Compilation of combinatory reduction systems

Combinatory Reduction Systems generalise Term Rewriting Systems. They are powerful enough to express β-reduction of λ-calculus as a single rewrite rule. The additional expressive power has its price — CRSs are much harder to implement than ordinary TRSs.

We propose an abstract machine suitable for executing CRSs. We define what it means to execute an instruction, and give a translation from CRS rules into sequences of instructions. Applying a rewrite rule to a term is realised by initialising the machine with this term, and then successively executing the instructions of the compiled rule.