module type Gen = sig .. end
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 -> [ `Above | `Below | `Interval_is_empty | `Within ]
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 type Gen_set = sig .. end
type 'a t
type 'a bound
type 'a interval
val create : ('a bound * 'a bound) list -> 'a t
val create_from_intervals : 'a interval list -> 'a t
val contains : 'a t -> 'a bound -> bool
val contains_set : container:'a t -> contained:'a t -> bool
val ubound_exn : 'a t -> 'a bound
val lbound_exn : 'a t -> 'a bound
val ubound : 'a t -> 'a bound option
val lbound : 'a t -> 'a bound option
module type S = sig .. end
type t
type bound
type 'a t_ = t
type 'a bound_ = bound
include Gen with type t := 'a t_ with type bound := 'a bound_
val create : bound -> bound -> t
type 'a poly_t
val to_poly : t -> bound poly_t
type 'a poly_set
module Set : sig .. end with type interval := 'a t_
type t
type 'a t_ = t
include Gen_set with type t := 'a t_ with type bound := 'a bound_
val to_poly : t -> bound poly_set
val t_of_sexp : Sexplib.Sexp.t -> t
val sexp_of_t : t -> Sexplib.Sexp.t
val bin_t : t Bin_prot.Type_class.t
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 t_of_sexp : Sexplib.Sexp.t -> t
val sexp_of_t : t -> Sexplib.Sexp.t
val bin_t : t Bin_prot.Type_class.t
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
module type S1 = sig .. end
type 'a t
type 'a bound_ = 'a
include Gen with type t := 'a t with type bound := 'a bound_
module Set : sig .. end with type bound := 'a bound_ with type interval := 'a t
type 'a t
include Gen_set with type t := '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_t : 'a Bin_prot.Type_class.t -> 'a t Bin_prot.Type_class.t
val bin_read_t : 'a Bin_prot.Read.reader -> 'a t Bin_prot.Read.reader
val __bin_read_t__ : 'a Bin_prot.Read.reader -> (int -> 'a t) Bin_prot.Read.reader
val bin_reader_t : 'a Bin_prot.Type_class.reader -> 'a t Bin_prot.Type_class.reader
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
val bin_writer_t : 'a Bin_prot.Type_class.writer -> 'a t Bin_prot.Type_class.writer
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_t : 'a Bin_prot.Type_class.t -> 'a t Bin_prot.Type_class.t
val bin_read_t : 'a Bin_prot.Read.reader -> 'a t Bin_prot.Read.reader
val __bin_read_t__ : 'a Bin_prot.Read.reader -> (int -> 'a t) Bin_prot.Read.reader
val bin_reader_t : 'a Bin_prot.Type_class.reader -> 'a t Bin_prot.Type_class.reader
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
val bin_writer_t : 'a Bin_prot.Type_class.writer -> 'a t Bin_prot.Type_class.writer