# Conditional Term Rewriting Systems Via Enriched Monads

Neil Ghani (University of Birmingham) LFCS Theory Seminar Room 2511, JCMB, King's Buildings 4pm, Tuesday 28th October 1997

Monads can be used to give a syntax-free presentation of algebraic theories such as monoids, groups etc. Infact, by enriching the theory many of the structures of use in category theory (SMC's, SMCC's, CCC's etc, w-CPO's) can also be seen as algebraic theories. Using this general framework, I will show that term rewriting systems are also algebraic and then ask the same question of conditional term rewriting systems.

A priori the answer should be no as CTRSs have the feel of essentially algebraic theories. However, I shall show that we can get around this problem by using a base category of algebras in which the conditions of a CTRS can be interpreted. I shall conclude by discussing the obstactles to applying this observation to problems in modular rewriting.

This is joint work with Stefan Kahrs and Christoph Lueth