I'm just not understanding the concept of a functor in this context: I have this plus :: Int -> Int -> Int plus n m = if (n == 0) then m else sCessor (plus (pCessor n) m) where sCessor x = x + 1 pCessor x = if (x == 0) then error "too small" else (x - 1) and this data MyNum = MNZero | OneMoreThan MyNum deriving (Show,Eq,Ord) plus2 :: MyNum -> MyNum -> MyNum plus2 n m = if (n == MNZero) then m else sCessor (plus2 (pCessor n) m) where sCessor x = (OneMoreThan x) pCessor x = if (x == MNZero) then (error "too small") else (oneLess x) oneLess MNZero = MNZero oneLess (OneMoreThan myn) = myn It seems there should be just one plus, function that would handle both an Int-based Peano and the MyNum-based Peano, not two. But in this definition fmap :: (a -> b) -> f a -> f b The (a -> b) should be "lifted" over the f a -> f b But I can't conceive of how this should all fit together, i.e., to create just one generic plus that would handle both the plus :: Int -> Int -> Int and the plus2 :: MyNum -> MyNum -> MyNum. Trying to get started, I would assume I need some sort of instance Functor MyNum describing, yeah, what? Or am I barking up the completely wrong tree here, i.e., this isn't a functor issue? LB