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Justifying algorithms for βη-conversion
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ACM Transactions on Computational Logic (TOCL)
Justifying algorithms for βη-conversion
FOSSACS'05 Proceedings of the 8th international conference on Foundations of Software Science and Computation Structures
Untyped Algorithmic Equality for Martin-Löf's Logical Framework with Surjective Pairs
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2005, Selected Papers
A Logical Framework with Dependently Typed Records
Fundamenta Informaticae - Typed Lambda Calculi and Applications 2003, Selected Papers
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This paper outlines an elementary approach for showing the decidability of type checking for type theories with βη-equality, relevant to foundations for modules systems and type theory-based proof systems. The key to the approach is a syntactic translation mapping terms in the βη presentation into their full η-expansions in the β presentation. Decidability of type checking is lifted from the target β presentation to the βη presentation. The approach extends to other inductive kinds with a single constructor, and is demonstrated for singletons and dependent pairs.