iterate -is:exact -package:storablevector package:utility-ht

iterate :: Monad m => (a -> m a) -> a -> m [a]
utility-ht Control.Monad.HT
I think this makes only sense in a lazy monad like Trans.State.Lazy or IO.Lazy.
iterateLimit :: Monad m => Int -> (a -> m a) -> a -> m [a]
utility-ht Control.Monad.HT
parameter order equal to that of nest
iterateLimitM :: Monad m => Int -> (a -> m a) -> a -> m [a]
utility-ht Control.Monad.HT
Deprecated: use M.iterateLimit
iterateAssociative :: (a -> a -> a) -> a -> [a]
utility-ht Data.List.HT
For an associative operation op this computes iterateAssociative op a = iterate (op a) a but it is even faster than map (powerAssociative op a a) [0..] since it shares temporary results. The idea is: From the list map (powerAssociative op a a) [0,(2*n)..] we compute the list map (powerAssociative op a a) [0,n..], and iterate that until n==1. 
\x -> equating (take 1000) (List.iterate (x+) x) (iterateAssociative (+) (x::Integer))
iterateLeaky :: (a -> a -> a) -> a -> [a]
utility-ht Data.List.HT
This is equal to iterateAssociative. The idea is the following: The list we search is the fixpoint of the function: "Square all elements of the list, then spread it and fill the holes with successive numbers of their left neighbour." This also preserves log n applications per value. However it has a space leak, because for the value with index n all elements starting at div n 2 must be kept. 
\x -> equating (take 1000) (List.iterate (x+) x) (iterateLeaky (+) (x::Integer))