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Towards Critical Pair Analysis for the Graph Programming Language GP 2

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Recent Trends in Algebraic Development Techniques (WADT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10644))

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Abstract

We present the foundations of critical pair analysis for the graph programming language GP 2. Our goal is to develop a static checker that can prove or refute confluence (functional behaviour) for a large class of graph programs. In this paper, we introduce symbolic critical pairs of GP 2 rule schemata, which are labelled with expressions, and establish the completeness and finiteness of the set of symbolic critical pairs over a finite set of rule schemata. We give a procedure for their construction.

I. Hristakiev—Supported by a Doctoral Training Grant from the Engineering and Physical Sciences Research Council (EPSRC) in the UK.

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Notes

  1. 1.

    We do not distinguish between nodes and edges in statements that hold analogously for both sets.

  2. 2.

    A pushout is natural if it is also a pullback.

  3. 3.

    Two unification problems are independent if they do not share list variables.

  4. 4.

    The paper [14] introduces symbolic critical pairs in the setting of symbolic graph transformation where graphs are combined with first-order logic formulas.

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Authors and Affiliations

  1. University of York, York, UK

    Ivaylo Hristakiev & Detlef Plump

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  1. Ivaylo Hristakiev
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  2. Detlef Plump
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Correspondence to Detlef Plump .

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Editors and Affiliations

  1. Swansea University, Swansea, United Kingdom

    Phillip James

  2. Swansea University, Swansea, United Kingdom

    Markus Roggenbach

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Hristakiev, I., Plump, D. (2017). Towards Critical Pair Analysis for the Graph Programming Language GP 2. In: James, P., Roggenbach, M. (eds) Recent Trends in Algebraic Development Techniques. WADT 2016. Lecture Notes in Computer Science(), vol 10644. Springer, Cham. https://doi.org/10.1007/978-3-319-72044-9_11

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  • DOI: https://doi.org/10.1007/978-3-319-72044-9_11

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-72044-9

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