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Reasoning About Connectors in Coq

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Formal Aspects of Component Software (FACS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10231))

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Abstract

Reo is a channel-based exogenous coordination model in which complex coordinators, called connectors, are compositionally built out of simpler ones. In this paper, we present a new approach to model connectors in Coq which is a proof assistant based on higher-order logic and \(\lambda \)-calculus. The model reflects the original structure of connectors simply and clearly. In our framework, basic connectors (channels) are interpreted as axioms and composition operations are specified as inference rules. Furthermore, connectors are interpreted as logical predicates which describe the relation between inputs and outputs. With such definitions provided, connector properties, as well as equivalence and refinement relations between different connectors, can be naturally formalized as goals in Coq and easily proved using pre-defined tactics.

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Notes

  1. 1.

    If we use \(\alpha ,\beta \) to denote the data streams that flow through the channel ends of a channel and a, b to denote the time stream corresponding to the data streams, i.e., the i-th element a(i) in a denotes exactly the time moment of the occurrence of \(\alpha (i)\), then we can easily obtain the specifications for different channels, as discussed in [17, 19]. For example, a synchronous channel can be expressed as \(\alpha =\beta \wedge a =b \).

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Acknowledgement

The work was partially supported by the National Natural Science Foundation of China under grant no. 61532019, 61202069 and 61272160.

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Authors and Affiliations

  1. Department of Informatics and LMAM, School of Mathematical Sciences, Peking University, Beijing, China

    Xiyue Zhang, Weijiang Hong, Yi Li & Meng Sun

Authors
  1. Xiyue Zhang
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  2. Weijiang Hong
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  3. Yi Li
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  4. Meng Sun
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Corresponding author

Correspondence to Meng Sun .

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Editors and Affiliations

  1. Université Bourgogne Franche-Comté, Besançon, France

    Olga Kouchnarenko

  2. University of Tehran , Tehran, Iran

    Ramtin Khosravi

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Zhang, X., Hong, W., Li, Y., Sun, M. (2017). Reasoning About Connectors in Coq. In: Kouchnarenko, O., Khosravi, R. (eds) Formal Aspects of Component Software. FACS 2016. Lecture Notes in Computer Science(), vol 10231. Springer, Cham. https://doi.org/10.1007/978-3-319-57666-4_11

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  • DOI: https://doi.org/10.1007/978-3-319-57666-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57665-7

  • Online ISBN: 978-3-319-57666-4

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