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An Ode to Arrows

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Practical Aspects of Declarative Languages (PADL 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5937))

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Abstract

We study a number of embedded DSLs for autonomous ordinary differential equations (autonomous ODEs) in Haskell. A naive implementation based on the lazy tower of derivatives is straightforward but has serious time and space leaks due to the loss of sharing when handling cyclic and infinite data structures. In seeking a solution to fix this problem, we explore a number of DSLs ranging from shallow to deep embeddings, and middle-grounds in between. We advocate a solution based on arrows, an abstract notion of computation that offers both a succinct representation and an effective implementation. Arrows are ubiquitous in their combinator style that happens to capture both sharing and recursion elegantly. We further relate our arrow-based DSL to a more constrained form of arrows called causal commutative arrows, the normalization of which leads to a staged compilation technique improving ODE performance by orders of magnitude.

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Authors and Affiliations

  1. Department of Computer Science, Yale University, New Haven, CT, 06520, U.S.A.

    Hai Liu & Paul Hudak

Authors
  1. Hai Liu
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  2. Paul Hudak
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Editors and Affiliations

  1. Facultad de Informática, Univrsidad Politécnica de Madrid (UPM), Campus Montegancedo, Boadilla del Monte, 28660, Madrid, Spain

    Manuel Carro

  2. Facultad de Informática, Universidad Complutense de Madrid (UPM), c/Profesor José García Santesmases s/n, 28040, Madrid, Spain

    Ricardo Peña

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Liu, H., Hudak, P. (2010). An Ode to Arrows. In: Carro, M., Peña, R. (eds) Practical Aspects of Declarative Languages. PADL 2010. Lecture Notes in Computer Science, vol 5937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11503-5_14

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  • DOI: https://doi.org/10.1007/978-3-642-11503-5_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11502-8

  • Online ISBN: 978-3-642-11503-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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