The π-calculus as a Universal Model of Computation

Using a novel approach, we define a compositional output -based encoding of the λ-calculus with explicit substitution into a variant of the π-calculus with pairing, and show that this encoding preserves full β-reduction (i.e. not just lazy) as well as assignable types. Furthermore, we apply this new approach to the context of sequent calculi (which embody both parameter and context call) by defining a new encoding of the calculus λμμ̃; we show that this encodings is strong, in the sense that it too preserves all λμμ̃-reduction (i.e. not just outermost reduction), and in the sense that the implicative fragment of classical logic can be embedded in to the π-calculus via the preservation of assignable contexts. These results show that the π-calculus is indeed a universal model of computation for both concurrent and sequential paradigms, and fully represents both parameter and context call, as well as functional composition.