The confusion about the kind of strictness in lazy and strict State monad pops up again and again. How about illustrating the difference using these examples: Control.Monad.Trans.State.Lazy> evalState (mapM (\n -> modify (n+) >> get) [1::Integer ..]) 0 [1,3,6,10,15,21,28,36,45,55,66,78,91,105,120 ... Control.Monad.Trans.State.Strict> evalState (mapM (\n -> modify (n+) >> get) [1::Integer ..]) 0 <<wait infinitely>> ? Now, often I like to have a kind of strictness where lists can be processed lazily but the state is updated strictly between the list cells. E.g. the following expression cannot be computed both in lazy and in strict State monad: evalState (mapM (\n -> modify (n+) >> get) [1::Integer ..]) 0 !! 10000000 Since the list shall still be processed lazily, we must stay in the lazy State monad. But the state shall be updated strictly for every list cell. I can achieve this for instance by replacing 'mapM' by the following 'mapS': mapS :: (a -> State s b) -> [a] -> State s [b] mapS _ [] = gets (\s -> seq s []) mapS f (x:xs) = do y <- f x; s <- get; ys <- mapS f xs; return (seq s (y:ys)) Now evalState (mapS (\n -> modify (n+) >> get) [1::Integer ..]) 0 !! 10000000 can be computed with constant memory consumption.