Regular Language Representations in the Constructive Type Theory of Coq

Christian Doczkal (1) , Gert Smolka (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 Saarland University [Saarbrücken]

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.

Mots clés: Regular languages; Two-way automata; WS1S; Constructive type theory; Interactive theorem proving; Coq; Ssreflect

Domaines: Théorie et langage formel [cs.FL]

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⟩