Why does Haskell use -> instead of =?

Question

Why does Haskell use "->" where it seemingly could have just used "="?

For example, what's wrong with this?

take m ys               = case (m,ys) of
                            (0,_)       =  []
                            (_,[])      =  []
                            (n,x:xs)    =  x : take (n-1) xs

or

(\x = x * x)

Answer 1

It would be unfortunate to write

(0, _) = []

because that is not true.

In the tradition of Robert Recorde, we try to write equations only when we intend the left-hand side to equal the right-hand side. So we write

dup x = (x, x)

to make dup x equal to (x, x), or

dup = \ x -> (x, x)

to make dup equal to the function which maps x to (x, x), but not

\ x = (x, x)

because there is no way to make x equal (x, x).

We depart from the tradition only slightly when we allow "falling through", e.g.,

f 0 = 1
f n = 2 * f (n - 1)

but only in the sense that the second line has a silent "otherwise".