A Generic Type System for Higher-Order Ψ-calculi

Alex Rønning Bendixen
Bjarke Bredow Bojesen
Hans Hüttel
Stian Lybech

The Higher-Order Ψ-calculus framework (HOΨ) is a generalisation of many first- and higher-order extensions of the π-calculus. It was proposed by Parrow et al. who showed that higher-order calculi such as HOπ and CHOCS can be expressed as HOΨ-calculi. In this paper we present a generic type system for HOΨ-calculi which extends previous work by Hüttel on a generic type system for first-order Ψ-calculi. Our generic type system satisfies the usual property of subject reduction and can be instantiated to yield type systems for variants of HOπ, including the type system for termination due to Demangeon et al.. Moreover, we derive a type system for the ρ-calculus, a reflective higher-order calculus proposed by Meredith and Radestock. This establishes that our generic type system is richer than its predecessor, as the ρ-calculus cannot be encoded in the π-calculus in a way that satisfies standard criteria of encodability.

In Valentina Castiglioni and Claudio A. Mezzina: Proceedings Combined 29th International Workshop on Expressiveness in Concurrency and 19th Workshop on Structural Operational Semantics (EXPRESS/SOS 2022), Warsaw, Poland, 12th September 2022, Electronic Proceedings in Theoretical Computer Science 368, pp. 43–59.
Published: 6th September 2022.

ArXived at: https://dx.doi.org/10.4204/EPTCS.368.3 bibtex PDF
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