Sets over ordered types.
This module implements the set data structure, given a total ordering function over the set elements. All operations over sets are purely applicative (no side-effects). The implementation uses balanced binary trees, and is therefore reasonably efficient: insertion and membership take time logarithmic in the size of the set, for instance.
Note OCaml, Batteries Included, provides two implementations of sets: polymorphic sets and functorized sets. Functorized sets (see S and Make) are slightly more complex to use but offer stronger type-safety. Polymorphic sets make it easier to shoot yourself in the foot. In case of doubt, you should use functorized sets.
The functorized set implementation is built upon Stdlib's Set module, but provides the complete interface.
module type OrderedType = BatInterfaces.OrderedTypeInput signature of the functor Set.Make.
Functor building an implementation of the set structure given a totally ordered type.
module Make2 (O1 : OrderedType) (O2 : OrderedType) : sig ... endThe definitions below describe the polymorphic set interface.
They are similar in functionality to the functorized Make module, but the compiler cannot ensure that sets using different element ordering have different types: the responsibility of not mixing non-sensical comparison functions together is to the programmer. If in doubt, you should rather use the Make functor for additional safety.
include BatEnum.Enumerable with type 'a enumerable = 'a ttype 'a enumerable = 'a tThe data structure, e.g. 'a List.t
include BatInterfaces.Mappable with type 'a mappable = 'a ttype 'a mappable = 'a tThe data structure, e.g. 'a List.t
val empty : 'a tThe empty set, using compare as comparison function
val is_empty : 'a t -> boolTest whether a set is empty or not.
val singleton : 'a -> 'a tCreates a new set with the single given element in it.
val mem : 'a -> 'a t -> boolmem x s tests whether x belongs to the set s.
val find : 'a -> 'a t -> 'afind x s returns the set element that compares equal to x.
val find_opt : 'a -> 'a t -> 'a optionfind_opt x s returns Some k for the element k in s that tests equal to x under its comparison function. If no element is equal, return None
val find_first : ('a -> bool) -> 'a t -> 'afind_first f m returns the first element e for which f e is true or raises Not_found if there is no such element. f must be monotonically increasing, i.e. if k1 < k2 && f k1 is true then f k2 must also be true.
val find_first_opt : ('a -> bool) -> 'a t -> 'a optionfind_first_opt f m returns Some e for the first element e for which f e is true or returns None if there is no such element. f must be monotonically increasing, i.e. if k1 < k2 && f k1 is true then f k2 must also be true.
val find_last : ('a -> bool) -> 'a t -> 'afind_last f m returns the last element e for which f e is true or raises Not_found if there is no such element. f must be monotonically decreasing, i.e. if k1 < k2 && f k2 is true then f k1 must also be true.
val find_last_opt : ('a -> bool) -> 'a t -> 'a optionfind_last_opt f m returns Some e for the last element e for which f e is true or returns None if there is no such element. f must be monotonically decreasing, i.e. if k1 < k2 && f k2 is true then f k1 must also be true.
add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged.
remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged.
remove_exn x s behaves like remove x s except that it raises an exception if x is not in s.
update x y s replace x by y in s. update is faster when x compares equal to y according to the comparison function used by your set. When x and y are physically equal, m is returned unchanged.
union s t returns the union of s and t - the set containing all elements in either s and t. The returned set uses t's comparison function. The current implementation works better for small s.
intersect s t returns a new set of those elements that are in both s and t. The returned set uses s's comparison function.
diff s t returns the set of all elements in s but not in t. The returned set uses s's comparison function.
sym_diff s t returns the set of all elements in s or t but not both, also known as the symmetric difference. This is the same as diff (union s t) (inter s t). The returned set uses s's comparison function.
Total ordering between sets. Can be used as the ordering function for doing sets of sets.
equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.
disjoint s1 s2 tests whether the sets s1 and s2 contain no shared elements. (i.e. inter s1 s2 is empty.)
val iter : ('a -> unit) -> 'a t -> unititer f s applies f in turn to all elements of s. The elements of s are presented to f in increasing order with respect to the ordering over the type of the elements.
val at_rank_exn : int -> 'a t -> 'aat_rank_exn i s returns element at rank i in s, that is the i-th element in increasing order (the 0-th element being the smallest element of s).
map f x creates a new set with elements f a0, f a1... f aN, where a0, a1, ..., aN are the elements of x.
This function places no restriction on f; it can map multiple input values to the same output value, in which case the resulting set will have smaller cardinality than the input. f does not need to be order preserving, although if it is, then Incubator.op_map may be more efficient.
map_endo f x creates a new set with elements f a0, f a1... f aN, where a0, a1, ..., aN are the elements of x.
