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2020 | OriginalPaper | Buchkapitel

Explanations for Dynamic Programming

verfasst von : Martin Erwig, Prashant Kumar, Alan Fern

Erschienen in: Practical Aspects of Declarative Languages

Verlag: Springer International Publishing

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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.

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Vorheriges Kapitel Whitebox Induction of Default Rules Using High-Utility Itemset Mining

Nächstes Kapitel A DSL for Integer Range Reasoning: Partition, Interval and Mapping Diagrams

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.

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.

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.

The additional argument of type

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for

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is required to keep the types in the multi-parameter type class unambiguous. Moreover, we can’t unfortunately simply give the generic definition for

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indicated by the equation, since that would also lead to an ambiguous type.

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Titel: Explanations for Dynamic Programming
verfasst von: Martin Erwig
Prashant Kumar
Alan Fern
Verlag: Springer International Publishing
Buch: Practical Aspects of Declarative Languages
Print ISBN: 978-3-030-39196-6

Electronic ISBN: 978-3-030-39197-3

Copyright-Jahr: 2020
DOI: https://doi.org/10.1007/978-3-030-39197-3_12

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