package core_unix

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Module Interval.MakeSource

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

module Bound : sig ... end

Signature

Sourcetype t = Bound.t t
include Core.Bin_prot.Binable.S with type t := t
include Bin_prot.Binable.S_only_functions with type t := t
Sourceval bin_size_t : t Bin_prot.Size.sizer
Sourceval bin_write_t : t Bin_prot.Write.writer
Sourceval bin_read_t : t Bin_prot.Read.reader
Sourceval __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.

Sourceval bin_shape_t : Bin_prot.Shape.t
include Sexplib0.Sexpable.S with type t := t
Sourceval t_of_sexp : Sexplib0.Sexp.t -> t
Sourceval sexp_of_t : t -> Sexplib0.Sexp.t
include Ppx_compare_lib.Comparable.S with type t := t
Sourceval compare : t -> t -> int
include Ppx_hash_lib.Hashable.S with type t := t
Sourceval hash_fold_t : Base.Hash.state -> t -> Base.Hash.state
Sourcetype bound = Bound.t
Sourceval empty : t
Sourceval intersect : t -> t -> t
Sourceval is_empty : t -> bool
Sourceval is_empty_or_singleton : t -> bool
Sourceval bounds : t -> (bound * bound) option
Sourceval lbound : t -> bound option
Sourceval ubound : t -> bound option
Sourceval bounds_exn : t -> bound * bound
Sourceval lbound_exn : t -> bound
Sourceval ubound_exn : t -> bound
Sourceval convex_hull : t list -> 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.

Sourceval contains : t -> bound -> bool
Sourceval compare_value : t -> bound -> [ `Below | `Within | `Above | `Interval_is_empty ]
Sourceval bound : t -> bound -> 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
Sourceval is_superset : t -> of_:t -> bool

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

Sourceval is_subset : t -> of_:t -> bool
Sourceval map : t -> f:(bound -> bound) -> 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].

Sourceval are_disjoint : t list -> bool

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

Sourceval are_disjoint_as_open_intervals : 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.

Sourceval list_intersect : t list -> t list -> 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.

Sourceval half_open_intervals_are_a_partition : 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.

Sourceval 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.

Sourceval to_poly : t -> bound t
Sourcemodule Set : sig ... end
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