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Programming language: Haskell
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The interval-algebra package implements Allen's interval algebra in Haskell. The main module provides data types and related classes for the interval-based temporal logic described in Allen (1983) and axiomatized in Allen and Hayes (1987).

A good primer on Allen's algebra can be found here.


The module is built around three typeclasses designed to separate concerns of constructing, relating, and combining Intervals:

  1. Intervallic provides an interface to the data structure of an Interval, defining how an Interval a (simply a pair (a, a)) is constructed.
  2. IntervalAlgebraic provides an interface to the IntervalRelations, the workhorse of Allen's temporal logic.
  3. IntervalCombinable provides an interface to methods of combining multiple Intervals.

An advantage of nested typeclass design is that developers can define an Interval of type a with just the amount of structure that they need.

Total Ordering of Intervals

The modules makes the (opinionated) choice of a total ordering for Intervallic Intervals. Namely, the ordering is based on first ordering the begins then the ends.

Axiom tests

The package [includes tests](test/IntervalAlgebraSpec.hs) that the functions of the IntervalAlgebraic typeclass meets the axioms for intervals (not points) as laid out in Allen and Hayes (1987).


This module is under development and the API may change in the future.