Idris TyRE: a dependently typed regex parser

Regular expressions -- regexes -- are widely used not only for validating, but also for parsing textual data. Generally, regex parsers output a loose structure, e.g. an unstructured list of matches, leaving it up to the user to validate the output's properties and transform it into the desired structure. Since the regex itself carries information about the structure, this design leads to unnecessary repetition. Radanne introduced typed regexes -- TyRE -- a type-indexed combinator layer that can be added on top of an existing regex engine. We extend Radanne's design, and implement a parser which maintains type-safety throughout all layers: the user-facing regexes; their internal, desugared, representation; its compiled finite-state automaton; and the automaton's associated instruction-set for constructing the parse-trees. We implemented TyRE in the dependently-typed language Idris 2.