Intensionality, Intensional Recursion, and the Gödel–Löb Axiom

G. A. Kavvos*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)
38 Downloads (Pure)

Abstract

The use of a necessity modality in a typed λ-calculus can be used to separate it into two regions. These can be thought of as intensional vs. extensional data: data in the first region, the modal one, are available as code, and their description can be examined. In contrast, data in the second region are only available as values up to ordinary equality. This allows us to add non-functional operations at modal types whilst maintaining consistency. In this setting, the Gödel-Löb axiom acquires a novel constructive reading: it affords the programmer the possibility of a very strong kind of recursion which enables them to write programs that have access to their own code. This is a type of computational reflection that is strongly reminiscent of Kleene’s Second Recursion Theorem.
Original languageEnglish
Pages (from-to)2287-2312
JournalIfCoLoG Journal of Logics and their Applications
Volume8
Issue number8
Publication statusPublished - 1 Sept 2021

Structured keywords

  • Programming Languages

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