Suppose you had no idea what function composition should do, but you were given the type:
(.) :: (b -> c) -> (a -> b) -> a -> c
and had to define it:
(f . g) x = ???
We want a c. The only way we know to get a c is with f, which will give us a c if we give it a b. The only way we're given to get a b is with g, which will give us a b if we give it an a. Hey, x is an a!
(f . g) x = f (g x)
is thus the only way to honor the declaration.
Yes, this is a simple example... but not only can the method be applied more generally, you can get ghc to help you with error messages of the form "I expected a here but {you gave me something else, I can't infer that}". For details and a video working through examples, check out Matthew Brecknell's blog post "Hole-Driven Haskell".
