package mopsa

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package mopsa
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type elt = int

The type of the set elements.

type t

The type of sets.

val empty : t

The empty set.

val is_empty : t -> bool

Test whether a set is empty or not.

val mem : elt -> t -> bool

mem x s tests whether x belongs to the set s.

val add : elt -> t -> t

add x s returns a set containing all elements of s, plus x. If x was already in s, s is returned unchanged (the result of the function is then physically equal to s).

  • before 4.03

    Physical equality was not ensured.

val singleton : elt -> t

singleton x returns the one-element set containing only x.

val remove : elt -> t -> t

remove x s returns a set containing all elements of s, except x. If x was not in s, s is returned unchanged (the result of the function is then physically equal to s).

  • before 4.03

    Physical equality was not ensured.

val union : t -> t -> t

Set union.

val inter : t -> t -> t

Set intersection.

val diff : t -> t -> t

Set difference.

val compare : t -> t -> int

Total ordering between sets. Can be used as the ordering function for doing sets of sets.

val equal : t -> t -> bool

equal s1 s2 tests whether the sets s1 and s2 are equal, that is, contain equal elements.

val subset : t -> t -> bool

subset s1 s2 tests whether the set s1 is a subset of the set s2.

val iter : (elt -> unit) -> t -> unit

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.

val map : (elt -> elt) -> t -> t

map f s is the set whose elements are f a0,f a1... f aN, where a0,a1...aN are the elements of s.

The elements are passed to f in increasing order with respect to the ordering over the type of the elements.

If no element of s is changed by f, s is returned unchanged. (If each output of f is physically equal to its input, the returned set is physically equal to s.)

  • since 4.04.0
val fold : (elt -> 'a -> 'a) -> t -> 'a -> 'a

fold f s a computes (f xN ... (f x2 (f x1 a))...), where x1 ... xN are the elements of s, in increasing order.

val for_all : (elt -> bool) -> t -> bool

for_all p s checks if all elements of the set satisfy the predicate p.

val exists : (elt -> bool) -> t -> bool

exists p s checks if at least one element of the set satisfies the predicate p.

val filter : (elt -> bool) -> t -> t

filter p s returns the set of all elements in s that satisfy predicate p. If p satisfies every element in s, s is returned unchanged (the result of the function is then physically equal to s).

  • before 4.03

    Physical equality was not ensured.

val partition : (elt -> bool) -> t -> t * t

partition p s returns a pair of sets (s1, s2), where s1 is the set of all the elements of s that satisfy the predicate p, and s2 is the set of all the elements of s that do not satisfy p.

val cardinal : t -> int

Return the number of elements of a set.

val elements : t -> elt list

Return the list of all elements of the given set. The returned list is sorted in increasing order with respect to the ordering Ord.compare, where Ord is the argument given to Set.Make.

val min_elt : t -> elt

Return the smallest element of the given set (with respect to the Ord.compare ordering), or raise Not_found if the set is empty.

val min_elt_opt : t -> elt option

Return the smallest element of the given set (with respect to the Ord.compare ordering), or None if the set is empty.

  • since 4.05
val max_elt : t -> elt

Same as Set.S.min_elt, but returns the largest element of the given set.

val max_elt_opt : t -> elt option

Same as Set.S.min_elt_opt, but returns the largest element of the given set.

  • since 4.05
val choose : t -> elt

Return one element of the given set, or raise Not_found if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.

val choose_opt : t -> elt option

Return one element of the given set, or None if the set is empty. Which element is chosen is unspecified, but equal elements will be chosen for equal sets.

  • since 4.05
val split : elt -> t -> t * bool * 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.

val find : elt -> t -> elt

find x s returns the element of s equal to x (according to Ord.compare), or raise Not_found if no such element exists.

  • since 4.01.0
val find_opt : elt -> t -> elt option

find_opt x s returns the element of s equal to x (according to Ord.compare), or None if no such element exists.

  • since 4.05
val find_first : (elt -> bool) -> t -> elt

find_first f s, where f is a monotonically increasing function, returns the lowest element e of s such that f e, or raises Not_found if no such element exists.

For example, find_first (fun e -> Ord.compare e x >= 0) s will return the first element e of s where Ord.compare e x >= 0 (intuitively: e >= x), or raise Not_found if x is greater than any element of s.

  • since 4.05
val find_first_opt : (elt -> bool) -> t -> elt option

find_first_opt f s, where f is a monotonically increasing function, returns an option containing the lowest element e of s such that f e, or None if no such element exists.

  • since 4.05
val find_last : (elt -> bool) -> t -> elt

find_last f s, where f is a monotonically decreasing function, returns the highest element e of s such that f e, or raises Not_found if no such element exists.

  • since 4.05
val find_last_opt : (elt -> bool) -> t -> elt option

find_last_opt f s, where f is a monotonically decreasing function, returns an option containing the highest element e of s such that f e, or None if no such element exists.

  • since 4.05
val of_list : elt list -> t

of_list l creates a set from a list of elements. This is usually more efficient than folding add over the list, except perhaps for lists with many duplicated elements.

