• DOI:10.1007/978-3-642-04081-8_7
• Corpus ID: 9474146

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

@inproceedings{Bakel2009ALI,
  title={A Logical Interpretation of the $\lambda$-Calculus into the $\pi$-Calculus, Preserving Spine Reduction and Types},
  author={Steffen van Bakel and Maria Grazia Vigliotti},
  booktitle={CONCUR},
  year={2009}
}

• S. V. Bakel, M. Vigliotti
• Published in CONCUR 1 September 2009
• Computer Science

We define a new, output-based encoding of the λ -calculus into the asynchronous η -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 assignment for the η -calculus that uses the type constructor →, and show that all Curry-assignable types are preserved by the encoding.