Genericity and the π-Calculus (with K. Honda, N. Yoshida)

Abstract. Types in processes delineate specific classes of interactive behaviour in a compositional way. Key elements of process theory, in particular behavioural equivalences, are deeply affected by types, leading to applications in the description and analysis of diverse forms of computing. As one of the examples of types for processes, this paper introduces a second-order polymorphic π-calculus based on duality principles, building on type structures coming from typed π-calculi, Linear Logic and game semantics. Of various extensions of first-order typed π-calculi with polymorphism, the present paper focusses on the linear polymorphic π-calculus, extending its first-order counterpart [46]. Fundamental elements of the theory of linear polymorphic processes are studied, including establishment of their strong normalisability using Girard's “candidates,” introduction of a behavioural theory of polymorphic labelled transitions which strengthens Pierce-Sangiorgi's polymorphic bisimulation via duality, and a fully abstract embedding of System F in polymorphic processes, establishing a precise connection between the universe of polymorphic functions and the universe of polymorphic processes. The proof combines process-theoretic reasoning with techniques from game semantics. The abstract nature of polymorphic labelled transitions plays an essential role in full abstraction, elucidating subtle aspects of polymorphism in functions and interaction.

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