  • since 4.02.0

Additional functions

val iter2 : (elt -> unit) -> (elt -> unit) -> (elt -> unit) -> t -> t -> unit

iter2 f1 f2 f s1 s2 applies f1 to the elements only in s1, f2 to the elements only in s2, and f to the elements in both s1 and s2. The elements are considered in increasing order.

val fold2 : (elt -> 'a -> 'a) -> (elt -> 'a -> 'a) -> (elt -> 'a -> 'a) -> t -> t -> 'a -> 'a

fold2 f1 f2 f s1 s2 acc applies f1 to the elements only in s1, f2 to the elements only in s2, and f to the elements both in s1 and s2. The elements are considered in increasing order.

val for_all2 : (elt -> bool) -> (elt -> bool) -> (elt -> bool) -> t -> t -> bool

for_all2 f1 f2 f s1 s2 is true if f1 is true on all the elements only in s1, f2 is true on all the elements only in s2, and f is true on all the elements both in s1 and s2. The elements are considered in increasing order.

val exists2 : (elt -> bool) -> (elt -> bool) -> (elt -> bool) -> t -> t -> bool

exists2 f1 f2 f s1 s2 is true if f1 is true on one element only in s1, or f2 is true on one element only in s2, or f is true on one element both in s1 and s2. The elements are considered in increasing order.

val iter2_diff : (elt -> unit) -> (elt -> unit) -> t -> t -> unit

iter2_diff f1 f2 s1 s2 applies f1 to the elements only in s1 and f2 to the elements only in s2. The elements both in s1 and s2 are ignored. The elements are considered in increasing order. It is equivalent to calling iter2 with f = ignore, but more efficient.

val fold2_diff : (elt -> 'a -> 'a) -> (elt -> 'a -> 'a) -> t -> t -> 'a -> 'a

fold2_diff f1 f2 s1 s2 applies f1 to the elements only in s1 and f2 to the elements only in s2. The elements both in s1 and s2 are ignored. The elements are considered in increasing order. It is equivalent to calling fold2 with f = fun v acc -> acc, but more efficient.

val for_all2_diff : (elt -> bool) -> (elt -> bool) -> t -> t -> bool

for_all2_diff f1 f2 f s1 s2 is true if f1 is true on all the elements only in s1 and f2 is true on all the elements only in s2. The elements both in s1 and s2 are ignored. The elements are considered in increasing order. It is equivalent to calling for_all2 with f = fun x -> true, but more efficient.

val exists2_diff : (elt -> bool) -> (elt -> bool) -> t -> t -> bool

exists2_diff f1 f2 f s1 s2 is true if f1 is true on one element only in s1 or if f2 is true on one element only in s2. The elements both in s1 and s2 are ignored. The elements are considered in increasing order. It is equivalent to calling exists2 with f = fun x -> false, but more efficient.

val diff_list : t -> t -> elt list

diff_list s1 s2 returns the list of elements in s1 and not s2.

val sym_diff_list : t -> t -> elt list * elt list

symb_diff_list s1 s2 returns the list of elements in s1 and not s2, and the list of elements in s2 and not in s1.

val add_sym_diff : t -> (elt list * elt list) -> t

add_sym_diff s2 d returns s1 assuming that d = sym_diff_list s1 s2, i.e., it reconstructs a set given its symmetric difference with another set.

val iter_slice : (elt -> unit) -> t -> elt -> elt -> unit

iter_slice f m k1 k2 is similar to iter f m, but only calls f on elements greater or equal to k1 and smaller or equal to k2. It is as if, outside this range, f k has no effect. The elements are considered in increasing order.

val fold_slice : (elt -> 'a -> 'a) -> t -> elt -> elt -> 'a -> 'a

fold_slice f m k1 k2 a is similar to fold f m, but only calls f on elements greater or equal to k1 and smaller or equal to k2. It is as if, outside this range, f k x = x and has no effect. The elements are considered in increasing order.

val for_all_slice : (elt -> bool) -> t -> elt -> elt -> bool

for_all_slice f m k1 k2 a is similar to for_all f m, but only calls f on elements greater or equal to k1 and smaller or equal to k2. It is as if, outside this range, f k = true and has no effect. The elements are considered in increasing order.

val exists_slice : (elt -> bool) -> t -> elt -> elt -> bool

exists_slice f m k1 k2 a is similar to exists f m, but only calls f on elements greater or equal to k1 and smaller or equal to k2. It is as if, outside this range, f k = false and has no effect. The elements are considered in increasing order.

Printing

val to_string : SetExtSig.set_printer -> (elt -> string) -> t -> string

String representation.

val print : SetExtSig.set_printer -> (Stdlib.out_channel -> elt -> unit) -> Stdlib.out_channel -> t -> unit

Prints to an output_channel (for Printf.(f)printf).

val fprint : SetExtSig.set_printer -> (Stdlib.Format.formatter -> elt -> unit) -> Stdlib.Format.formatter -> t -> unit

Prints to a formatter (for Format.(f)printf).

val bprint : SetExtSig.set_printer -> (Stdlib.Buffer.t -> elt -> unit) -> Stdlib.Buffer.t -> t -> unit

Prints to a string buffer (for Printf.bprintf).

Translation to polymorphic sets

val to_poly_set : t -> elt SetExtPoly.t
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