How about a function for the Endo monoid, that lifts from a single value. toEndo :: (Monoid a) => a -> Endo a toEndo x = Endo (mappend x) For 'a' being a list type one would have a nice difference list. This may also occur in the documentation - both in the ones of Monoid.Endo and the of http://hackage.haskell.org/cgi-bin/hackage-scripts/package/dlist . A similar application is Peano number with efficient addition. Would also be a nice type for ShowS.