2017/11/02 by Bernardo Toninho, Nobuko Yoshida, Toninho, Bernardo +1
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, programming, and type systems #Programming Languages (cs.PL) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1711.00878
openalex publication_date 2017/11/02 · openalex created_date 2017/11/17 · openalex updated_date 2026/07/28
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the soundness and completeness of sequent calculus and natural deduction presentations of linear logic, we develop the first mutually inverse and fully abstract processes-as-functions and functions-as-processes encodings between a polymorphic session pi-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the lambda-calculus: (1) we obtain a characterisation of inductive and coinductive session types via their algebraic representations in System F; and (2) we extend our results to account for value and process passing, entailing strong normalisation.