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Explanations for Dynamic Programming

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Practical Aspects of Declarative Languages (PADL 2020)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 12007))

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Abstract

We present an approach for explaining dynamic programming that is based on computing with a granular representation of values that are typically aggregated during program execution. We demonstrate how to derive more detailed and meaningful explanations of program behavior from such a representation than would otherwise be possible. To illustrate the practicality of this approach we also present a Haskell library for dynamic programming that allows programmers to specify programs by recurrence relationships from which implementations are derived that can run with granular representation and produce explanations. The explanations essentially answer questions of why one result was obtained instead of another. While usually the alternatives have to be provided by a user, we will show that with our approach such alternatives can be in some cases anticipated and that corresponding explanations can be generated automatically.

This work is partially supported by DARPA under the grant N66001-17-2-4030 and by the National Science Foundation under the grant CCF-1717300.

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Notes

  1. 1.

    This definition allows dominators to contain negative components, which are counter-productive to the goal of dominators. However, the definition of minimal-size dominators will never produce a dominator with a negative component, so that the general definition does not hurt.

  2. 2.

    See http://hackage.haskell.org/package/DP. The code has not been maintained in some time and doesn’t seem to work currently. Our implementation is available at https://github.com/prashant007/XDP.

  3. 3.

    Note that the Counting semiring is not monotonic. The implementation of Fibonacci numbers is still correct, since the \(\oplus \) function isn’t used to select among different alternatives.

  4. 4.

    The additional argument of type for is required to keep the types in the multi-parameter type class unambiguous. Moreover, we can’t unfortunately simply give the generic definition for indicated by the equation, since that would also lead to an ambiguous type.

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Authors and Affiliations

  1. Oregon State University, Corvallis, USA

    Martin Erwig, Prashant Kumar & Alan Fern

Authors
  1. Martin Erwig
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  2. Prashant Kumar
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  3. Alan Fern
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Corresponding author

Correspondence to Martin Erwig .

Editor information

Editors and Affiliations

  1. Heriot-Watt University, Edinburgh, UK

    Ekaterina Komendantskaya

  2. Stony Brook University, New York, USA

    Yanhong Annie Liu

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Erwig, M., Kumar, P., Fern, A. (2020). Explanations for Dynamic Programming. In: Komendantskaya, E., Liu, Y. (eds) Practical Aspects of Declarative Languages. PADL 2020. Lecture Notes in Computer Science(), vol 12007. Springer, Cham. https://doi.org/10.1007/978-3-030-39197-3_12

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  • DOI: https://doi.org/10.1007/978-3-030-39197-3_12

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  • Online ISBN: 978-3-030-39197-3

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