Module Interval.Int

include S with type bound = Core__.Import.Int.t
type t
include Bin_prot.Binable.S with type t := t
type t
include Bin_prot.Binable.S_only_functions with type t := t
type t
val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (int -> t) Bin_prot.Read.reader

This function only needs implementation if t exposed to be a polymorphic variant. Despite what the type reads, this does *not* produce a function after reading; instead it takes the constructor tag (int) before reading and reads the rest of the variant t afterwards.

val bin_shape_t : Bin_prot.Shape.t
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_t : t Bin_prot.Type_class.t
include Ppx_sexp_conv_lib.Sexpable.S with type t := t
type t
val t_of_sexp : Sexplib0.Sexp.t -> t
val sexp_of_t : t -> Sexplib0.Sexp.t
val compare : t -> t -> int
val hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
val hash : t -> Base.Hash.hash_value
type bound = Core__.Import.Int.t
type 'a t
type 'a bound

bound is the type of points in the interval (and therefore of the bounds). bound is instantiated in two different ways below: in module type S as a monotype and in module type S1 as 'a.

val create : 'a bound -> 'a bound -> 'a t

create l u returns the interval with lower bound l and upper bound u, unless l > u, in which case it returns the empty interval.

val empty : 'a t
val intersect : 'a t -> 'a t -> 'a t
val is_empty : 'a t -> bool
val is_empty_or_singleton : 'a t -> bool
val bounds : 'a t -> ('a bound * 'a bound) option
val lbound : 'a t -> 'a bound option
val ubound : 'a t -> 'a bound option
val bounds_exn : 'a t -> 'a bound * 'a bound
val lbound_exn : 'a t -> 'a bound
val ubound_exn : 'a t -> 'a bound
val convex_hull : 'a t list -> 'a t

convex_hull ts returns an interval whose upper bound is the greatest upper bound of the intervals in the list, and whose lower bound is the least lower bound of the list.

Suppose you had three intervals a, b, and c:

             a:  (   )
             b:    (     )
             c:            ( )

          hull:  (           )

In this case the hull goes from lbound_exn a to ubound_exn c.

val contains : 'a t -> 'a bound -> bool
val compare_value : 'a t -> 'a bound -> [ `Below | `Within | `Above | `Interval_is_empty ]
val bound : 'a t -> 'a bound -> 'a bound option

bound t x returns None iff is_empty t. If bounds t = Some (a, b), then bound returns Some y where y is the element of t closest to x. I.e.:

        y = a  if x < a
        y = x  if a <= x <= b
        y = b  if x > b
val is_superset : 'a t -> of_:'a t -> bool

is_superset i1 of_:i2 is whether i1 contains i2. The empty interval is contained in every interval.

val is_subset : 'a t -> of_:'a t -> bool
val map : 'a t -> f:('a bound -> 'b bound) -> 'b t

map t ~f returns create (f l) (f u) if bounds t = Some (l, u), and empty if t is empty. Note that if f l > f u, the result of map is empty, by the definition of create.

If you think of an interval as a set of points, rather than a pair of its bounds, then map is not the same as the usual mathematical notion of mapping f over that set. For example, map ~f:(fun x -> x * x) maps the interval [-1,1] to [1,1], not to [0,1].

val are_disjoint : 'a t list -> bool

are_disjoint ts returns true iff the intervals in ts are pairwise disjoint.

val are_disjoint_as_open_intervals : 'a t list -> bool

Returns true iff a given set of intervals would be disjoint if considered as open intervals, e.g., (3,4) and (4,5) would count as disjoint according to this function.

val list_intersect : 'a t list -> 'a t list -> 'a t list

Assuming that ilist1 and ilist2 are lists of disjoint intervals, list_intersect ilist1 ilist2 considers the intersection (intersect i1 i2) of every pair of intervals (i1, i2), with i1 drawn from ilist1 and i2 from ilist2, returning just the non-empty intersections. By construction these intervals will be disjoint, too. For example:

let i = Interval.create;;
list_intersect [i 4 7; i 9 15] [i 2 4; i 5 10; i 14 20];;
[(4, 4), (5, 7), (9, 10), (14, 15)]

