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Lightweight Higher-Order Rewriting in Haskell

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Trends in Functional Programming (TFP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9547))

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Abstract

We present a generic Haskell library for expressing rewrite rules with a safe treatment of variables and binders. Both sides of the rules are written as typed EDSL expressions, which leads to syntactically appealing rules and hides the underlying term representation. Matching is defined as an instance of Miller’s higher-order pattern unification and has the same complexity as first-order matching. The restrictions of pattern unification are captured in the types of the library, and we show by example that the library is capable of expressing useful simplifications that might be used in a compiler.

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Notes

  1. 1.

    http://hackage.haskell.org/package/ho-rewriting-0.2.

  2. 2.

    https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/ghc-language-features.html.

  3. 3.

    Note the partial type annotation in . It is used to constrain the type parameter of the RHS without saying anything about the representation of the RHS. Partial type signatures require the recent extension to GHC. However, this extension is not strictly needed: an equivalent formulation of the RHS would be .

  4. 4.

    The property is almost true: it holds if we replace all wildcards in \(l\) with unique meta-variables.

  5. 5.

    https://github.com/emilaxelsson/ho-rewriting/blob/0.2/examples/Feldspar.hs.

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Acknowledgements

This research was funded by the Swedish Foundation for Strategic Research (in the RAWFP project). The anonymous referees provided useful input.

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Authors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Emil Axelsson & Andrea Vezzosi

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  1. Emil Axelsson
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  2. Andrea Vezzosi
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Correspondence to Emil Axelsson .

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Editors and Affiliations

  1. INRIA Sophia Antipolis, Sophia Antipolis, France

    Manuel Serrano

  2. Dept.Information and Computing Sc., Utrecht University, Utrecht, The Netherlands

    Jurriaan Hage

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Axelsson, E., Vezzosi, A. (2016). Lightweight Higher-Order Rewriting in Haskell. In: Serrano, M., Hage, J. (eds) Trends in Functional Programming. TFP 2015. Lecture Notes in Computer Science(), vol 9547. Springer, Cham. https://doi.org/10.1007/978-3-319-39110-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-39110-6_1

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