Abstract

Effect and session type systems are two expressive behavioural type systems. The former is usually developed in the context of the λ- calculus and its variants, the latter for the π-calculus. In this talk, I explore their relative expressive power. Firstly, I give an embedding from PCF , augmented with a parameterised effect system, into a session-typed π-calculus (session calculus), showing that session types are powerful enough to express effects. Secondly, I give a reverse embedding, from the session calculus back into PCF , by instantiating PCF with concurrency primitives and its effect system with a session-like effect algebra; effect systems are powerful enough to express sessions. The embedding of session types into an effect system is leveraged to give a new implementation of session types in Haskell, via an effect system encoding. The correctness of this implementation follows from the second embedding result. This is joint work with Nobuko Yoshida, presented at POPL ’16.