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arXiv · 2209.02354

A Generic Type System for Higher-Order $\Psi$-calculi

Alex Rønning Bendixen·Bjarke Bredow Bojesen·Hans Hüttel·Stian Lybech
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Abstract

The Higher-Order $\Psi$-calculus framework (HO$\Psi$) is a generalisation of many first- and higher-order extensions of the $\pi$-calculus. It was proposed by Parrow et al. who showed that higher-order calculi such as HO$\pi$ and CHOCS can be expressed as HO$\Psi$-calculi. In this paper we present a generic type system for HO$\Psi$-calculi which extends previous work by H\"uttel on a generic type system for first-order $\Psi$-calculi. Our generic type system satisfies the usual property of subject reduction and can be instantiated to yield type systems for variants of HO{\pi}, including the type system for termination due to Demangeon et al. Moreover, we derive a type system for the $\rho$-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 $\rho$-calculus cannot be encoded in the $\pi$-calculus in a way that satisfies standard criteria of encodability.

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Alex Rønning Bendixen, Bjarke Bredow Bojesen, Hans Hüttel, Stian Lybech. 2022-09-06. A Generic Type System for Higher-Order $\Psi$-calculi. https://doi.org/10.4204/eptcs.368.3

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