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Module Core.IntervalSource

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.

Sourcetype '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_kernel.Bin_prot.Binable.S1 with type 'a t := 'a t
Sourceval bin_size_t : ('a, 'a t) Bin_prot.Size.sizer1
Sourceval bin_write_t : ('a, 'a t) Bin_prot.Write.writer1
Sourceval bin_read_t : ('a, 'a t) Bin_prot.Read.reader1
Sourceval __bin_read_t__ : ('a, int -> 'a t) Bin_prot.Read.reader1
Sourceval bin_writer_t : ('a, 'a t) Bin_prot.Type_class.S1.writer
Sourceval bin_reader_t : ('a, 'a t) Bin_prot.Type_class.S1.reader
Sourceval bin_t : ('a, 'a t) Bin_prot.Type_class.S1.t
include Ppx_sexp_conv_lib.Sexpable.S1 with type 'a t := 'a t
Sourceval t_of_sexp : (Sexplib0__.Sexp.t -> 'a) -> Sexplib0__.Sexp.t -> 'a t
Sourceval sexp_of_t : ('a -> Sexplib0__.Sexp.t) -> 'a t -> Sexplib0__.Sexp.t
Sourceval compare : ('a -> 'a -> int) -> 'a t -> 'a t -> int
Sourceval 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.

Sourceval empty : 'a t
Sourceval intersect : 'a t -> 'a t -> 'a t
Sourceval is_empty : 'a t -> bool
Sourceval is_empty_or_singleton : 'a t -> bool
Sourceval bounds : 'a t -> ('a * 'a) option
Sourceval lbound : 'a t -> 'a option
Sourceval ubound : 'a t -> 'a option
Sourceval bounds_exn : 'a t -> 'a * 'a
Sourceval lbound_exn : 'a t -> 'a
Sourceval ubound_exn : 'a t -> 'a
Sourceval 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.

Sourceval contains : 'a t -> 'a -> bool
Sourceval compare_value : 'a t -> 'a -> [ `Below | `Within | `Above | `Interval_is_empty ]
Sourceval 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
Sourceval 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.

Sourceval is_subset : 'a t -> of_:'a t -> bool
Sourceval 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].

Sourceval are_disjoint : 'a t list -> bool

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

Sourceval 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.

Sourceval 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.

Sourceval 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.

Sourcemodule 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.

Sourcemodule type S1 = Interval_intf.S1
Sourcemodule type S = Interval_intf.S with type 'a poly_t := 'a t with type 'a poly_set := 'a Set.t
Sourcemodule type S_time = Interval_intf.S_time with type 'a poly_t := 'a t with type 'a poly_set := 'a Set.t

S_time is a signature that's used below to define the interfaces for Time and Time_ns without duplication.

Specialized interval types

Sourcemodule Time : S_time with module Time := Core__.Import_time.Time and type t = Core_kernel.Time.t t
Sourcemodule Float : S with type bound = Core_kernel.Float.t
Sourcemodule Int : sig ... end
Sourcemodule Make (Bound : sig ... end) : S with type bound = Bound.t

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.

Sourcemodule 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.

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