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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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Editor information

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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