Functions as session-typed processes

Authors:
Bernardo Toninho;Luis Caires;Frank Pfenning
Affiliations:
Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA and CITI and Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisboa, Portugal;CITI and Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisboa, Portugal;Computer Science Department, Carnegie Mellon University, Pittsburgh, PA
Venue:
FOSSACS'12 Proceedings of the 15th international conference on Foundations of Software Science and Computational Structures
Year:
2012

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Abstract

We study type-directed encodings of the simply-typed λ-calculus in a session-typed π-calculus. The translations proceed in two steps: standard embeddings of simply-typed λ-calculus in a linear λ-calculus, followed by a standard translation of linear natural deduction to linear sequent calculus. We have shown in prior work how to give a Curry-Howard interpretation of the proofs in the linear sequent calculus as π-calculus processes subject to a session type discipline. We show that the resulting translations induce sharing and copying parallel evaluation strategies for the original λ-terms, thereby providing a new logically motivated explanation for these strategies.