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I suggest adding a strict variant of the iterate function to the Data.List module, as others seem to have had a need for it too. It is useful when you want to repeatedly apply a function a large number of times and get the final result. Using the standard iterate function in this way results in the whole list being held in memory, as exemplified in the following GHCi session (code compiled with -O2 behaves similarly):

 > let f = (+1) in iterate f 0 !! 10000000
 *** Exception: stack overflow

Using a strict variant of iterate seems to be sufficient for this code to run in O(1) memory:

 > let iterate' f x = x `seq` x : iterate' f (f x)
 > let f = (+1) in iterate' f 0 !! 10000000
 10000000

I have no idea if this is something that could/should be detected by the strictness analyzer; that would obviously be preferable if it is indeed possible.