A Logical Interpretation of the λ-Calculus into the π-Calculus, Preserving Spine Reduction and Types

We define a new, output-based encoding of the λ-calculus into the asynchronous π-calculus – enriched with pairing – that has its origin in mathematical logic, and show that this encoding respects one-step spine-reduction up to substitution, and that normal substitution is respected up to similarity. We will also show that it fully encodes lazy reduction of closed terms, in that termsubstitution as well as each reduction step are modelled up to similarity. We then define a notion of type assignment for the π-calculus that uses the type constructor →, and show that all Curry-assignable types are preserved by the encoding.