Why doesn't Haskell accept arguments after a function composition?

Question

Considering Haskell has currying functions, we can do this:

foo a b = a + b -- equivalent to `foo a = \b -> a + b`

foo 1 -- ok, returns `\b -> 1 + b`
foo 1 2 -- ok, returns 3

Declaring the function returning a lambda, just like in the comment, works just fine as well.

But when I compose these functions, like this:

foo a b = a + b
bar x = x * x

bar . foo 1 -- ok, returns a lambda
bar . foo 1 2 -- wrong, I need to write `(bar . foo 1) 2`

Then it results in an error.

The question is: why are the parentheses around the function composition necessary?

Answer 1

Let's assume that you've define the following in GHCi:

λ> let foo a b = a + b
λ> let bar x = x * x

Based on some of your follow-up comments, it seems that you believe

bar . foo 1 2

to be equivalent to

(bar . foo 1) 2

However, remember that function application (space) has higher precedence than the composition operator (.); therefore

bar . foo 1 2

is really equivalent to

bar . ((foo 1) 2)

Now, let's look at the types:

• . has type (b -> c) -> (a -> b) -> a -> c; its two arguments are functions (that can be composed).
• bar has type Num a => a -> a, and is therefore compatible with the type (b -> c) of the first argument of ..
• foo 1 2 has type Num a => a; it's a (polymorphic) numeric constant, not a function, and is therefore not compatible with the type (a -> b) of the second argument of ..

That's why you're getting a type error in bar . foo 1 2. What you can do, though, is

bar $ foo 1 2

because the $ operator has type (a -> b) -> a -> b. See Haskell: difference between . (dot) and $ (dollar sign)