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Certified parsing of regular languages. (English) Zbl 1303.68077
Gonthier, Georges (ed.) et al., Certified programs and proofs. Third international conference, CPP 2013, Melbourne, VIC, Australia, December 11–13, 2013. Proceedings. Berlin: Springer (ISBN 978-3-319-03544-4/pbk). Lecture Notes in Computer Science 8307, 98-113 (2013).
Summary: 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.
For the entire collection see [Zbl 1298.68028].

MSC:
68Q45 Formal languages and automata
Software:
Agda
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