[Haskell-cafe] Memoization-question

[Mattias Bengtsson]

The program below computes (f 27) almost instantly but if i replace the
definition of (f n) below with (f n = f (n - 1) * f (n -1)) then it
takes around 12s to terminate. I realize this is because the original
version caches results and only has to calculate, for example, (f 25)
once instead of (i guess) four times.
There is probably a good reason why this isn't caught by the compiler.
But I'm interested in why. Anyone care to explain?

> main = print (f 27)
> 
> f 0 = 1
> f n = let f' = f (n-1)
>       in f' * f'

(compiled with ghc --make -O2)

Mattias