Span Algebra

This is a simple F# library to compute intersections and unions on list of spans.

Operations

Type

But, what is a span ? It is a type with a value spanning on an interval [start, end[ (ie: start is included but end is not). Also, according to the definition, the interval can't be empty.

Type has constraints:

start and end can be whatever you want until it's comparable (intersection & union)
value can also be whatever you want until it's equatable (merge)

type Span<'t, 'v when 't : comparison and 'v : equality> = 
    { Start : 't
      Stop : 't
      Value : 'v}

Several operations are defined:

new (Span.create): validate parameters and create a new Span.
intersection (Span.intersect): compute the intersection of two lists. A combinator is applied for resulting spans.
union (Span.union): compute the union of two lists. A combinator is applied for resulting spans.
merge (Span.merge): merge adjacent spans if possible.
fill (Span.fill): fill holes with a default value.
validate (Span.validate): check for correctness.

Warnings:

the list of spans must be ordered with no overlaps before using operations. It's better to build a list using Span.union. If you are not sure, use Span.validate to check for correctness.
Span can be constructed directly but it's advised to build them using Span.create. Again you can use Span.validate to check for correctness.

Intersection

Compute the intersection of two lists of spans.

input1:
  [0, 1[ = A
  [4, 5[ = A
  [7, 10[ = A
  [13, 15[ = A
  [17, 20[ = A
  [25, 200[ = A

input2:
  [2, 3[ = B
  [5, 6[ = B
  [8, 11[ = B
  [12, 14[ = B
  [16, 21[ = B
  [26, 40[ = B
  [45, 50[ = B
  [80, 100[ = B

result:
  [8, 10[ = AnB
  [13, 14[ = AnB
  [17, 20[ = AnB
  [26, 40[ = AnB
  [45, 50[ = AnB
  [80, 100[ = AnB

Union

Compute the union of two lists of spans.

input1:
  [0, 1[ = A
  [4, 5[ = A
  [7, 10[ = A
  [13, 15[ = A
  [17, 20[ = A
  [25, 200[ = A

input2:
  [2, 3[ = B
  [5, 6[ = B
  [8, 11[ = B
  [12, 14[ = B
  [16, 21[ = B
  [26, 40[ = B
  [45, 50[ = B
  [80, 100[ = B

result:
  [0, 1[ = A
  [2, 3[ = B
  [4, 5[ = A
  [5, 6[ = B
  [7, 8[ = A
  [8, 10[ = AnB
  [10, 11[ = B
  [12, 13[ = B
  [13, 14[ = AnB
  [14, 15[ = A
  [16, 17[ = B
  [17, 20[ = AnB
  [20, 21[ = B
  [25, 26[ = A
  [26, 40[ = AnB
  [40, 45[ = A
  [45, 50[ = AnB
  [50, 80[ = A
  [80, 100[ = AnB
  [100, 200[ = A

Merge

Merge adjacent spans of a list.

input:
  [0, 1[ = A
  [2, 3[ = A
  [3, 10[ = A
  [13, 15[ = B
  [15, 20[ = B

result:
  [0, 1[ = A
  [2, 10[ = A
  [13, 20[ = B

pchalamet / SpanAlgebra