# A Journey from Total to Partial Algebras

## Uwe Wolter

(Bergen)

Partial Algebras have the reputation of being difficult in theory and

practice. Their bad reputation arises from the fact that many concepts

known from Total Algebras split up into at least three different

concepts in the context of Partial Algebras.

In our talk we argue that partiality is not too complicated at all.

Especially if seen from Algebraic Specification, Partial Algebras turn

out to be only slighty more difficult to understand and to use than

Total Algebras.

We revise basic concepts and constructions such as algebra,

homomorphism, subalgebra, congruence, quotient algebra, initial

algebra, (conditional) equations,..., and discuss the changes emerging

by moving from Total Algebras to Partial Algebras.

**Thursday 25th May 2006, 14:00**

Robert Recorde Room

Department of Computer Science