for [x] which is unbound in the returned map. *)
val merge:
(key -> 'a option -> 'b option -> 'c option) -> 'a t -> 'b t -> 'c t
(** [merge f m1 m2] computes a map whose keys is a subset of keys of [m1]
and of [m2]. The presence of each such binding, and the corresponding
value, is determined with the function [f].
@since 3.12.0
*)
val compare: ('a -> 'a -> int) -> 'a t -> 'a t -> int
(** Total ordering between maps. The first argument is a total ordering
used to compare data associated with equal keys in the two maps. *)
val equal: ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
(** [equal cmp m1 m2] tests whether the maps [m1] and [m2] are
equal, that is, contain equal keys and associate them with
equal data. [cmp] is the equality predicate used to compare
the data associated with the keys. *)
val iter: (key -> 'a -> unit) -> 'a t -> unit
(** [iter f m] applies [f] to all bindings in map [m].
[f] receives the key as first argument, and the associated value
as second argument. The bindings are passed to [f] in increasing
order with respect to the ordering over the type of the keys. *)
val fold: (key -> 'a -> 'b -> 'b) -> 'a t -> 'b -> 'b
(** [fold f m a] computes [(f kN dN ... (f k1 d1 a)...)],
where [k1 ... kN] are the keys of all bindings in [m]
(in increasing order), and [d1 ... dN] are the associated data. *)
val for_all: (key -> 'a -> bool) -> 'a t -> bool
(* [AM] now guarantees the evaluation order *)
(** [for_all p m] checks if all the bindings of the map
satisfy the predicate [p].
The predicate [p] is tested on bindings according to the key order.
@since 3.12.0
*)
val exists: (key -> 'a -> bool) -> 'a t -> bool
(* [AM] now guarantees the evaluation order *)
(** [exists p m] checks if at least one binding of the map
satisfy the predicate [p].
The predicate [p] is tested on bindings according to the key order.
@since 3.12.0
*)
val filter: (key -> 'a -> bool) -> 'a t -> 'a t
(* [AM] now guarantees the evaluation order *)
(** [filter p m] returns the map with all the bindings in [m]
that satisfy predicate [p].
The predicate [p] is tested on bindings according to the key order.
@since 3.12.0
*)
val partition: (key -> 'a -> bool) -> 'a t -> 'a t * 'a t
(** [partition p m] returns a pair of maps [(m1, m2)], where
[m1] contains all the bindings of [s] that satisfy the
predicate [p], and [m2] is the map with all the bindings of
[s] that do not satisfy [p].
@since 3.12.0
*)
val cardinal: 'a t -> int
(** Return the number of bindings of a map.
@since 3.12.0
*)
val bindings: 'a t -> (key * 'a) list
(** Return the list of all bindings of the given map.
The returned list is sorted in increasing order with respect
to the ordering [Ord.compare], where [Ord] is the argument
given to {!Map.Make}.
@since 3.12.0
*)
val min_binding: 'a t -> (key * 'a)
(** Return the smallest binding of the given map
(with respect to the [Ord.compare] ordering), or raise
[Not_found] if the map is empty.
@since 3.12.0
*)
val max_binding: 'a t -> (key * 'a)
(** Same as {!Map.S.min_binding}, but returns the largest binding
of the given map.
@since 3.12.0
*)
val choose: 'a t -> (key * 'a)
(** Return one binding of the given map, or raise [Not_found] if
the map is empty. Which binding is chosen is unspecified,
but equal bindings will be chosen for equal maps.
@since 3.12.0
*)
val split: key -> 'a t -> 'a t * 'a option * 'a t
(** [split x m] returns a triple [(l, data, r)], where
[l] is the map with all the bindings of [m] whose key
is strictly less than [x];
[r] is the map with all the bindings of [m] whose key
is strictly greater than [x];
[data] is [None] if [m] contains no binding for [x],
or [Some v] if [m] binds [v] to [x].
