module type T = sig .. end
type +'a t
The tree type.
module Key: sig .. end
A module defining the type of the key.
val nil : 'a t
The empty tree.
val empty : 'a t -> bool
Use empty m to test whether the tree m is empty.
val size : 'a t -> int
Use size m to count the number of elements in the tree m.
val min : 'a t -> Key.t * 'a
Use min m to obtain the key-value pair with the ordinally minimum key
in the tree m. Raises Not_found if the tree is empty.
val max : 'a t -> Key.t * 'a
Use max m to obtain the key-value pair with the ordinally maximum key
in the tree m. Raises Not_found if the tree is empty.
val search : Key.t -> 'a t -> 'a
Use search k m to obtain the value associated with the key k in the
tree m. Raise Not_found if the tree does not contain the key.
val member : Key.t -> 'a t -> bool
Use member k m to test whether the tree m contains the key k.
val insert : Key.t * 'a -> 'a t -> 'a t * 'a option
Use insert p m to insert the key-value pair p into the tree m,
producing a new tree with the inserted element and, if the key k is
already present in m, the value replaced by the insertion.
val replace : Key.t * 'a -> 'a t -> 'a t
Use replace p m to obtain a new tree produced by inserting the
key-value pair p into the tree m, replacing any existing pair
associated to the same key.
val modify : Key.t -> ('a -> 'a) -> 'a t -> 'a t
Use modify k f m to obtain a new tree produced by replacing the value
in the tree m associated with the key k with the result of applying
it to the continuation function f. Raises Not_found if the tree
does not contain the key.
: Key.t -> 'a t -> 'a * 'a t
Use extract k m to obtain the value associated with the key k in
the tree m and a new tree with the key deleted from the tree. Raises
Not_found if the tree does not contain the key.
val delete : Key.t -> 'a t -> 'a t
Use delete k m to obtain a new tree produced by deleting the key k
from the tree m. If the tree does not contain the key, then the
function simply returns its argument.
val of_list : (Key.t * 'a) list -> 'a t
Use of_list s to compose a tree by iterating the list of key-value
pairs s and inserting them in order into a new tree.
val of_list_incr : (Key.t * 'a) list -> 'a t
Use of_list_incr s to compose a tree with the key-value pairs in the
ordered list s. Runs in linear time if the keys in the list s are
known to be in increasing order. Otherwise, there is an additional
linear cost beyond of_list s.
val of_list_decr : (Key.t * 'a) list -> 'a t
Use of_list_decr s to compose a tree with the key-value pairs in the
ordered list s. Runs in linear time if the keys in the list s are
known to be in decreasing order. Otherwise, there is an additional
linear cost beyond of_list s.
val of_seq : (Key.t * 'a) Cf_seq.t -> 'a t
Use of_seq z to compose a tree by evaluating the entire sequence of
key-value pairs z and inserting them in order into a new tree.
val of_seq_incr : (Key.t * 'a) Cf_seq.t -> 'a t
Use of_seq_incr z to compose a tree with the key-value pairs in the
ordered sequence z. Runs in linear time if the keys in the sequence
z are known to be in increasing order. Otherwise, there is an
additional linear cost beyond of_seq z.
val of_seq_decr : (Key.t * 'a) Cf_seq.t -> 'a t
Use of_seq_decr z to compose a tree with the key-value pairs in the
ordered sequence z. Runs in linear time if the keys in the sequence
z are known to be in decreasing order. Otherwise, there is an
additional linear cost beyond of_seq z.
val to_list_incr : 'a t -> (Key.t * 'a) list
Use to_list_incr m to obtain a sequence of the key-value pairs in the
tree m in order of increasing ordinality.
val to_list_decr : 'a t -> (Key.t * 'a) list
Use to_list_decr m to obtain a sequence of the key-value pairs in the
tree m in order of descreasing ordinality.
val to_seq_incr : 'a t -> (Key.t * 'a) Cf_seq.t
Use to_seq_incr m to obtain a sequence of the key-value pairs in the
tree m in order of increasing ordinality.
val to_seq_decr : 'a t -> (Key.t * 'a) Cf_seq.t
Use to_seq_decr m to obtain a sequence of the key-value pairs in the
tree m in order of descreasing ordinality.
val nearest_decr : Key.t -> 'a t -> (Key.t * 'a) Cf_seq.t
Use nearest_decr k m to obtain the key-value pair ordinally less than
or equal to the key k in the map m. Raises Not_found if the map
is empty or all the keys are ordinally greater.
val nearest_incr : Key.t -> 'a t -> (Key.t * 'a) Cf_seq.t
Use nearest_incr k m to obtain the key-value pair ordinally greater
than or equal to the key k in the map m. Raises Not_found if the
map is empty or all the keys are ordinally less.
val iterate : (Key.t * 'a -> unit) -> 'a t -> unit
Use iterate f m to apply the function f to each key-value pair in
the tree m in an arbitrary order (not increasing or decreasing).
val predicate : (Key.t * 'a -> bool) -> 'a t -> bool
Use predicate f m to test whether all the key-value pairs in the tree
m satisfy the predicate function f. The nodes of the tree are
visited in an arbitrary order (not increasing or decreasing).
val fold : ('b -> Key.t * 'a -> 'b) -> 'b -> 'a t -> 'b
Use fold f s m to fold the every key-value pair in the tree m into
the state s with the folding function f, visiting the elements in
an arbitrary order (not increasing or decreasing). Runs in O(log N)
space, i.e. not tail-recursive.
val filter : (Key.t * 'a -> bool) -> 'a t -> 'a t
Use filter f m to obtain a new tree comprised of all the key-value
pairs in the tree m that satisfy the filtering function f. The
elements in m are visited in arbitrary order (not increasing or
decreasing). Runs in O(log N) space, i.e. not tail-recursive.
val map : (Key.t * 'a -> 'b) -> 'a t -> 'b t
Use map f m to obtain a new tree produced by applying the mapping
function f to the key and the value of each key-value pair in the
tree m and associating the resulting value to the key in the new
tree. Elements in the tree are visited in arbitrary order (not
increasing or descreasing. Runs in O(log N) space, i.e. not
tail-recursive.
val optmap : (Key.t * 'a -> 'b option) -> 'a t -> 'b t
Use optmap f m to obtain a new tree produced by applying the mapping
function f to the key and the value of each key-value pair in the
tree m and associating the resulting value to the key in the new
tree. If the function f returns None then no value for that key
will be present in the new tree. Elements in the tree are visited in
arbitrary order (not increasing or descreasing. Runs in O(log N)
space, i.e. not tail-recursive.
val partition : (Key.t * 'a -> bool) ->
'a t -> 'a t * 'a t
Use partition f m to obtain a pair of new trees produced by applying
the partitioning function f to all the elements in the tree m in an
arbitrary order (not increasing or descreasing). The first tree will
contain all the elements for which f returns true, and the second
tree will have all the elements for which f returns false. Runs in
O(log N) space, i.e. not tail-recursive.