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Journal Articles Journal of Automated Reasoning Year : 2018

Regular Language Representations in the Constructive Type Theory of Coq

Abstract

We explore the theory of regular language representations in the constructive type theory of Coq. We cover various forms of automata (deterministic, nondeterministic, one-way, two-way), regular expressions, and the logic WS1S. We give translations between all representations, show decidability results, and provide operations for various closure properties. Our results include a constructive decidability proof for the logic WS1S, a constructive refinement of the Myhill-Nerode characterization of regularity, and translations from two-way automata to one-way automata with verified upper bounds for the increase in size. All results are verified with an accompanying Coq development of about 3000 lines.
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Dates and versions

hal-01832031 , version 1 (06-07-2018)

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Christian Doczkal, Gert Smolka. Regular Language Representations in the Constructive Type Theory of Coq. Journal of Automated Reasoning, 2018, Special Issue: Milestones in Interactive Theorem Proving, 61 (1-4), pp.521-553. ⟨10.1007/s10817-018-9460-x⟩. ⟨hal-01832031⟩
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