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International Workshop on Coalgebraic Methods in Computer Science

CMCS 2012: Coalgebraic Methods in Computer Science pp 218–237Cite as

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Permutations in Coinductive Graph Representation

Permutations in Coinductive Graph Representation

  • Celia Picard18 &
  • Ralph Matthes18 
  • Conference paper
  • 596 Accesses

  • 5 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7399)

Abstract

In the proof assistant Coq, one can model certain classes of graphs by coinductive types. The coinductive aspects account for infinite navigability already in finite but cyclic graphs, as in rational trees. Coq’s static checks exclude simple-minded definitions with lists of successors of a node. In previous work, we have shown how to mimic lists by a type of functions and built a Coq theory for such graphs. Naturally, these coinductive structures have to be compared by a bisimulation relation, and we defined it in a generic way.

However, there are many cases in which we would not like to distinguish between graphs that are constructed differently and that are thus not bisimilar, in particular if only the order of elements in the lists of successors is not the same. We offer a wider bisimulation relation that allows permutations. Technical problems arise with their specification since (1) elements have to be compared by a not necessarily decidable relation and (2) coinductive types are mixed with inductive ones. Still, a formal development has been carried out in Coq, by using its built-in language for proof automation.

Another extension of the original bisimulation relation based on cycle analysis provides indifference concerning the root node of the term graphs.

Keywords

  • Base Relation
  • Inductive Tree
  • Proof Assistant
  • Pigeonhole Principle
  • Bisimulation Relation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Institut de Recherche en Informatique de Toulouse (IRIT), University of Toulouse and C.N.R.S., France

    Celia Picard & Ralph Matthes

Authors
  1. Celia Picard
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  2. Ralph Matthes
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Editor information

Editors and Affiliations

  1. Research School of Information Sciences and Engineering, The Australian National University, 0200, Canberra, ACT, Australia

    Dirk Pattinson

  2. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany

    Lutz Schröder

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© 2012 IFIP International Federation for Information Processing

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Picard, C., Matthes, R. (2012). Permutations in Coinductive Graph Representation. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_12

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