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Tree-Like Grammars and Separation Logic

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Programming Languages and Systems (APLAS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9458))

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Abstract

Separation Logic with inductive predicate definitions (\(\texttt {SL}\)) and hyperedge replacement grammars (HRG) are established formalisms to describe the abstract shape of data structures maintained by heap-manipulating programs. Fragments of both formalisms are known to coincide, and neither the entailment problem for \(\texttt {SL}\) nor its counterpart for HRGs, the inclusion problem, are decidable in general.

We introduce tree-like grammars (TLG), a fragment of HRGs with a decidable inclusion problem. By the correspondence between HRGs and \(\texttt {SL}\), we simultaneously obtain an equivalent \(\texttt {SL}\) fragment (\(\texttt {SL}_{\texttt {tl}}\)) featuring some remarkable properties including a decidable entailment problem.

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Notes

  1. 1.

    Intuitively, G and \(\varphi \) are language-equivalent if \(L({G})\) equals the set of all graphs corresponding to models of \(\varphi \).

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Authors and Affiliations

  1. Software Modeling and Verification Group, RWTH Aachen University, Aachen, Germany

    Christoph Matheja, Christina Jansen & Thomas Noll

Authors
  1. Christoph Matheja
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  2. Christina Jansen
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  3. Thomas Noll
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Correspondence to Christoph Matheja .

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Editors and Affiliations

  1. Univ. of Science and Technology of China, Hefei, Anhui, China

    Xinyu Feng

  2. Pohang Univ. of Science and Technology, Nam-Gu, Pohang, Korea (Republic of)

    Sungwoo Park

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Matheja, C., Jansen, C., Noll, T. (2015). Tree-Like Grammars and Separation Logic. In: Feng, X., Park, S. (eds) Programming Languages and Systems. APLAS 2015. Lecture Notes in Computer Science(), vol 9458. Springer, Cham. https://doi.org/10.1007/978-3-319-26529-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-26529-2_6

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  • Online ISBN: 978-3-319-26529-2

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