Locally Nameless Permutation Types

TL;DR

This paper introduces Locally Nameless Permutation Types, combining permutation types with locally nameless representations to improve formalization of programming languages involving name extrusion, supporting complex reasoning about renaming and infinite support.

Contribution

It presents a novel type framework that integrates permutation types with locally nameless representations, facilitating formal reasoning about languages with name extrusion.

Findings

Supports reasoning about extrusion in process calculi

Inherits properties from Nominal and locally nameless approaches

Handles infinite support for countable choice

Abstract

We define "Locally Nameless Permutation Types", which fuse permutation types as used in Nominal Isabelle with the locally nameless representation. We show that this combination is particularly useful when formalizing programming languages where bound names may become free during execution ("extrusion"), common in process calculi. It inherits the generic definition of permutations and support, and associated lemmas, from the Nominal approach, and the ability to stay close to pencil-and-paper proofs from the locally nameless approach. We explain how to use cofinite quantification in this setting, show why reasoning about renaming is more important here than in languages without extrusion, and provide results about infinite support, necessary when reasoning about countable choice.