Module Core.Interval.Make

Interval.Make is a functor that takes a type that you'd like to create intervals for and returns a module with functions over intervals of that type.

For example, suppose you had a Percent.t type and wanted to work with intervals over it, i.e., inclusive ranges like 40-50% or 0-100%. You would create your Percent_interval module by calling:

module Percent_interval = Interval.Make(Percent)

You now have a module with lots of functionality ready to use. For instance you could call Percent_interval.empty to create an empty interval, or:

Percent_interval.create (Percent.of_percentage 3) (Percent.of_percentage 30)

to get an actual interval that ranges from 3% to 30%. You can then ask questions of this interval, like whether it's a subset of another interval or whether it contains a particular value.

NB. In order to use the Interval.Make functor, your type must satisfy Comparable and support bin-io and s-expression conversion. At a minimum, then, Percent must look like this:

      module Percent = struct
        module T = struct
          type t = float [@@deriving bin_io, compare, sexp]
        end
        include T
        include Comparable.Make_binable(T)
      end

Parameters

Bound : sig ... end

Signature

type t
include sig ... end
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (int ‑> t) Bin_prot.Read.reader
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_shape_t : Bin_prot.Shape.t
val t_of_sexp : Base.Sexp.t ‑> t
val sexp_of_t : t ‑> Base.Sexp.t
type bound = Bound.t
type 'a t_ = t
type 'a bound_ = bound
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 := a t_