You have to figure out here how you can use the function which is the argument to map. It seems you want to end up with a function of type a -> Evaluator b, to be used as an argument to mapM. One idea is to add a new constructor Var to represent variables, and something like evalVar :: Obs b -> a -> Evaluator b which handles Var by "return"ing the second argument, and everything else as in evalObs. Then you can evaluate Map like evalObs (Map f) as = evalObs as >>= mapM (evalVar (f Var)) Except, this won't quit work because the type for evalVar is wrong. That can be fixed by adding an extra parameter for the variable type: data Obs varType a where ... Var :: Obs v v Map :: (Obs a a -> Obs a b) -> Obs v [a] -> Obs v [b] or something like that. Brandon