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Certified Parsing of Regular Languages

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Certified Programs and Proofs (CPP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8307))

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Abstract

We report on a certified parser generator for regular languages using the Agda programming language. Specifically, we programmed a transformation of regular expressions into a Boolean-matrix based representation of nondeterministic finite automata (NFAs). And we proved (in Agda) that a string matches a regular expression if and only if the NFA accepts it. The proof of the if-part is effectively a function turning acceptance of a string into a parse tree while the only-if part gives a function turning rejection into a proof of impossibility of a parse tree.

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Author information

Authors and Affiliations

  1. Institute of Cybernetics, Tallinn University of Technology, Akadeemia tee 21, 12618, Tallinn, Estonia

    Denis Firsov & Tarmo Uustalu

Authors
  1. Denis Firsov
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  2. Tarmo Uustalu
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Editors and Affiliations

  1. Microsoft Research Cambridge, 21 Station Road, CB1 2FB, Cambridge, UK

    Georges Gonthier

  2. Canberra Research Lab., NICTA, PO Box 8001, 2601, Canberra, ACT, Australia

    Michael Norrish

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© 2013 Springer International Publishing Switzerland

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Firsov, D., Uustalu, T. (2013). Certified Parsing of Regular Languages. In: Gonthier, G., Norrish, M. (eds) Certified Programs and Proofs. CPP 2013. Lecture Notes in Computer Science, vol 8307. Springer, Cham. https://doi.org/10.1007/978-3-319-03545-1_7

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  • DOI: https://doi.org/10.1007/978-3-319-03545-1_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03544-4

  • Online ISBN: 978-3-319-03545-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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