Intervals of ordered types, and their monoids under union.

There are many implementations of intervals on Hackage:

• intervals
  • Has a nonempty variant
  • Geared toward numerical computation
• numbers
  • Self-described as incomplete
• data-interval
  • Sophisticated library with many utilities and boundary handling
  • Implements Allen's interval algebra

This package aims to simplify working with intervals by providing several patterns on which to match, many of which are bidirectional (and hence can also be used as constructors). The patterns are designed to be mnemonically significant, so that dealing with Bound types is conveniently swept under the rug.

Another strong use case for this library is its use of Allen's interval algebra. Unlike in data-interval, where the relationship is essentially meaningless, this library turns it into a proof-relevant structure that demonstrates exactly how two intervals may relate, by decomposing them into the parts that constitute the relationship itself. See Data.Interval.adjacency for details.

Also like data-interval, this package provides a monoid under union (which we call Borel as opposed to IntervalSet), as well as a slightly different version of IntervalMap which is named Layers. This latter monoid preserves the overlap of the intervals as they get inserted, as opposed to agglomerating overlapping intervals as would be the case with Borel. This allows complex calculations, that could otherwise be modelled as integrals of step functions.