関数適用($)と関数合成(.)

Haskell の関数適用($)と関数合成(.)の操作上の違いを端的に説明

ghci> sum . replicate 5 $ max 6.7 8.9
44.5
ghci> sum $ replicate 5 $ max 6.7 8.9
44.5

演算の優先順位は . > $
. は右側に関数がくる
$ は右側に値がくる

従って以下は上記の例と等価

ghci> (sum . replicate 5) $ max 6.7 8.9
44.5
ghci> sum $ (replicate 5 $ max 6.7 8.9)
44.5

以下の例は当然エラーになる

-- .の右側が値なのでエラー
ghci> sum $ replicate 5 . max 6.7 8.9

<interactive>:132:1: error:
    * Non type-variable argument in the constraint: Foldable ((->) a1)
      (Use FlexibleContexts to permit this)
    * When checking the inferred type
        it :: forall a1 a2.
              (Foldable ((->) a1), Ord (a1 -> a2), Fractional (a1 -> a2),
               Num [a2]) =>
              [a2]

-- $の右側が関数なのでエラー
ghci> (sum $ replicate 5) $ max 6.7 8.9

<interactive>:137:8: error:
    * Couldn't match type `[a0]' with `Double -> t'
      Expected type: a0 -> Double -> t
        Actual type: a0 -> [a0]
    * Possible cause: `replicate' is applied to too many arguments
      In the second argument of `($)', namely `replicate 5'
      In the expression: (sum $ replicate 5)
      In the expression: (sum $ replicate 5) $ max 6.7 8.9
    * Relevant bindings include it :: t (bound at <interactive>:137:1)

-- .の右側が値なのでエラー
ghci> sum . (replicate 5 $ max 6.7 8.9)

<interactive>:133:8: error:
    * Couldn't match expected type `a -> [c]'
                  with actual type `[Double]'
    * In the second argument of `(.)', namely
        `(replicate 5 $ max 6.7 8.9)'
      In the expression: sum . (replicate 5 $ max 6.7 8.9)
      In an equation for `it': it = sum . (replicate 5 $ max 6.7 8.9)
    * Relevant bindings include
        it :: a -> c (bound at <interactive>:133:1)

Thanks!!

@yuchiki1000yen