Rewriting the Conditions in Conditional Rewriting

Category theory has been used to provide a semantics for term rewriting systems at an intermediate level of abstraction between the actual syntax and the relational model. Recently we have developed a semantics for TRSs using monads which generalises the equivalnece between algebraic theories and nitary monads on the category Sets. This semantics underpins the recent categorical proofs of state-of-the-art results in modular rewriting. We believe that our methods can be applied to modularity for conditional rewriting where several open problems exist. Any results we achieve here would be highly signiicant as, for the rst time, substantial open problems in rewriting would have been solved using categorical techniques. This paper reports on the rst step in this project, namely the construction of a semantics for CTRS using monads.