> But I think that we miss the point doing that. A transducer should be able to lead to a new reducer which use a different type to accumulate inputs.

So, instead of

  type Transducer a b = (Reducer a r s) -> (Reducer b r s)

you have:

  type Transducer a b r r' = (Reducer a r s) -> (Reducer b r' s)

Or, most generally (adding in the ability to change not only the type of the accumulator but also the type of the final result):

  type Transducer a b r r' s s' = (Reducer a r s) -> (Reducer b r' s')