@since 3.12.0
*)
val find: key -> 'a t -> 'a
(** [find x m] returns the current binding of [x] in [m],
or raises [Not_found] if no such binding exists. *)
val map: ('a -> 'b) -> 'a t -> 'b t
(** [map f m] returns a map with same domain as [m], where the
associated value [a] of all bindings of [m] has been
replaced by the result of the application of [f] to [a].
The bindings are passed to [f] in increasing order
with respect to the ordering over the type of the keys. *)
val mapi: (key -> 'a -> 'b) -> 'a t -> 'b t
(** Same as {!Map.S.map}, but the function receives as arguments both the
key and the associated value for each binding of the map. *)
(* [AM] additions *)
(** {2 Additional functions} *)
val of_list: (key * 'a) list -> 'a t
(** [of_list l] converts an association list to a map. *)
val map2: (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
(** [map2 f m1 m2] is similar to [map] but applies [f] to pairs
of bindings [a1] from [m1] and [a2] from [m2] corresponding to
the same key to construct a new map with the same key set.
[m1] and [m2] must have the same key sets.
The binging are passed to [f] in increasing order of key. *)
val iter2: (key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
(** [iter2 f m1 m2] is similar to [map] but applies [f] to pairs
of bindings [a1] from [m1] and [a2] from [m2] corresponding to
the same key.
[m1] and [m2] must have the same key sets.
The binging are passed to [f] in increasing order of key. *)
val fold2: (key -> 'a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c
(** [fold2 f m1 m2 x] is similar to [fold] but applies [f] to pairs
of bindings [a1] from [m1] and [a2] from [m2] corresponding to
the same key.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val for_all2: (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
(** [for_all2 f m1 m2] is similar to [for_all] but applies [f] to pairs
of bindings [a1] from [m1] and [a2] from [m2] corresponding to
the same key.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val exists2: (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
(** [exists2 f m1 m2] is similar to [exists] but applies [f] to pairs
of bindings [a1] from [m1] and [a2] from [m2] corresponding to
the same key.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val map2z: (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
(** [map2z f m1 m2] is similar to [map2 f m1 m2], but physically
equal subtrees are put unchanged into the result instead of
being traversed.
This is more efficient than [map2], and equivalent if [f] is
side-effect free and idem-potent ([f k a a = a]).
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val iter2z: (key -> 'a -> 'a -> unit) -> 'a t -> 'a t -> unit
(** [iter2z f m1 m2] is similar to [iter2 f m1 m2], but physically
equal subtrees are ignored.
This is more efficient than [iter2], and equivalent if
[f k a a] has no effect.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val fold2z: (key -> 'a -> 'a -> 'b -> 'b) -> 'a t -> 'a t -> 'b -> 'b
(** [fold2z f m1 m2 a] is similar to [fold2 f m1 m2 a], but physically
equal subtrees are ignored.
This is more efficient than [fold2], and equivalent if
[f k a a x = x] and has no effect.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val for_all2z: (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
(** [for_all2z f m1 m2] is similar to [for_all2 f m1 m2], but returns
[true] for physically equal subtrees without traversing them.
This is more efficient than [for_all2z], and equivalent if
[f k a a = true] and has no effect.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val exists2z: (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
(** [exists2z f m1 m2] is similar to [exists2 f m1 m2], but returns
[false] for physically equal subtrees without traversing them.
This is more efficient than [exists2z], and equivalent if
[f k a a = false] and has no effect.
[m1] and [m2] must have the same key sets.
The bindings are passed to [f] in increasing order of keys. *)
val map2o: (key -> 'a -> 'c) -> (key -> 'b -> 'c) -> (key -> 'a -> 'b -> 'c) -> 'a t -> 'b t -> 'c t
(** [map2o f1 f2 f m1 m2] is similar to [map2 f m1 m2], but
accepts maps defined over different sets of keys.
To get a new binding, [f1] is used for keys appearing only
in [m1], [f2] for keys appearing only in [m2], and [f] for
keys appearing in both maps.
The returned map has bindings for all keys appearing in either
[m1] or [m2].
