Changing the written data in a Writer monad

Question

Given a Writer monad action, I want to modify it by mapping a function over the written data inside the monad action.

Something like:

retell :: (w -> w') -> Writer w a -> Writer w' a

Does such a function already exists in the libraries? If not, how can one be defined?

Answer 1

retell f = Writer . second f $ runWriter 

There is also a mapWriter function provided by the libraries. So you could do this:

retell = mapWriter . second

The second function is in Control.Arrow, but you can define a less general version of it yourself like this:

second f (a, b) = (a, f b)