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Generic Programming with Dependent Types

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Generic and Indexed Programming

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7470))

Abstract

Some programs are doubly generic. For example, map is datatype-generic in that many different data structures support a mapping operation. A generic programming language like Generic Haskell can use a single definition to generate map for each type. However, map is also arity-generic because it belongs to a family of related operations that differ in the number of arguments. For lists, this family includes familiar functions from the Haskell standard library (such as repeat, map, and zipWith).

This tutorial explores these forms of genericity individually and together. These two axes are not orthogonal: datatype-generic versions of repeat, map and zipWith have different arities of kind-indexed types. We explore these forms of genericity in the context of the Agda programming language, using the expressiveness of dependent types to capture both forms of genericity in a common framework. Therefore, this tutorial serves as an introduction to dependently typed languages as well as generic programming.

The target audience of this work is someone who is familiar with functional programming languages, such as Haskell or ML, but would like to learn about dependently typed languages. We do not assume prior experience with Agda, type- or arity-generic programming.

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Authors and Affiliations

  1. University of Pennsylvania, USA

    Stephanie Weirich & Chris Casinghino

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  1. Stephanie Weirich
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  2. Chris Casinghino
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Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Jeremy Gibbons

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Weirich, S., Casinghino, C. (2012). Generic Programming with Dependent Types. In: Gibbons, J. (eds) Generic and Indexed Programming. Lecture Notes in Computer Science, vol 7470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32202-0_5

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  • DOI: https://doi.org/10.1007/978-3-642-32202-0_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32201-3

  • Online ISBN: 978-3-642-32202-0

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