An output - based semantic interpretation of λ in π ( Extended

We define a compositional output-based interpretation of the λ-calculus with explicit substitution into a variant of the π-calculus with pairing, and show that this interpretation preserves full single-step β-reduction (i.e. not just open applicative bisimilarity) with respect to contextual equivalence. For this interpretation, we show the customary operational soundness for β-reduction, adequacy, and operational completeness; using a notion of implicative type-context assignment for the π-calculus, we also show that assignable Curry types are preserved by the interpretation. We finish by showing that termination is preserved for spine reduction with respect to lazy reduction for the π-calculus.