Dear Dimitri:

I am having a hard time with.
doTwice f x = f (f x)
what does this do? What is the systematic way to evaluate these expressions?

You might recognize the numeral two from pure http://en.wikipedia.org/wiki/Lambda_calculus and the fact that some lambda expressions are irreducible while others never arrive at such a normal form.

Are there any resources with many practice exercises like this one?

None that I am aware of. You mostly find theoretical revelations. Possibly because there is often nothing more practical than the right theory. But it is easy to make up some practical examples to play with:

let pow2 f x = f (f x) in [ pow2 (pow2 (pow2 (1+)))) 0, pow2 pow2 pow2 (1+) 0] == [2^3, 2^2^2^2]

Current Haskell compilers will not tell you directly that pow2 pow2 pow2 pow2 = do65536times and pow 2 pow2 (pow2 pow2) = do256times but just do so in concrete cases.

Try pow2 pow2 (+1) 0

Or pow2 pow2 (++"-") "."

Thanks,
Dimiti
[1] http://www.seas.upenn.edu/~cis552/lectures/Lec2.html