Memoization
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Memoization is a technique for storing values of a function instead of recomputing them each time the function is called.
A classic example is the recursive computation of Fibonacci numbers.
The immediate implementation of Fibonacci numbers without memoization is horribly slow.
Try slow_fib 30, not too much higher than that and it hangs.
slow_fib :: Integer -> Integer
slow_fib 1 = 1
slow_fib 2 = 1
slow_fib n = slow_fib (n-2) + slow_fib (n-1)
The memoized version is much faster.
Try memoized_fib 10000.
memoized_fib :: Integer -> Integer
memoized_fib =
let fib' 0 = 0
fib' 1 = 1
fib' n = memoized_fib (n-2) + memoized_fib (n-1)
in (map fib' [0 ..] !!)