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# ModuleInterval

Module for simple closed intervals over arbitrary types that are ordered correctly using polymorphic compare.

### Signature

module type S1 = Interval_intf.S1
include S1
type 'a t
val t_of_sexp : (Sexplib.Sexp.t -> 'a) -> Sexplib.Sexp.t -> 'a t
val sexp_of_t : ('a -> Sexplib.Sexp.t) -> 'a t -> Sexplib.Sexp.t
val bin_size_t : 'a Bin_prot.Size.sizer -> 'a t Bin_prot.Size.sizer
val bin_write_t : 'a Bin_prot.Write.writer -> 'a t Bin_prot.Write.writer
type 'a bound_ = 'a
include Interval_intf.Gen with type 'a t := 'a t with type 'a bound := 'a bound_
type 'a t
type 'a bound

Module for simple closed intervals over arbitrary types that are ordered correctly using polymorphic compare.

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 create 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 upperbound is the greatest upperbound of the intervals in the list, and whose lowerbound is the least lowerbound of the list.

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 one thinks 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, ~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. i.e., (3,4) and (4,5) would count as disjoint.

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 returns the list of disjoint intervals that correspond to the intersection of ilist1 with ilist2.

val half_open_intervals_are_a_partition : 'a t list -> bool
module Set : sig .. end
module type S = Interval_intf.S with type 'a poly_t := 'a t with type 'a poly_set := 'a Set.t
module Make (Bound : sig .. end) : S with type bound = Bound.t
module Float : S with type bound = Core_kernel.Std.Float.t
module Int : sig .. end
module Time : sig .. end
module Ofday : S with type bound = Ofday.t
module Stable : sig .. end