Functions as Session-Typed Processes

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.