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Restriction on Cut in Cyclic Proof System for Symbolic Heaps

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Functional and Logic Programming (FLOPS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12073))

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Abstract

It has been shown that some variants of cyclic proof systems for symbolic heap entailments in separation logic do not enjoy the cut elimination property. To construct complete system, we have to consider the cut rule, which requires some heuristics to find cut formulas in bottom-up proof search. Hence, we hope to achieve some restricted variant of cut rule which does not change provability and does not interfere with automatic proof search without heuristics. This paper gives a limit on this challenge. We propose a restricted cut rule, called the presumable cut, in which cut formula is restricted to those which can occur below the cut. This paper shows that there is an entailment which is provable with full cuts in cyclic proof system for symbolic heaps, but not with only presumable cuts.

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Authors and Affiliations

  1. Nagoya University, Nagoya, Japan

    Kenji Saotome & Koji Nakazawa

  2. Toho University, Funabashi, Japan

    Daisuke Kimura

Authors
  1. Kenji Saotome
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  2. Koji Nakazawa
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  3. Daisuke Kimura
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Corresponding author

Correspondence to Kenji Saotome .

Editor information

Editors and Affiliations

  1. Tohoku University, Sendai, Japan

    Keisuke Nakano

  2. Uppsala University, Uppsala, Sweden

    Konstantinos Sagonas

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Saotome, K., Nakazawa, K., Kimura, D. (2020). Restriction on Cut in Cyclic Proof System for Symbolic Heaps. In: Nakano, K., Sagonas, K. (eds) Functional and Logic Programming. FLOPS 2020. Lecture Notes in Computer Science(), vol 12073. Springer, Cham. https://doi.org/10.1007/978-3-030-59025-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-59025-3_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-59024-6

  • Online ISBN: 978-3-030-59025-3

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