Translating regular expression matching into transducers

Regular expression matching is an essential tool in string manipulating programs and plays crucial roles in scripting languages. We focus on regular expression matching based on the strategy of Perl and develop a translation from regular expression matching into transducers. The representation makes it possible to apply the theory of formal languages in static analysis and verification of string manipulating programs.We first formulate the semantics of regular expression matching as a nondeterministic parser by using the composition of the list and output monads. Then, we transform the nondeterministic parser into deterministic one by introducing lookahead. The deterministic parser is formulated with the option monad instead of the list monad and derived through equational reasoning involving monads. From the definition of the deterministic parser, we can easily construct transducers through transducers with regular lookahead. We have implemented the translation and conducted experiments on regular expressions found in several popular PHP programs.