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Verified Memoization and Dynamic Programming

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Book cover Interactive Theorem Proving (ITP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10895))

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Abstract

We present a lightweight framework in Isabelle/HOL for the automatic verified (functional or imperative) memoization of recursive functions. Our tool constructs a memoized version of the recursive function and proves a correspondence theorem between the two functions. A number of simple techniques allow us to achieve bottom-up computation and space-efficient memoization. The framework’s utility is demonstrated on a number of representative dynamic programming problems.

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Notes

  1. 1.

    If f has type \(\tau _1 \rightarrow \cdots \rightarrow \tau _n\) and x has type \(\tau \), the variables \( f _\textsf {m}'\) and \( x _\textsf {m}\) are assumed to have types \(M'(\tau _1)\rightarrow \cdots \rightarrow M'(\tau _n)\) and \(M(\tau )\), respectively. For a term \(x\,{:}{:}\,\tau \) that satisfies \(M'(\tau )=\tau \), x and \( x _\textsf {m}'\) are used interchangeably.

  2. 2.

    https://projecteuler.net/problem=114.

  3. 3.

    http://www.pm.inf.ethz.ch/research/verifythis.html.

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Acknowledgments

Tobias Nipkow is supported by DFG Koselleck grant NI 491/16-1. The authors would like to thank Andreas Lochbihler for a fruitful discussion on monadification.

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Authors and Affiliations

  1. Fakultät für Informatik, Technische Universität München, Munich, Germany

    Simon Wimmer, Shuwei Hu & Tobias Nipkow

Authors
  1. Simon Wimmer
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  2. Shuwei Hu
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  3. Tobias Nipkow
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Corresponding author

Correspondence to Simon Wimmer .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Jeremy Avigad

  2. Inria, Nantes, France

    Assia Mahboubi

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Wimmer, S., Hu, S., Nipkow, T. (2018). Verified Memoization and Dynamic Programming. In: Avigad, J., Mahboubi, A. (eds) Interactive Theorem Proving. ITP 2018. Lecture Notes in Computer Science(), vol 10895. Springer, Cham. https://doi.org/10.1007/978-3-319-94821-8_34

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  • DOI: https://doi.org/10.1007/978-3-319-94821-8_34

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  • Print ISBN: 978-3-319-94820-1

  • Online ISBN: 978-3-319-94821-8

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