When I previously asked about memoization, I got the impression that memoization is not something that just happens magically in Haskell. Yet, on a Haskell wiki page about Memoization, an example given is

memoized_fib :: Int -> Integer
memoized_fib = (map fib [0 ..] !!)
   where fib 0 = 0
         fib 1 = 1
         fib n = memoized_fib (n-2) + memoized_fib (n-1)

I guess this works because, for example, I tried "memoized_fib 10000" and the interpreter took three or four seconds to calculate. But every subsequent call to "memoized_fib 10000" returns instantaneously (as does "memoized_fib 10001").

Could someone explain the technical details of why this works? Why is "map fib [0 ..]" not recalculated every time I call memoized_fib?

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