BBB http://stackoverflow.com/a/15030372/849891

gistfile1.txt

B is simply defined as

  B f g x = f (g x)

When we supply it with two args, 
it still needs the third. (B f g) needs one more argument.

Let's see what is B B B. It supplies two args to the first B,
so we need to add the third there:

  B B B f = B (B f)

and so we need two more:

  B B B f g x = B (B f) g x
              = (B f) (g x)
              = B f (g x)

and so there's need for one more argument,

  B B B f g x y = B f (g x) y
                = f (g x y)