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Asynchronous Unfold/Fold Transformation for Fixpoint Logic

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Functional and Logic Programming (FLOPS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13215))

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Abstract

Various program verification problems for functional programs can be reduced to the validity checking problem for formulas of a fixpoint logic. Recently, Kobayashi et al. have shown that the unfold/fold transformation originally developed for logic programming can be extended and applied to prove the validity of fixpoint logic formulas. In the present paper, we refine their unfold/fold transformation, so that each predicate can be unfolded a different number of times in an asynchronous manner. Inspired by the work of Lee et al. on size change termination, we use a variant of size change graphs to find an appropriate number of unfoldings of each predicate. We have implemented an unfold/fold transformation tool based on the proposed method, and evaluated its effectiveness.

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Notes

  1. 1.

    Actually, because of the negative occurrences of \(\mathrm {Div6}\), we have to check some sanity conditions: see [5] for the sanity condition and the reason why \(=_\mu \) can be replaced with \(=_\nu \).

  2. 2.

    In the original paper on size change termination [8], each label is called a size change graph; here we call the whole graph a size change graph.

  3. 3.

    Similarly for the case \(\varphi \equiv X_1(t_{1,1},\ldots ,t_{1,k_1})\wedge \cdots \wedge X_n(t_{n,1},\ldots ,t_{n,k_n})\).

References

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Acknowledgments

We would like to thank anonymous referees for useful comments. This work was supported by JSPS KAKENHI Grant Numbers JP20H05703.

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Authors and Affiliations

  1. The University of Tokyo, Tokyo, Japan

    Mahmudul Faisal Al Ameen, Naoki Kobayashi & Ryosuke Sato

Authors
  1. Mahmudul Faisal Al Ameen
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  2. Naoki Kobayashi
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  3. Ryosuke Sato
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Corresponding author

Correspondence to Mahmudul Faisal Al Ameen .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Michael Hanus

  2. Kyoto University, Kyoto, Japan

    Atsushi Igarashi

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Faisal Al Ameen, M., Kobayashi, N., Sato, R. (2022). Asynchronous Unfold/Fold Transformation for Fixpoint Logic. In: Hanus, M., Igarashi, A. (eds) Functional and Logic Programming. FLOPS 2022. Lecture Notes in Computer Science, vol 13215. Springer, Cham. https://doi.org/10.1007/978-3-030-99461-7_3

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  • DOI: https://doi.org/10.1007/978-3-030-99461-7_3

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