[Haskell-cafe] Intuitive function given type signature

[Brent Yorgey]

On Wed, May 19, 2010 at 04:27:14AM +0000, R J wrote:
> 
> What are some simple functions that would naturally have the following type signatures:
> f :: (Integer -> Integer) -> Integer

Well, this means f is given a function from Integer to Integer, and it
has to somehow return an Integer, (possibly) using the function it is
given.  For example, f could just ignore its argument:

  f _ = 6

Or it could apply it to a particular input value:

  f g = g 0

I'll let you think of some other possibilities.

> g :: (Integer -> Integer) -> (Integer -> Integer)

g is given an Integer->Integer function and has to produce a different
one.  But as someone else pointed out, you can also think of this as

  g :: (Integer -> Integer) -> Integer -> Integer

That is, g is given an Integer->Integer function as well as an
Integer, and must somehow use these things to produce another Integer.
There are lots of ways to do this--I'll let you figure this one out.

-Brent