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Impredicative Encodings of Inductive-Inductive Data in Cedille

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Trends in Functional Programming (TFP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13868))

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Abstract

Cedille is a dependently typed programming language known for expressive and efficient impredicative encodings. In this work, we show that encodings of induction-induction are also possible by employing a standard technique from other encodings in Cedille, where a type representing the shape of data is intersected with a predicate that further constrains. Thus, just as with indexed inductive data, Cedille can encode a notion that is often axiomatically postulated or directly implemented in other dependent type theories without sacrificing efficiency.

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Authors and Affiliations

  1. The University of Iowa, Iowa City, IA, USA

    Andrew Marmaduke, Larry Diehl & Aaron Stump

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  1. Andrew Marmaduke
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  2. Larry Diehl
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  3. Aaron Stump
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Correspondence to Andrew Marmaduke .

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  1. University of Massachusetts Boston, Boston, MA, USA

    Stephen Chang

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Marmaduke, A., Diehl, L., Stump, A. (2023). Impredicative Encodings of Inductive-Inductive Data in Cedille. In: Chang, S. (eds) Trends in Functional Programming. TFP 2023. Lecture Notes in Computer Science, vol 13868. Springer, Cham. https://doi.org/10.1007/978-3-031-38938-2_1

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  • DOI: https://doi.org/10.1007/978-3-031-38938-2_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-38937-5

  • Online ISBN: 978-3-031-38938-2

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