package pds-reachability

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package pds-reachability
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Class type
type elt = Node.t

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 is_singleton : t -> bool

Test if the set is a singleton.

val singleton : elt -> t

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

val mem : elt -> t -> bool

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

val find : elt -> t -> elt

find x s returns the element in s that tests equal to x under its comparison function.

  • raises Not_found

    if no element is equal

val find_opt : elt -> t -> elt option

find_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

  • since 3.3.0
val find_first : (elt -> bool) -> t -> elt

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.

  • since 3.3.0
val find_first_opt : (elt -> bool) -> t -> elt option

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.

  • since 3.3.0
val find_last : (elt -> bool) -> t -> elt

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.

  • since 3.3.0
val find_last_opt : (elt -> bool) -> t -> elt option

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.

  • since 3.3.0
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.

  • before 3.3.0

    or OCaml 4.03 Physical equality was not ensured.

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.

  • before 3.3.0

    or OCaml 4.03 Physical equality was not ensured.

val remove_exn : elt -> t -> t

remove_exn x s behaves like remove x s except that it raises an exception if x is not in s.

  • raises Not_found

    if x is not in s.

  • since 3.2.0
val update : elt -> elt -> t -> t

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.

  • raises Not_found

    if x is not in s.

  • before 3.3.0

    Physical equality was not ensured.

  • since 2.4
val union : t -> t -> t

Set union.

val inter : t -> t -> t

Set intersection.

val diff : t -> t -> t

Set difference.

val sym_diff : t -> t -> t

sym_diff s t returns the set of all elements in s or t but not both. This is the same as diff (union s t) (inter s t).

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 disjoint : t -> t -> bool

disjoint s1 s2 tests whether the sets s1 and s2 contain no shared elements. (i.e. inter s1 s2 is empty.)

val compare_subset : t -> t -> int

Partial ordering between sets as generated by subset

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 at_rank_exn : int -> t -> elt

at_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).

  • raises Not_found

    if s = empty.

  • raises Invalid_argument

    error_message if i < 0 || i >= cardinal s

  • since 2.4
val map : (elt -> elt) -> t -> t

map f x creates a new set with elements f a0, f a1... f aN, where a0,a1..aN are the values contained in x

if f returns all elements unmodified then x is returned unmodified.

  • before 3.3.0

    Physical equality was not ensured.

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

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.

  • before 3.3.0

    or OCaml 4.03 Physical equality was not ensured.

val filter_map : (elt -> elt option) -> t -> t

filter_map f m combines the features of filter and map. It calls f a0, f a1, f aN where a0,a1..aN are the elements of m and returns the set of elements bi such as f ai = Some bi (when f returns None, the corresponding element of m is discarded).

if f returns true for all elements then s is returned unmodified.

  • before 3.3.0

    Physical equality was not ensured.

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

fold f s a computes (f xN ... (f x1 (f x0 a))...), where x0,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 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 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 split_opt : elt -> t -> t * elt option * t

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.

  • since 2.2.0
val split_lt : elt -> t -> t * t

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.

  • since 2.2.0
val split_le : elt -> t -> t * t

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.

  • since 2.2.0
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 to_list : t -> elt list

Alias for elements.

  • since 2.2.0
val to_array : t -> elt array

Same as to_list but with an array instead of a list.

  • since 2.4
val min_elt : t -> elt

Return the smallest element of the given set (with respect to the Ord.compare ordering).

  • raises Not_found

    if the set is empty.

val min_elt_opt : t -> elt option

Return 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.

  • since 3.3.0
val pop_min : t -> elt * t

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)

  • raises Not_found

    if the set is empty.

  • since 2.4
val pop_max : t -> elt * t

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)

  • raises Not_found

    if the set is empty.

  • since 2.4
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 for the largest element of the given set.

  • since 3.3.0
val choose : t -> elt

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

  • raises Not_found

    if the set is empty.

val choose_opt : t -> elt option

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.

  • since 3.3.0
val any : t -> elt

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)).

  • raises Not_found

    if the set is empty.

val pop : t -> elt * t

returns one element of the set and the set without that element.

  • raises Not_found

    if given an empty set

val enum : t -> elt BatEnum.t

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

val backwards : t -> elt BatEnum.t

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

val of_enum : elt BatEnum.t -> t
val of_list : elt list -> t

builds a set from the given list.

  • since 2.3.0
val of_array : elt array -> t

builds a set from the given array.

  • since 2.4
val to_seq : t -> elt BatSeq.t

Iterate on the whole set, in ascending order.

  • since 3.3.0
val to_rev_seq : t -> elt BatSeq.t

Iterate on the whole set, in descending order.

  • since 3.3.0
val to_seq_from : elt -> t -> elt BatSeq.t

to_seq_from x s iterates on a subset of the elements in s, namely those greater or equal to x, in ascending order.

  • since 3.3.0
val add_seq : elt BatSeq.t -> t -> t

add the given elements to the set, in order.

  • since 3.3.0
val of_seq : elt BatSeq.t -> t

build a set from the given elements

  • since 3.3.0
Boilerplate code
Printing
val print : ?first:string -> ?last:string -> ?sep:string -> ('a BatInnerIO.output -> elt -> unit) -> 'a BatInnerIO.output -> t -> unit
Override modules

The following modules replace functions defined in Set with functions behaving slightly differently but having the same name. This is by design: the functions meant to override the corresponding functions of Set.

module Exceptionless : sig ... end

Operations on Set without exceptions.

module Labels : sig ... end

Operations on Set with labels.

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