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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.
The 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.
find_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.
find_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.
find_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.
find_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.
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.
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.
iter 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.
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_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.
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.
Return 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.
Return 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.