Abstract
Sized types provides a type-based mechanism to enforce termination of recursive definitions in typed λ-calculi. Previous work has provided strong indications that type-based termination provides an appropriate foundation for proof assistants based on type theory; however, most work to date has been confined to non-dependent type systems. In this article, we introduce a variant of the Calculus of Inductive Constructions with sized types and study its meta theoretical properties: subject reduction, normalization, and thus consistency and decidability of type-checking and of size-inference. A prototype implementation has been developed alongside case studies.
More details on difficulties with Coq, case studies, remaining issues and proofs and an implementation are available from the second author’s web page.
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Barthe, G., Grégoire, B., Pastawski, F. (2006). CIC\(\widehat{~}\): Type-Based Termination of Recursive Definitions in the Calculus of Inductive Constructions. In: Hermann, M., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2006. Lecture Notes in Computer Science(), vol 4246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11916277_18
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DOI: https://doi.org/10.1007/11916277_18
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