On Polymorphic Sessions and Functions

Abstract

This work exploits the logical foundation of session types to determine what kind of type discipline for the π-calculus can exactly capture, and is captured by, λ-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 functionsas-processes encodings between a polymorphic session π-calculus and a linear formulation of System F. We are then able to derive results of the session calculus from the theory of the λ-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.

On Polymorphic Sessions and Functions

“…Outline. This article revises and extends an earlier version of this work [73] with additional materials and full proofs. § 2 was extended to include all the necessary formal definitions for the development of the coming sections, namely the definitions of structural and extended structural congruence, typed barbed congruence and logical equivalence.…”

“…This, combined with the subsequent encodings of fixed-points [37], can be seen as the semantic foundation for the works extending the web-based programming language Links with session types [19,20,38]. We further note the addition of session-based concurrency to the language C0 [69,77], drawing upon the semantic foundation provided by the encodings for the intuitionistic setting [70,73].…”

“…Section 5.2 now includes the development of the strong normalisation result (Theorem 5.24) for the higher-order process passing calculus via a modification of the encoding presented previously in the section, which also includes the reestablishment of the properties of operational correspondence, and the inverse theorem for the reformulated encoding. Finally, Section 6 has been enhanced with additional discussion of related work, including works that were published after the conference version of this work [73].…”

Zooid: a DSL for certified multiparty computation: from mechanised metatheory to certified multiparty processes

“…For more than two processes, ensuring deadlock-freedom in BST requires either complicated additional causality-based typing systems on top of plain BST, e.g. [1,17] or limitation to deterministic, strongly-normalising session types [48,49].…”