From bcde99fbe99174a094f38fdda70ad69d65a423f4 Mon Sep 17 00:00:00 2001 From: Alex AUVOLAT Date: Wed, 30 Apr 2014 17:19:08 +0200 Subject: Fist commit (WIP) --- libs/mapext.mli | 473 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 473 insertions(+) create mode 100644 libs/mapext.mli (limited to 'libs/mapext.mli') diff --git a/libs/mapext.mli b/libs/mapext.mli new file mode 100644 index 0000000..abee2c0 --- /dev/null +++ b/libs/mapext.mli @@ -0,0 +1,473 @@ +(* + 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. *) -- cgit v1.2.3