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Well-Founded Recursion over Contextual Objects

Authors Brigitte Pientka, Andreas Abel

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Brigitte Pientka
Andreas Abel

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Brigitte Pientka and Andreas Abel. Well-Founded Recursion over Contextual Objects. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 273-287, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.TLCA.2015.273

Abstract

We present a core programming language that supports writing well-founded structurally recursive functions using simultaneous pattern matching on contextual LF objects and contexts. The main technical tool is a coverage checking algorithm that also generates valid recursive calls. To establish consistency, we define a call-by-value small-step semantics and prove that every well-typed program terminates using a reducibility semantics. Based on the presented methodology we have implemented a totality checker as part of the programming and proof environment Beluga where it can be used to establish that a total Beluga program corresponds to a proof.

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Keywords
  • Type systems
  • Dependent Types
  • Logical Frameworks

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References

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