Derivatives of Regular Expressions
Journal of the ACM (JACM)
Constructively formalizing automata theory
Proof, language, and interaction
Automata and Computability
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
TYPES '00 Selected papers from the International Workshop on Types for Proofs and Programs
Formal languages and their relation to automata
Formal languages and their relation to automata
Adapting functional programs to higher order logic
Higher-Order and Symbolic Computation
Regular-expression derivatives re-examined
Journal of Functional Programming
Formalizing the Logic-Automaton Connection
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Proof Pearl: Regular Expression Equivalence and Relation Algebra
Journal of Automated Reasoning
A decision procedure for regular expression equivalence in type theory
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Automated reasoning in higher-order regular algebra
RAMiCS'12 Proceedings of the 13th international conference on Relational and Algebraic Methods in Computer Science
Ribbon proofs for separation logic
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Verified decision procedures for MSO on words based on derivatives of regular expressions
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming
A Formalisation of the Myhill-Nerode Theorem Based on Regular Expressions
Journal of Automated Reasoning
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There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOL-based theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Also convenient operations for disjoint unions of graphs and functions are not easily formalisiable in HOL. In contrast, regular expressions can be defined conveniently as a datatype and a corresponding reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory--the Myhill-Nerode theorem--can be recreated using only regular expressions.