package core

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package core
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include S with type bound = Core_kernel.Int.t
type t
val bin_size_t : t Bin_prot.Size.sizer
val bin_write_t : t Bin_prot.Write.writer
val bin_read_t : t Bin_prot.Read.reader
val __bin_read_t__ : (int -> t) Bin_prot.Read.reader
val bin_shape_t : Bin_prot.Shape.t
val bin_writer_t : t Bin_prot.Type_class.writer
val bin_reader_t : t Bin_prot.Type_class.reader
val bin_t : t Bin_prot.Type_class.t
include Ppx_sexp_conv_lib.Sexpable.S with type t := t
val t_of_sexp : Sexplib0.Sexp.t -> t
val sexp_of_t : t -> Sexplib0.Sexp.t
val compare : t -> t -> int
val hash_fold_t : Ppx_hash_lib.Std.Hash.state -> t -> Ppx_hash_lib.Std.Hash.state
val hash : t -> Ppx_hash_lib.Std.Hash.hash_value
type bound = Core_kernel.Int.t
type 'a t_ = t
type 'a bound_ = bound
val empty : 'a t_
val intersect : 'a t_ -> 'a t_ -> 'a t_
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 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 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 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.

val 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.

val to_poly : t -> bound t
module Set : sig ... end
include Core_kernel.Container.S0 with type t := t with type elt := bound
val mem : t -> bound -> bool
val length : t -> int
val is_empty : t -> bool
val iter : t -> f:(bound -> unit) -> unit
val fold : t -> init:'accum -> f:('accum -> bound -> 'accum) -> 'accum
val fold_result : t -> init:'accum -> f:('accum -> bound -> ('accum, 'e) Base__.Result.t) -> ('accum, 'e) Base__.Result.t
val fold_until : t -> init:'accum -> f: ('accum -> bound -> ('accum, 'final) Base__.Container_intf.Continue_or_stop.t) -> finish:('accum -> 'final) -> 'final
val exists : t -> f:(bound -> bool) -> bool
val for_all : t -> f:(bound -> bool) -> bool
val count : t -> f:(bound -> bool) -> int
val sum : (module Base__.Container_intf.Summable with type t = 'sum) -> t -> f:(bound -> 'sum) -> 'sum
val find : t -> f:(bound -> bool) -> bound option
val find_map : t -> f:(bound -> 'a option) -> 'a option
val to_list : t -> bound list
val to_array : t -> bound array
val min_elt : t -> compare:(bound -> bound -> int) -> bound option
val max_elt : t -> compare:(bound -> bound -> int) -> bound option
include Core_kernel.Binary_searchable.S with type t := t with type elt := bound
val binary_search_segmented : (t, bound) Base__.Binary_searchable_intf.binary_search_segmented
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