package elpi

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package elpi
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Module Set.MakeSource

Parameters

module Ord : OrderedType

Signature

include Set.S with type elt = Ord.t

Sets

Sourcetype elt = Ord.t

The type of the set elements.

Sourcetype t

The type of sets.

Sourceval empty : t

The empty set.

Sourceval 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.

Sourceval singleton : elt -> t

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

Sourceval 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.

Sourceval union : t -> t -> t

Set union.

Sourceval inter : t -> t -> t

Set intersection.

Sourceval disjoint : t -> t -> bool

Test if two sets are disjoint.

  • since 4.08
Sourceval diff : t -> t -> t

Set difference: diff s1 s2 contains the elements of s1 that are not in s2.

Sourceval cardinal : t -> int

Return the number of elements of a set.

Elements

Sourceval 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.

Sourceval 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.

Sourceval 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
Sourceval max_elt : t -> elt

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

Sourceval max_elt_opt : t -> elt option

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

  • since 4.05
Sourceval 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.

Sourceval 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

Searching

Sourceval 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
Sourceval 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
Sourceval 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
Sourceval 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
Sourceval 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
Sourceval 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

Traversing

Sourceval 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.

Sourceval fold : (elt -> 'acc -> 'acc) -> t -> 'acc -> 'acc

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

Transforming

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

filter f s returns the set of all elements in s that satisfy predicate f. If f 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.

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

filter_map f s returns the set of all v such that f x = Some v for some element x of s.

For example,

filter_map (fun n -> if n mod 2 = 0 then Some (n / 2) else None) s

is the set of halves of the even elements of s.

If no element of s is changed or dropped by f (if f x = Some x for each element x), then s is returned unchanged: the result of the function is then physically equal to s.

  • since 4.11
Sourceval partition : (elt -> bool) -> t -> t * t

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

Sourceval 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.

Predicates and comparisons

Sourceval is_empty : t -> bool

Test whether a set is empty or not.

Sourceval mem : elt -> t -> bool

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

Sourceval equal : t -> t -> bool

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

Sourceval compare : t -> t -> int

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

Sourceval subset : t -> t -> bool

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

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

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

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

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

Converting

Sourceval to_list : t -> elt list

to_list s is elements s.

  • since 5.1
Sourceval 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
Sourceval to_seq_from : elt -> t -> elt Seq.t

to_seq_from x s iterates on a subset of the elements of s in ascending order, from x or above.

  • since 4.07
Sourceval to_seq : t -> elt Seq.t

Iterate on the whole set, in ascending order

  • since 4.07
Sourceval to_rev_seq : t -> elt Seq.t

Iterate on the whole set, in descending order

  • since 4.12
Sourceval add_seq : elt Seq.t -> t -> t

Add the given elements to the set, in order.

  • since 4.07
Sourceval of_seq : elt Seq.t -> t

Build a set from the given bindings

  • since 4.07
include Show with type t := t
Sourceval pp : Format.formatter -> t -> unit
Sourceval show : t -> string