Locally nameless sigma calculus

Henrio, Ludovic, Kammueller, Florian ORCID: https://orcid.org/0000-0001-5839-5488, Lutz, Bianca and Sudhof, Henry (2010) Locally nameless sigma calculus. Archive of Formal Proof . ISSN 2150-914X [Article]

Abstract

We present a Theory of Objects based on the original functional sigma-calculus by Abadi and Cardelli but with an additional parameter to methods. We prove confluence of the operational semantics following the outline of Nipkow's proof of confluence for the lambda-calculus reusing his theory Commutation, a generic diamond lemma reduction. We furthermore formalize a simple type system for our sigma-calculus including a proof of type safety. The entire development uses the concept of Locally Nameless representation for binders. We reuse an earlier proof of confluence for a simpler sigma-calculus based on de Bruijn indices and lists to represent objects.

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