Avoid repeating the calculation, retain the results

It would be really cool if the calculated result of some cell in an array was somehow saved for repeated access:

fun(x) = (sleep(1/3); 2x)
x = rand(3)
fun.(x) # this takes about 1 second
mx = mappedarray(fun, x); # this is ultra quick
for i in 1:3 # first iteration should take 1/3 seconds, the two subsequent iterations should be instantaneous 
    mx[1]
end # they're not, this loop takes about a second to complete

The rational behind this is that with normal arrays you pay computation time for the map for ALL the cells (while you really might not need all of them), but that's a one-time cost, repeated access is cheap. With mapped arrays you pay the calculation price only for the cells you need, winning, but if you need to access them repeatedly then this gain in time can be quickly lost.

Note that I think I can get this by using Memoize and @memoizeing the mapped function...

Start by examining the mappedarray entry point and how indexed access invokes the mapped function. Define the behavior for retaining results so the first access computes a cell and repeated access avoids recomputation, while preserving lazy evaluation for cells that have not been accessed.