Composing monad actions with folds

Question

Let\'s take a function of type (Monad m) => a -> m a. For example:

ghci> let f x = Just (x+1)

I\'d like to be able to

Answer 1

I'd probably create some stricter variants of existing functions.

{-# LANGUAGE BangPatterns #-}
iterate' f !x = x : iterate' f (f x)
ma >>=! f = do !a <- ma; f a
times' n f a = iterate' (>>=! f) (return a) !! n

Perhaps your problems stem from the fact that seq only evaluates the first argument to WHNF? If you're working on a complex structure, you may need a deeper seq, like deepseq.

Answer 2

If you make f strict as in

f x = let y = x+1 in y `seq` Just y

or

-- remember to enable -XBangPatterns
f !x = Just (x+1)

and leave the rest alone, your code runs in constant space (albeit slowly) even with very large n:

ghci> times 4000000000 f 3
Just 4000000003

Answer 3

I came up with this:

 last $ take n $ iterate (>>= f) $ Just 1

But it also overflows the stack on large numbers of n. I don't have the time right now to look into it more :-(