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

Steffen van Bakel, Maria Grazia Vigliotti
2009 Lecture Notes in Computer Science  
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 term-substitution as well as each reduction step are modelled up to similarity. We then define a notion of type
more » ... t for the π-calculus that uses the type constructor →, and show that all Curry-assignable types are preserved by the encoding.
doi:10.1007/978-3-642-04081-8_7 fatcat:tav3tb74mzdvnaejf4uu5bs5gq