This function places no restriction on f (beyond the type signature being more restricted than for map above); it can map multiple input values to the same output value, in which case the resulting set will have smaller cardinality than the input. f does not need to be order preserving, although if it is, then Incubator.op_map may be more efficient.
This version of map will result in a physically equal map if f returns physically equal keys.
filter p s returns the set of all elements in s that satisfy predicate p.
if p returns true for all elements then s is returned unmodified.
filter_map f m combines the features of filter and map. It calls calls f a0, f a1, f aN where a0,a1..an are the elements of m and returns the set of pairs bi such as f ai = Some bi (when f returns None, the corresponding element of m is discarded).
The resulting map uses the polymorphic compare function to order elements.
filter_map_endo f m combines the features of filter and map. It calls calls f a0, f a1, f aN where a0,a1..an are the elements of m and returns the set of pairs bi such as f ai = Some bi (when f returns None, the corresponding element of m is discarded).
The resulting map uses the polymorphic compare function to order elements.
If the filter function f returns true for all elements in m, the resulting map is physically equal to m.
val fold : ('a -> 'b -> 'b) -> 'a t -> 'b -> 'bfold f s a computes (f xN ... (f x1 (f x0 a))...), where x0,x1..xN are the elements of s, in increasing order.
val exists : ('a -> bool) -> 'a t -> boolexists p s checks if at least one element of the set satisfies the predicate p.
val for_all : ('a -> bool) -> 'a t -> boolReturns whether the given predicate applies to all elements in the set
returns two disjoint subsets, those that satisfy the given predicate and those that don't
split x s returns a triple (l, present, r), where l is the set of elements of s that are strictly less than x; r is the set of elements of s that are strictly greater than x; present is false if s contains no element equal to x, or true if s contains an element equal to x.
split_opt x s returns a triple (l, maybe_v, r), where l is the set of elements of s that are strictly less than x; r is the set of elements of s that are strictly greater than x; maybe_v is None if s contains no element equal to x, or Some v if s contains an element v that compares equal to x.
split_lt x s returns a pair of sets (l, r), such that l is the subset of s with elements < x; r is the subset of s with elements >= x.
split_le x s returns a pair of sets (l, r), such that l is the subset of s with elements <= x; r is the subset of s with elements > x.
val cardinal : 'a t -> intReturn the number of elements of a set.
val elements : 'a t -> 'a listReturn the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering of the given set.
val to_list : 'a t -> 'a listAlias for elements.
val to_array : 'a t -> 'a arraySame as to_list but with an array instead of a list.
val min_elt : 'a t -> 'areturns the smallest element of the set.
val min_elt_opt : 'a t -> 'a optionReturn Some e for the smallest element e of the given set (with respect to the Ord.compare ordering). Return None if the set is empty.
Returns the smallest element of the given set along with the rest of the set. Semantically equivalent and faster than
let mini = min_elt s in (mini, remove mini s)
Returns the biggest element of the given set along with the rest of the set. Semantically equivalent and faster than
let maxi = max_elt s in (maxi, remove maxi s)
val max_elt : 'a t -> 'areturns the largest element of the set.
val max_elt_opt : 'a t -> 'a optionSame as Set.S.min_elt_opt, but for the largest element of the given set.
val choose : 'a t -> 'areturns an arbitrary (but deterministic) element of the given set.
val choose_opt : 'a t -> 'a optionReturn Some e for one element e of the given set. Which element is chosen is unspecified, but equal elements will be chosen for equal sets. Return None if the set is empty.
val any : 'a t -> 'aReturn one element of the given set. The difference with choose is that there is no guarantee that equals elements will be picked for equal sets. This merely returns the quickest element to get (O(1)).
Return an enumeration of all elements of the given set. The returned enumeration is sorted in increasing order with respect to the ordering of this set.
Return an enumeration of all elements of the given set. The returned enumeration is sorted in decreasing order with respect to the ordering Pervasives.compare.
val of_list : 'a list -> 'a tbuilds a set from the given list, using the default comparison function
val of_array : 'a array -> 'a tbuilds a set from the given array, using the default comparison function
to_seq_from x s iterates on a subset of the elements in s, namely those greater or equal to x, in ascending order.
val print :
?first:string ->
?last:string ->
?sep:string ->
('a BatInnerIO.output -> 'c -> unit) ->
'a BatInnerIO.output ->
'c t ->
unitmodule Incubator : sig ... endmodule PSet : sig ... end