IntervalAlgebra

A C extension module for Python implementing a basic Interval type and the key relations of Allen's Interval Algebra.

This was primarily a quick toy project for me to familiarise myself with some of the intracacies of the CPython API. It may be a useful starting point for something more ambitious and serves as a usable type in the meantime.

Installation

Clone the repository and then python setup.py install should work. Run pytest at the command line to run the tests. I've only tried the module with Python 3.6 on Linux. Other versions of Python 3 on other operating systems should work fine, but Python 2 probably won't be compatible.

Examples

An interval captures a (possibly infinite) collection of points between a left bound and a right bound. For instance a has a left bound of 3 and a right bound of 7. Intervals are closed, meaning that the bounds are included in the set of points belonging to the interval:

>>> from interval import interval
>>> a = interval(3, 7)
>>> a
interval(3, 7)
>>> 5.89 in a
True
>>> 3 in a # the interval is closed
True
>>> 0 in a
False

The left and right attributes can theoretically be any Python objects at all, but must satisfy left < right. You can also add metadata (any Python object you like) to an interval when it is created. The .span() method shows the length of the interval:

>>> a.span()
4
>>> from datetime import datetime
>>> feb2000 = interval(datetime(2000, 2, 1), datetime(2000, 2, 29), 'leap month!')
>>> feb2000.data
'Leap month!'
>>> feb2000.span()
timedelta(28)

Intervals are compared by looking at the left and right attributes internally. One interval is strictly greater than another if ends before the other begins:

>>> b = interval(6, 12)
>>> a == b # equivalent to a.equals(b)
False
>>> a < b  # equivalent to a.before(b)
False
>>> a > b  # equivalent to a.after(b)
False

Note the <= and >= are not supported as they are ambiguous in the context of Allen's Interval Algebra.

We can also test if there is any overlap between two intervals (i.e. they contain common points - not just an endpoint). Two intervals are said to meet if the left of one equals the right of the other:

>>> c = interval(0, 3)
>>> a.overlaps(b)
True
>>> a.meets(c) # they meet at 3
True
>>> b.overlaps(c)
False

An interval may occur during another, or it may start or finish another interval:

>>> x = interval(0, 5)
>>> interval(1, 2).during(x)
True
>>> interval(0, 2).starts(x)
True
>>> interval(1, 5).finishes(x)
True
>>> interval(4, 7).during(x)
False

Future work

Given more time and fewer distractions, I'll add more of Python's object protocol for the class (hashing, pickling, alternative constructors). Allen's original paper contains an algorithm for reasoning on temporal intervals that may be insightful to implement.