Two ways to combine Foo values

data Foo = Foo { alpha :: Int, beta :: Int, gamma :: Int
               , delta :: Int, eta :: Int } deriving (Eq, Ord, Show)

plusOn :: Num a => (Foo -> a) -> Foo -> Foo -> a
plusOn = on (+)
maxOn :: Ord a => (Foo -> a) -> Foo -> Foo -> a
maxOn = on max

newtype AddFoo = AddFoo { getAddFoo :: Foo }
instance Semigroup AddFoo where
  AddFoo x <> AddFoo y =
    AddFoo $ Foo (plusOn alpha x y) (maxOn beta x y) (plusOn gamma x y)
                 (maxOn delta x y) (plusOn eta x y)
instance Monoid AddFoo where
  mempty = AddFoo (Foo 0 0 0 0 0)
  mappend = (<>)

newtype MaxFoo = MaxFoo { getMaxFoo :: Foo }
instance Semigroup MaxFoo where
  MaxFoo x <> MaxFoo y =
    MaxFoo $ Foo (maxOn alpha x y) (maxOn beta x y) (maxOn gamma x y)
                 (maxOn delta x y) (maxOn eta x y)
instance Monoid MaxFoo where
  mempty = MaxFoo (Foo 0 0 0 0 0)
  mappend = (<>)