Intrinsically Typed Sessions with Callbacks (Functional Pearl)

All formalizations of session types rely on linear types for soundness as session-typed communication channels must change their type at every operation. Embedded language implementations of session types follow suit. They either rely on clever typing constructions to guarantee linearity statically, or on run-time checks that approximate linearity. We present a new language-embedded implementation of session types, which is inspired by the inversion-of-control design principle. With our approach, all application programs are intrinsically session-typed and unable to break linearity by construction. Our design relies on a tiny encapsulated library, for which linearity remains a proof obligation that can be discharged once and for all when the library is built. We demonstrate that our proposed design extends to a wide range of features of session type systems: branching, recursion, multichannel and higher-order sessions, as well as context-free sessions. The multichannel extension provides an embedded implementation of session types which guarantees deadlock freedom by construction. The development reported in this paper is fully backed by type-checked Agda code.