documentation of difference between lazy and strict State monad

[Henning Thielemann]

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.