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val iter2o: (key -> 'a -> unit) -> (key -> 'b -> unit) -> (key -> 'a -> 'b -> unit) -> 'a t -> 'b t -> unit
(** [iter2o f1 f2 f m1 m2] is similar to [iter2 f m1 m2], but
accepts maps defined over different sets of keys.
[f1] is called for keys appearing only in [m1],
[f2] for keys appearing only in [m2],
and [f] for keys appearing in both maps.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val fold2o: (key -> 'a -> 'c -> 'c) -> (key -> 'b -> 'c -> 'c) -> (key -> 'a -> 'b -> 'c -> 'c) -> 'a t -> 'b t -> 'c -> 'c
(** [fold2o f1 f2 f m1 m2 a] is similar to [fold2 f m1 m2 a], but
accepts maps defined over different sets of keys.
[f1] is called for keys appearing only in [m1],
[f2] for keys appearing only in [m2],
and [f] for keys appearing in both maps.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val for_all2o: (key -> 'a -> bool) -> (key -> 'b -> bool) -> (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
(** [for_all2o f1 f2 f m1 m2] is similar to [for_all2 f m1 m2], but
accepts maps defined over different sets of keys.
[f1] is called for keys appearing only in [m1],
[f2] for keys appearing only in [m2],
and [f] for keys appearing in both maps.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val exists2o: (key -> 'a -> bool) -> (key -> 'b -> bool) -> (key -> 'a -> 'b -> bool) -> 'a t -> 'b t -> bool
(** [fexists2o f1 f2 f m1 m2] is similar to [fexists2 f m1 m2], but
accepts maps defined over different sets of keys.
[f1] is called for keys appearing only in [m1],
[f2] for keys appearing only in [m2],
and [f] for keys appearing in both maps.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val map2zo: (key -> 'a -> 'a) -> (key -> 'a -> 'a) -> (key -> 'a -> 'a -> 'a) -> 'a t -> 'a t -> 'a t
(** [map2zo f1 f2 f m1 m2] is similar to [map2o f1 f2 f m1 m2] but,
similary to [map2z], [f] is not called on physically equal
subtrees.
This is more efficient than [map2o], and equivalent if [f] is
side-effect free and idem-potent ([f k a a = a]).
The returned map has bindings for all keys appearing in either
[m1] or [m2].
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val iter2zo: (key -> 'a -> unit) -> (key -> 'a -> unit) -> (key -> 'a -> 'a -> unit) -> 'a t -> 'a t -> unit
(** [iter2zo f1 f2 f m1 m2] is similar to [iter2o f1 f2 f m1 m2] but,
similary to [iter2z], [f] is not called on physically equal
subtrees.
This is more efficient than [iter2o], and equivalent if [f] is
side-effect free.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val fold2zo: (key -> 'a -> 'b -> 'b) -> (key -> 'a -> 'b -> 'b) -> (key -> 'a -> 'a -> 'b -> 'b) -> 'a t -> 'a t -> 'b -> 'b
(** [fold2zo f1 f2 f m1 m2 a] is similar to [fold2o f1 f2 f m1 m2 a] but,
similary to [fold2z], [f] is not called on physically equal
subtrees.
This is more efficient than [fold2o], and equivalent if
[f k a a x = x] and has no side-effect.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val for_all2zo: (key -> 'a -> bool) -> (key -> 'a -> bool) -> (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
(** [for_all2zo f1 f2 f m1 m2] is similar to [for_all2o f1 f2 f m1 m2] but,
similary to [for_all2z], [f] is not called on physically equal
subtrees.
This is more efficient than [for_all2o], and equivalent if
[f k a a = true] and has no side-effect.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val exists2zo: (key -> 'a -> bool) -> (key -> 'a -> bool) -> (key -> 'a -> 'a -> bool) -> 'a t -> 'a t -> bool
(** [exists2zo f1 f2 f m1 m2] is similar to [exists2o f1 f2 f m1 m2] but,
similary to [exists2z], [f] is not called on physically equal
subtrees.
