Module Interval_lib.Interval

Intervals using polymorphic compare

This part of the interface is for polymorphic intervals, which are well ordered by polymorphic compare. Using this with types that are not (like sets) will lead to crazy results.

type 'a t

This type t supports bin-io and sexp conversion by way of the [@@deriving bin_io, sexp] extensions, which inline the relevant function signatures (like bin_read_t and t_of_sexp).

include Core.Bin_prot.Binable.S1__local with type 'a t := 'a t
val bin_shape_t : Bin_prot.Shape.t -> Bin_prot.Shape.t
include sig ... end
val bin_size_t : 'a. ('a, 'a t) Bin_prot.Size.sizer1
val bin_write_t : 'a. ('a, 'a t) Bin_prot.Write.writer1
val bin_read_t : 'a. ('a, 'a t) Bin_prot.Read.reader1
val __bin_read_t__ : 'a. ('a, 'a t) Bin_prot.Read.vtag_reader1
val bin_writer_t : 'a. ('a, 'a t) Bin_prot.Type_class.S1.writer
val bin_reader_t : 'a. ('a, 'a t) Bin_prot.Type_class.S1.reader
val bin_t : 'a. ('a, 'a t) Bin_prot.Type_class.S1.t
include Sexplib0.Sexpable.S1 with type 'a t := 'a t
val t_of_sexp : 'a. (Sexplib0.Sexp.t -> 'a) -> Sexplib0.Sexp.t -> 'a t
val sexp_of_t : 'a. ('a -> Sexplib0.Sexp.t) -> 'a t -> Sexplib0.Sexp.t
include Ppx_compare_lib.Comparable.S1 with type 'a t := 'a t
val compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
include Ppx_compare_lib.Comparable.S1__local with type 'a t := 'a t
include Ppx_compare_lib.Equal.S1 with type 'a t := 'a t
val equal : ('a -> 'a -> bool) -> 'a t -> 'a t -> bool
include Ppx_compare_lib.Equal.S1__local with type 'a t := 'a t
include Ppx_hash_lib.Hashable.S1_any with type 'a t := 'a t
val create : 'a -> 'a -> '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 * 'a) option
val lbound : 'a t -> 'a option
val ubound : 'a t -> 'a option
val bounds_exn : 'a t -> 'a * 'a
val lbound_exn : 'a t -> 'a
val ubound_exn : 'a t -> 'a
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 -> bool
val compare_value : 'a t -> 'a -> [ `Below | `Within | `Above | `Interval_is_empty ]
val bound : 'a t -> 'a -> 'a 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 -> 'b) -> '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.

module Set : sig ... end

Type-specialized intervals

The module type S is used to define signatures for intervals over a specific type, like Interval.Ofday (whose bounds are Time.Ofday.t) or Interval.Float, whose bounds are floats.

Note the heavy use of destructive substitution, which removes the redefined type or module from the signature. This allows for clean type constraints in codebases, like Core's, where there are lots of types going by the same name (e.g., "t").

Signatures

The following signatures are used for specifying the types of the type-specialized intervals.

module type S1 = sig ... end
module type S = sig ... end
module type S_time = sig ... end

Specialized interval types

module Ofday : sig ... end
module Ofday_ns : sig ... end
module Time : sig ... end
module Time_ns : sig ... end
module Float : sig ... end
module Int : sig ... end
module Make (Bound : sig ... end) : sig ... end

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.

module Stable : sig ... end

Stable is used to build stable protocols. It ensures backwards compatibility by checking the sexp and bin-io representations of a given module. Here it's also applied to the Float, Int, Time, Time_ns, and Ofday intervals.