Raises an exception if either input list is non-disjoint.

val half_open_intervals_are_a_partition : 'a t list -> bool

Returns true if the intervals, when considered as half-open intervals, nestle up cleanly one to the next. I.e., if you sort the intervals by the lower bound, then the upper bound of the nth interval is equal to the lower bound of the n+1th interval. The intervals do not need to partition the entire space, they just need to partition their union.

val create : bound -> bound -> t

create has the same type as in Gen, but adding it here prevents a type-checker issue with nongeneralizable type variables.

type 'a poly_t
val to_poly : t -> bound poly_t
type 'a poly_set
module Set : sig ... end with type 'a interval := t
include Core__.Import.Container.S0 with type t := t with type elt := bound
type t
type elt
val mem : t -> elt -> bool

Checks whether the provided element is there, using equality on elts.

val length : t -> int
val is_empty : t -> bool
val iter : t -> f:(elt -> unit) -> unit

iter must allow exceptions raised in f to escape, terminating the iteration cleanly. The same holds for all functions below taking an f.

val fold : t -> init:'accum -> f:('accum -> elt -> 'accum) -> 'accum

fold t ~init ~f returns f (... f (f (f init e1) e2) e3 ...) en, where e1..en are the elements of t.

val fold_result : t -> init:'accum -> f:('accum -> elt -> ('accum, 'e) Base.Result.t) -> ('accum, 'e) Base.Result.t

fold_result t ~init ~f is a short-circuiting version of fold that runs in the Result monad. If f returns an Error _, that value is returned without any additional invocations of f.

val fold_until : t -> init:'accum -> f:('accum -> elt -> ('accum, 'final) Base__.Container_intf.Continue_or_stop.t) -> finish:('accum -> 'final) -> 'final

fold_until t ~init ~f ~finish is a short-circuiting version of fold. If f returns Stop _ the computation ceases and results in that value. If f returns Continue _, the fold will proceed. If f never returns Stop _, the final result is computed by finish.

Example:

type maybe_negative =
  | Found_negative of int
  | All_nonnegative of { sum : int }

(** [first_neg_or_sum list] returns the first negative number in [list], if any,
    otherwise returns the sum of the list. *)
let first_neg_or_sum =
  List.fold_until ~init:0
    ~f:(fun sum x ->
      if x < 0
      then Stop (Found_negative x)
      else Continue (sum + x))
    ~finish:(fun sum -> All_nonnegative { sum })
;;

let x = first_neg_or_sum [1; 2; 3; 4; 5]
val x : maybe_negative = All_nonnegative {sum = 15}

let y = first_neg_or_sum [1; 2; -3; 4; 5]
val y : maybe_negative = Found_negative -3
val exists : t -> f:(elt -> bool) -> bool

Returns true if and only if there exists an element for which the provided function evaluates to true. This is a short-circuiting operation.

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

Returns true if and only if the provided function evaluates to true for all elements. This is a short-circuiting operation.

val count : t -> f:(elt -> bool) -> int

Returns the number of elements for which the provided function evaluates to true.

val sum : (module Base__.Container_intf.Summable with type t = 'sum) -> t -> f:(elt -> 'sum) -> 'sum

Returns the sum of f i for all i in the container.

val find : t -> f:(elt -> bool) -> elt option

Returns as an option the first element for which f evaluates to true.

val find_map : t -> f:(elt -> 'a option) -> 'a option

Returns the first evaluation of f that returns Some, and returns None if there is no such element.

val to_list : t -> elt list
val to_array : t -> elt array
val min_elt : t -> compare:(elt -> elt -> int) -> elt option

Returns a min (resp. max) element from the collection using the provided compare function. In case of a tie, the first element encountered while traversing the collection is returned. The implementation uses fold so it has the same complexity as fold. Returns None iff the collection is empty.

val max_elt : t -> compare:(elt -> elt -> int) -> elt option
include Core__.Import.Binary_searchable.S with type t := t with type elt := bound
type elt
type t

See Binary_search.binary_search in binary_search.ml

val binary_search_segmented : (t, elt) Base__.Binary_searchable_intf.binary_search_segmented

See Binary_search.binary_search_segmented in binary_search.ml