Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
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
Journal of Functional Programming
Formal languages and their relation to automata
Formal languages and their relation to automata
EDUCATIONAL PEARL: ‘Proof-directed debugging’ revisited for a first-order version
Journal of Functional Programming
A Second Course in Formal Languages and Automata Theory
A Second Course in Formal Languages and Automata Theory
Adapting functional programs to higher order logic
Higher-Order and Symbolic Computation
Regular-expression derivatives re-examined
Journal of Functional Programming
The Complexity of Finding SUBSEQ(A)
Theory of Computing Systems
Formalizing the Logic-Automaton Connection
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Elements of Automata Theory
Partial derivative automata formalized in Coq
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
A formalisation of the Myhill-Nerode theorem based on regular expressions (proof pearl)
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Succinctness of the Complement and Intersection of Regular Expressions
ACM Transactions on Computational Logic (TOCL)
A decision procedure for regular expression equivalence in type theory
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
Proof Pearl: Regular Expression Equivalence and Relation Algebra
Journal of Automated Reasoning
Regular expression sub-matching using partial derivatives
Proceedings of the 14th symposium on Principles and practice of declarative programming
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There are numerous textbooks on regular languages. Many of them focus on finite automata for proving properties. Unfortunately, automata are not so straightforward to formalise in theorem provers. The reason is that natural representations for automata are graphs, matrices or functions, none of which are inductive datatypes. Regular expressions can be defined straightforwardly as a datatype and a corresponding reasoning infrastructure comes for free in theorem provers. We show in this paper that a central result from formal language theory--the Myhill-Nerode Theorem--can be recreated using only regular expressions. From this theorem many closure properties of regular languages follow.