{- - Hi all, - - I'm having trouble tying the recursive knot in one of my programs. - - Suppose I have the following data structures and functions: -} module Recursion where import Control.Monad.Fix import Data.Map ((!)) import qualified Data.Map as M import Debug.Trace newtype Key = Key { unKey :: String } deriving (Eq, Ord, Show) data Chain = Link Int Chain | Trace String Chain | Ref Key deriving (Show) reduce :: M.Map Key Chain -> Key -> [Int] reduce env k = follow (env ! k) where follow (Link i c) = i : follow c follow (Ref k) = reduce env k follow (Trace message c) = trace message (follow c) -- Now I want a "force" function that expands all of the chains into int sequences. force1, force2 :: M.Map Key Chain -> M.Map Key [Int] -- This is pretty easy to do: force1 mp = M.fromList (map (\k -> (k, reduce mp k)) (M.keys mp)) -- But I want the int sequences to be lazy. The following example illustrates that they are not: example = M.fromList [(Key "ones", Link 1 . Trace "expensive computation here" . Ref . Key $ "ones")] -- Run "force1 example" in ghci, and you will see the "expensive computation here" messages interleaved with an infinite -- list of ones. I would prefer for the "expensive computation" to happen only once. -- Here was my first attempt at regaining laziness: fixpointee :: M.Map Key Chain -> M.Map Key [Int] -> M.Map Key [Int] fixpointee env mp = M.fromList (map (\k -> (k, reduce env k)) (M.keys mp)) force2 env = fix (fixpointee env) main = print $ force2 example {- - However, this gets stuck in an infinite loop and doesn't make it past printing "fromList ". - (It was not difficult for me to see why, once I thought about it.) - - How do I recover laziness? A pure solution would be nice, but in the actual program - I am working on, I am in the IO monad, so I am ok with an impure solution. - It's also perfectly ok for me to modify the reduce function. - - Thanks in advance for you help, - Josh "Ua" Ball -}