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Quotients by Idempotent Functions in Cedille

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Trends in Functional Programming (TFP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12053))

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Abstract

We present a simple characterization of definable quotient types as being induced by idempotent functions, and an encoding of this in Cedille (a dependently typed programming language) in which both equational constraints and the packaging that associates these with elements of the carrier type are irrelevant, facilitating equational reasoning in proofs. We provide several concrete examples of definable quotients using this encoding and give combinators for function lifting (with one variant having zero run-time cost).

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Notes

  1. 1.

    The listing of function rem omits necessary type coercions for Cedille to ensure that the recursive call on minus n’ k’ is well-founded.

  2. 2.

    github.com/cedille/cedille-developments/tree/master/idem-quotients.

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Authors and Affiliations

  1. The University of Iowa, Iowa City, IA, 52242, USA

    Andrew Marmaduke, Christopher Jenkins & Aaron Stump

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  1. Andrew Marmaduke
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  2. Christopher Jenkins
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  3. Aaron Stump
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Correspondence to Andrew Marmaduke .

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Editors and Affiliations

  1. University of British Columbia, Vancouver, BC, Canada

    William J. Bowman

  2. University of British Columbia, Vancouver, BC, Canada

    Ronald Garcia

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Marmaduke, A., Jenkins, C., Stump, A. (2020). Quotients by Idempotent Functions in Cedille. In: Bowman, W., Garcia, R. (eds) Trends in Functional Programming. TFP 2019. Lecture Notes in Computer Science(), vol 12053. Springer, Cham. https://doi.org/10.1007/978-3-030-47147-7_1

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  • DOI: https://doi.org/10.1007/978-3-030-47147-7_1

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