[Haskell-cafe] Tying the recursive knot
Luke Palmer
lrpalmer at gmail.com
Fri Mar 25 00:23:53 CET 2011
On Thu, Mar 24, 2011 at 4:02 PM, Joshua Ball <joshbball at gmail.com> wrote:
> Never mind. I figured it out on my own. Here's my solution for
> posterity. There's probably a "fix" hiding in there somewhere - notice
> the new type of reduce.
Yep, there is:
> force :: M.Map Key Chain -> M.Map Key [Int]
> force mp = ret where
> ret = M.fromList (map (\k -> (k, reduce mp (ret !) k)) (M.keys mp))
^^^_________________________________________^^^
There's your knot. You could have written it like this:
force mp = fix (\ret -> M.fromList (map (\k -> (k, reduce mp (ret !) k))
(M.keys mp))
> reduce :: M.Map Key Chain -> (Key -> [Int]) -> Key -> [Int]
> reduce mp lookup key = follow (mp ! key) where
> follow (Link i c) = i : follow c
> follow (Ref k) = lookup k
> follow (Trace message c) = trace message (follow c)
>
> example = M.fromList [(Key "ones", Link 1 . Trace "expensive
> computation here" . Ref . Key $ "ones")]
>
> main = print $ take 10 $ (force example ! Key "ones")
>
> On Thu, Mar 24, 2011 at 12:35 PM, Joshua Ball <joshbball at gmail.com> wrote:
>> {-
>> - 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
>> -}
>>
>
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