Two ways to combine Foo values.hs

data FooF = Foo { alpha :: HKD f Int, beta :: HKD f Int, gamma :: HKD f Int
               , delta :: HKD f Int, eta :: HKD f Int } deriving (Eq, Ord, Show)
type Foo = FooF Identity

newtype Combine a = C { applyC :: a -> a -> a }

combineFoos :: FooF Combine -> Foo -> Foo -> Foo
combineFoos (Foo fa fb fg fd fe) (Foo a0 b0 g0 d0 e0) (Foo a1 b1 g1 d1 e1)
  = Foo (applyC fa a0 a1) (applyC fb b0 b1) (applyC fg g0 g1) (applyC fd d0 d1) (applyC fe e0 e1)

newtype AddFoo = AddFoo { getAddFoo :: Foo }
instance Semigroup AddFoo where
  AddFoo x <> AddFoo y = coerce $ combineFoos $ Foo (C (+)) (C max) (C (+)) (C max) (C (+))
instance Monoid AddFoo where
  mempty = AddFoo (Foo 0 0 0 0 0)
  mappend = (<>)

newtype MaxFoo = MaxFoo { getMaxFoo :: Foo }
instance Semigroup MaxFoo where
  (<>) = coerce $ combineFoos $ Foo (C max) (C max) (C max) (C max) (C max)
instance Monoid MaxFoo where
  mempty = MaxFoo (Foo 0 0 0 0 0)
  mappend = (<>)