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Well-Founded Recursion over Contextual Objects Pientka, Brigitte Abel, Andreas Type systems Dependent Types Logical Frameworks 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Brigitte Pientka and Andreas Abel 2015 Is Part Of LIPIcs, Volume 38, 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.TLCA.2015.273 urn:nbn:de:0030-drops-51699 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TLCA.2015.273 eng https://creativecommons.org/licenses/by/3.0/legalcode