#### logtk 2.1 2.0 1.6 1.5.1 0.8.1

Core types and algorithms for logic
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Library logtk
Module . .
include Map.S with type key = term
type key = term

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 key data m returns a map containing the same bindings as m, plus a binding of key to data. If key was already bound in m to a value that is physically equal to data, m is returned unchanged (the result of the function is then physically equal to m). Otherwise, the previous binding of key in m disappears.

• before 4.03

Physical equality was not ensured.

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. If x was not in m, m is returned unchanged (the result of the function is then physically equal to m).

• before 4.03

Physical equality was not ensured.

val merge : ( key -> 'a option -> 'b option -> 'c option ) -> 'a t -> 'b t -> 'c t

merge f m1 m2 computes a map whose keys are a subset of the keys of m1 and of m2. The presence of each such binding, and the corresponding value, is determined with the function f. In terms of the find_opt operation, we have find_opt x (merge f m1 m2) = f x (find_opt x m1) (find_opt x m2) for any key x, provided that f x None None = None.

• since 3.12.0
val union : ( key -> 'a -> 'a -> 'a option ) -> 'a t -> 'a t -> 'a t

union f m1 m2 computes a map whose keys are a subset of the keys of m1 and of m2. When the same binding is defined in both arguments, the function f is used to combine them. This is a special case of merge: union f m1 m2 is equivalent to merge f' m1 m2, where

• f' _key None None = None
• f' _key (Some v) None = Some v
• f' _key None (Some v) = Some v
• f' key (Some v1) (Some v2) = f key v1 v2
• since 4.03.0
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 init computes (f kN dN ... (f k1 d1 init)...), 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

for_all f m checks if all the bindings of the map satisfy the predicate f.

• since 3.12.0
val exists : ( key -> 'a -> bool ) -> 'a t -> bool

exists f m checks if at least one binding of the map satisfies the predicate f.

• since 3.12.0
val filter : ( key -> 'a -> bool ) -> 'a t -> 'a t

filter f m returns the map with all the bindings in m that satisfy predicate p. If every binding in m satisfies f, m is returned unchanged (the result of the function is then physically equal to m)

• since 3.12.0
• before 4.03

Physical equality was not ensured.

val filter_map : ( key -> 'a -> 'b option ) -> 'a t -> 'b t

filter_map f m applies the function f to every binding of m, and builds a map from the results. For each binding (k, v) in the input map:

• if f k v is None then k is not in the result,
• if f k v is Some v' then the binding (k, v') is in the output map.

For example, the following function on maps whose values are lists

filter_map
(fun _k li -> match li with [] -> None | _::tl -> Some tl)
m

drops all bindings of m whose value is an empty list, and pops the first element of each value that is non-empty.

• since 4.11.0
val partition : ( key -> 'a -> bool ) -> 'a t -> 'a t * 'a t

partition f m returns a pair of maps (m1, m2), where m1 contains all the bindings of m that satisfy the predicate f, and m2 is the map with all the bindings of m that do not satisfy f.

• 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 of keys with respect to the ordering Ord.compare, where Ord is the argument given to Make.

• since 3.12.0
val min_binding : 'a t -> key * 'a

Return the binding with the smallest key in a 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 S.min_binding, but returns the binding with the largest key in 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 value of x in m, or raises Not_found if no binding for x exists.

val find_last : ( key -> bool ) -> 'a t -> key * 'a

find_last f m, where f is a monotonically decreasing function, returns the binding of m with the highest key k such that f k, or raises Not_found if no such key exists.

• since 4.05
val find_last_opt : ( key -> bool ) -> 'a t -> (key * 'a) option

find_last_opt f m, where f is a monotonically decreasing function, returns an option containing the binding of m with the highest key k such that f k, or None if no such key exists.

• since 4.05
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 S.map, but the function receives as arguments both the key and the associated value for each binding of the map.

## Iterators

val to_seq : 'a t -> (key * 'a) Seq.t

Iterate on the whole map, in ascending order of keys

• since 4.07
val to_rev_seq : 'a t -> (key * 'a) Seq.t

Iterate on the whole map, in descending order of keys

• since 4.12
val to_seq_from : key -> 'a t -> (key * 'a) Seq.t

to_seq_from k m iterates on a subset of the bindings of m, in ascending order of keys, from key k or above.

• since 4.07
val get : key -> 'a t -> 'a option

get k m returns Some v if the current binding of k in m is v, or None if the key k is not present. Safe version of find.

val get_or : key -> 'a t -> default:'a -> 'a

get_or k m ~default returns the value associated to k if present, and returns default otherwise (if k doesn't belong in m).

• since 0.16
val update : key -> ( 'a option -> 'a option ) -> 'a t -> 'a t

update k f m calls f (Some v) if find k m = v, otherwise it calls f None. In any case, if the result is None k is removed from m, and if the result is Some v' then add k v' m is returned.

val choose_opt : 'a t -> (key * 'a) option

choose_opt m returns one binding of the given map m, or None if m is empty. Safe version of choose.

