Certified Bit-Coded Regular Expression Parsing

We describe the formalization of a regular expression (RE) parsing algorithm that produces a bit representation of its parse tree in the dependently typed language Agda. The algorithm computes bit-codes using Brzozowski derivatives and we prove that produced codes are equivalent to parse trees ensuring soundness and completeness w.r.t an inductive RE semantics. We include the certified algorithm in a tool developed by us, named verigrep, for regular expression based search in the style of the well known GNU grep. Practical experiments conducted with this tool are reported.