Monadic Expressions and their Derivatives

We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order abstract the underlying data structures (e.g. sets linear combinations) using notion monad. As an example this generalization advantage, we introduce a new derivation technique based on graded module also extend operators defining expressions any n-ary functions over value sets, such as classical operations (like negation intersection for Boolean weights) more exotic ones algebraic mean rational weights). Moreover, present how compute (non-necessarily finite) automaton extended expression, Colcombet Petrisan categorical definition automata. These category theory concepts allow us perform construction unified way, whatever Finally, illustrate our work, Haskell implementation these notions advanced techniques functional programming, provide web interface manipulate concrete examples.