This is more efficient than [exists2o], and equivalent if
[f k a a = false] and has no side-effect.
The bindings are passed to [f], [f1], [f2] in increasing order of keys. *)
val map_slice: (key -> 'a -> 'a) -> 'a t -> key -> key -> 'a t
(** [map_slice f m k1 k2] is similar to [map f m], but only applies
[f] to bindings with key greater or equal to [k1] and smaller
or equal to [k2] to construct the returned map. Bindings with
keys outside this range in [m] are put unchanged in the result.
It is as if, outside this range, [f k a = a] and has no effect.
The result has the same key set as [m].
The bindings are passed to [f] in increasing order of keys,
between [k1] and [k2]. *)
val iter_slice: (key -> 'a -> unit) -> 'a t -> key -> key -> unit
(** [iter_slice f m k1 k2] is similar to [iter f m], but only calls
[f] on bindings with key greater or equal to [k1] and smaller
or equal to [k2].
It is as if, outside this range, [f k a] has no effect.
The bindings are passed to [f] in increasing order of keys,
between [k1] and [k2]. *)
val fold_slice: (key -> 'a -> 'b -> 'b) -> 'a t -> key -> key -> 'b -> 'b
(** [fold_slice f m k1 k2 a] is similar to [fold f m], but only calls
[f] on bindings with key greater or equal to [k1] and smaller
or equal to [k2].
It is as if, outside this range, [f k a x = x] and has no effect.
The bindings are passed to [f] in increasing order of keys,
between [k1] and [k2]. *)
val for_all_slice: (key -> 'a -> bool) -> 'a t -> key -> key -> bool
(** [for_all_slice f m k1 k2 a] is similar to [for_all f m], but only calls
[f] on bindings with key greater or equal to [k1] and smaller
or equal to [k2].
It is as if, outside this range, [f k a = true] and has no effect.
The bindings are passed to [f] in increasing order of keys,
between [k1] and [k2]. *)
val exists_slice: (key -> 'a -> bool) -> 'a t -> key -> key -> bool
(** [exists_slice f m k1 k2 a] is similar to [exists f m], but only calls
[f] on bindings with key greater or equal to [k1] and smaller
or equal to [k2].
It is as if, outside this range, [f k a = false] and has no effect.
The bindings are passed to [f] in increasing order of keys,
between [k1] and [k2]. *)
val key_equal: 'a t -> 'a t -> bool
(** [key_equal m1 m2] returns true if [m1] and [m2] are defined
over exactly the same set of keys (but with possibly different
values).
*)
val key_subset: 'a t -> 'a t -> bool
(** [key_equal m1 m2] returns true if [m1] is defined on a subset of
the keys of [m2] (but with possibly different values).
*)
val find_greater: key -> 'a t -> key * 'a
(** [find_greater k m] returns the binding (key and value) in [m]
with key strictly greater than [k] and as small as possible.
Raises [Not_found] if [m] has no binding for a key strictly greater
than [k].
*)
val find_less: key -> 'a t -> key * 'a
(** [find_less k m] returns the binding (key and value) in [m]
with key strictly less than [k] and as large as possible.
Raises [Not_found] if [m] has no binding for a key strictly less
than [k].
*)
val find_greater_equal: key -> 'a t -> key * 'a
(** [find_greater_euql k m] returns the binding (key and value) in [m]
with key greater or equal to [k] and as small as possible.
Raises [Not_found] if [m] has no binding for a key greater or equal
to [k].
*)
val find_less_equal: key -> 'a t -> key * 'a
(** [find_less_equal k m] returns the binding (key and value) in [m]
with key less or equal to [k] and as large as possible.
Raises [Not_found] if [m] has no binding for a key less or equal
to [k].
*)
end
(** Output signature of the functor {!Map.Make}. *)
module Make (Ord : OrderedType) : S with type key = Ord.t
(** Functor building an implementation of the map structure
given a totally ordered type. *)
