You don't have worry about the modulo math if you use automatic deriving of the Enum and Bounded typeclasses.
data Day = Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday deriving (Show, Eq, Enum, Bounded)
next :: (Eq a, Enum a, Bounded a) => a -> a
next d = if d == maxBound then minBound else succ d
back :: (Eq a, Enum a, Bounded a) => a -> a
back d = if d == minBound then maxBound else pred d
applyN:: Int -> (a -> a) -> (a -> a)
applyN n _ | n < 1 = id
applyN n f = (applyN (n-1) f) . f
*Main> applyN 9 next Sunday
Tuesday