Computing with Contexts

We investigate a representation of contexts, expressions with holes in them, that enables them to be meaningfully transformed, in particular α-converted and β-reduced. In particular we generalize the set of λ-expressions to include holes, and on these generalized entities define β-reduction (i.e., substitution) and filling so that these operations preserve α-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.

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