  We show how computation of left Kan extensions can be reduced to computation
of free models of cartesian (finite-limit) theories. We discuss how the
standard and parallel chase compute weakly free models of regular theories and
free models of cartesian theories, and compare the concept of "free model" with
a similar concept from database theory known as "universal model". We prove
that, as algorithms for computing finite free models of cartesian theories, the
standard and parallel chase are complete under fairness assumptions. Finally,
we describe an optimized implementation of the parallel chase specialized to
left Kan extensions that achieves an order of magnitude improvement in our
performance benchmarks compared to the next fastest left Kan extension
algorithm we are aware of.
