Computing with Contexts

We investigate a representation of contexts, expressions with holes in them, that enables them to be meaningfully transformed, in particular -converted and -reduced. In particular we generalize the set of -expressions to include holes, and on these generalized entities define -reduction (i.e., substitution) and filling so that these operations preserve -congruence and commute. The theory is then applied to allow the encoding of reduction systems and operational semantics of call-by-value calculi enriched with control, imperative and concurrent features.