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Module for simple closed intervals over arbitrary types. Used by calling the Make functor with a type that satisfies Base.Comparable (for correctly ordering elements).
Note that the actual interface for intervals is in Interval_intf.Gen, following a Core pattern of defining an interface once in a Gen module, then reusing it across monomorphic (S) and polymorphic (S1, S2, ... SN) variants, where SN denotes a signature of N parameters. Here, S1 is included in this module because the signature of one 'a parameter is the default.
See the documentation of Interval.Make for a more detailed usage example.
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).
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.
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].
are_disjoint ts returns true iff the intervals in ts are pairwise disjoint.
val are_disjoint_as_open_intervals : 'at 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.
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 : 'at 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.
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.
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 applied to the Float, Int, Time, Time_ns, and Ofday intervals.