有人可以解释下面的代码如何工作？

Question

I am doing a coding challenge in codewar: Write function avg which calculates average of numbers in given list. My solution works but I don't quite understand one of the solutions of others. Can anyone explain?

avg :: [Float] -> Float
avg = (/) <$> sum <*> fromIntegral . length

Shouldn't it be:

avg l = pure (/) <*> sum l <*> fromIntegral . length  $ l 

Answer 1

This code uses the Applicative instance of the (->) a type, which is defined here as:

instance Applicative ((->) a) where
    pure = const
    (<*>) f g x = f x (g x)

You can interpret this implementation by thinking of naryFunction <$> f1 <*> f2 <*> ... <*> fn as "apply the same parameter to all n functions and apply the resulting arguments to naryFunction ".

In your case, (/) <$> sum <*> fromIntegral . length (/) <$> sum <*> fromIntegral . length can be thought as \\ xs -> (/) (sum xs) ((fromIntegral . length) xs) which is just sum xs / fromIntegral (length xs) .

You can prove this by simply expanding your expression with the definition of (<*>) :

avg = (/) <$> sum <*> fromIntegral . length
avg = fmap (/) sum <*> fromIntegral . length
avg xs = (fmap (/) sum) xs ((fromIntegral . length) xs)
avg xs = ((/) . sum xs) (fromIntegral (length xs))  -- fmap f g = f . g
avg xs = sum xs / fromIntegral (length xs)