• since 1.5
val min_binding_opt : 'a t -> (key * 'a) option

min_binding_opt m returns the smallest binding of the given map m, or None if m is empty. Safe version of min_binding.

• since 1.5
val max_binding_opt : 'a t -> (key * 'a) option

max_binding_opt m returns the largest binding of the given map m, or None if m is empty. Safe version of max_binding.

• since 1.5
val find_opt : key -> 'a t -> 'a option

find_opt k m returns Some v if the current binding of k in m is v, or None if the key k is not present. Safe version of find.

• since 1.5
val find_first : ( key -> bool ) -> 'a t -> key * 'a

find_first f m where f is a monotonically increasing function, returns the binding of m with the lowest key k such that f k, or raises Not_found if no such key exists. See Map.S.find_first.

• since 1.5
val find_first_opt : ( key -> bool ) -> 'a t -> (key * 'a) option

find_first_opt f m where f is a monotonically increasing function, returns an option containing the binding of m with the lowest key k such that f k, or None if no such key exists. Safe version of find_first.

• since 1.5
val merge_safe : f:( key -> [ `Left of 'a | `Right of 'b | `Both of 'a * 'b ] -> 'c option ) -> 'a t -> 'b t -> 'c t

merge_safe ~f a b merges the maps a and b together.

• since 0.17
val add_seq : 'a t -> (key * 'a) Seq.t -> 'a t

• since 3.0
val add_seq_with : f:( key -> 'a -> 'a -> 'a ) -> 'a t -> (key * 'a) Seq.t -> 'a t

add_seq ~f m l adds the given seq l of bindings to the map m, using f to combine values that have the same key. If a key occurs several times, all its bindings are combined using the function f, with f key v1 v2 being called with v1 occurring later in the seq than v2.

• since 3.3
val of_seq : (key * 'a) Seq.t -> 'a t

of_seq seq builds a map from the given Seq.t of bindings. Like of_list. Renamed from of_std_seq since 3.0.

• since 3.0
val of_seq_with : f:( key -> 'a -> 'a -> 'a ) -> (key * 'a) Seq.t -> 'a t

of_seq_with ~f l builds a map from the given seq l of bindings k_i -> v_i, added in order using add. If a key occurs several times, all its bindings are combined using the function f, with f key v1 v2 being called with v1 occurring later in the seq than v2.

• since 3.3
val add_iter : 'a t -> (key * 'a) CCMap.iter -> 'a t

• since 2.8
val add_iter_with : f:( key -> 'a -> 'a -> 'a ) -> 'a t -> (key * 'a) CCMap.iter -> 'a t

add_iter ~f m l adds the given iter l of bindings to the map m, using f to combine values that have the same key. If a key occurs several times, all its bindings are combined using the function f, with f key v1 v2 being called with v1 occurring later in the seq than v2.

• since 3.3
val of_iter : (key * 'a) CCMap.iter -> 'a t

of_iter iter builds a map from the given iter of bindings. Like of_list.

• since 2.8
val of_iter_with : f:( key -> 'a -> 'a -> 'a ) -> (key * 'a) CCMap.iter -> 'a t

of_iter_with ~f l builds a map from the given iter l of bindings k_i -> v_i, added in order using add. If a key occurs several times, all its bindings are combined using the function f, with f key v1 v2 being called with v1 occurring later in the iter than v2.

• since 3.3
val to_iter : 'a t -> (key * 'a) CCMap.iter

to_iter m iterates on the whole map m, creating an iter of bindings. Like to_list.

• since 2.8
val of_list : (key * 'a) list -> 'a t

of_list l builds a map from the given list l of bindings k_i -> v_i, added in order using add. If a key occurs several times, only its last binding will be present in the result.

val of_list_with : f:( key -> 'a -> 'a -> 'a ) -> (key * 'a) list -> 'a t

of_list_with ~f l builds a map from the given list l of bindings k_i -> v_i, added in order using add. If a key occurs several times, all its bindings are combined using the function f, with f key v1 v2 being called with v1 occurring later in the list than v2.

• since 3.3
val add_list : 'a t -> (key * 'a) list -> 'a t

add_list m l adds the given list l of bindings to the map m.

• since 0.14
val add_list_with : f:( key -> 'a -> 'a -> 'a ) -> 'a t -> (key * 'a) list -> 'a t

add_list ~f m l adds the given list l of bindings to the map m, using f to combine values that have the same key. If a key occurs several times, all its bindings are combined using the function f, with f key v1 v2 being called with v1 occurring later in the seq than v2.

• since 3.3
val keys : _ t ->

keys m iterates on the keys of m only, creating an iter of keys.

• since 0.15
val values : 'a t ->

values m iterates on the values of m only, creating an iter of values.

• since 0.15
val to_list : 'a t -> (key * 'a) list

to_list m builds a list of the bindings of the given map m. The order is unspecified.

val pp : ?pp_start:unit CCMap.printer -> ?pp_stop:unit CCMap.printer -> ?pp_arrow:unit CCMap.printer -> ?pp_sep:unit CCMap.printer -> ->

pp ?pp_start ?pp_stop ?pp_arrow ?pp_sep pp_key pp_v m pretty-prints the contents of the map.