Locally nameless sigma calculus

Article

Henrio, L., Kammueller, F., Lutz, B. and Sudhof, H. 2010. Locally nameless sigma calculus. Archive of Formal Proof.
TypeArticle
TitleLocally nameless sigma calculus
AuthorsHenrio, L., Kammueller, F., Lutz, B. and Sudhof, H.
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.

Research GroupFoundations of Computing group
Artificial Intelligence group
JournalArchive of Formal Proof
ISSN2150-914X
Publication dates
Print30 Apr 2010
Publication process dates
Deposited25 May 2012
Output statusPublished
Web address (URL)http://afp.sourceforge.net/entries/Locally-Nameless-Sigma.shtml
LanguageEnglish
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