Year: 2022
Type: article
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.
DOI: 10.4204/eptcs.368.3
Institutions: Reykjavík University, University of Copenhagen, Aalborg University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4293452343