Abstract
We introduce a foundational lambda calculus, System F i , for studying programming languages with term-indexed datatypes – higher-kinded datatypes whose indices range over data such as natural numbers or lists. System F i is an extension of System F ω that introduces the minimal features needed to support term-indexing. We show that System F i provides a theory for analysing programs with term-indexed types and also argue that it constitutes a basis for the design of logically-sound light-weight dependent programming languages. We establish erasure properties of F i -types that capture the idea that term-indices are discardable in that they are irrelevant for computation. Index erasure projects typing in System F i to typing in System F ω . So, System F i inherits strong normalization and logical consistency from System F ω .
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Ahn, K.Y., Sheard, T., Fiore, M., Pitts, A.M. (2013). System F i . In: Hasegawa, M. (eds) Typed Lambda Calculi and Applications. TLCA 2013. Lecture Notes in Computer Science, vol 7941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38946-7_4
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DOI: https://doi.org/10.1007/978-3-642-38946-7_4
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