Compose
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(composeReader' = foldr local id) 

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Latest revision as of 06:26, 18 September 2008
This page illustrates the solution in different monads. Most are a bit of a joke; you'd probably only ever use the first solution presented, but nevertheless the nice features of the various monads are demonstrated.
Contents 
[edit] 1 The sane solution
compose :: [a > a] > a > a compose fs v = foldl (flip (.)) id fs $ v
[edit] 2 Using State
composeState :: [a > a] > a > a composeState = execState . mapM modify
composeState fs v = execState (mapM modify fs) v
fs = mapM modify [(*2), (+1), \n > (n  5) * 4]  fs is entirely equivalent to the following doblock: fs' = do modify (*2) modify (+1) modify (\n > (n  5) * 4)
In other words, we obtain a stateful computation that modifies the state with the first function in the list, then the second, and so on.
[edit] 3 Using Reader
composeReader :: [a > a] > a > a composeReader fs v = runReader (compose' fs) v where compose' [] = ask compose' (f:fs) = local f (compose' fs)  compose' = foldr local ask  alternative: no runReader or ask required  TODO: explain why this works composeReader' :: [a > a] > a > a composeReader' = foldr local id
fs = compose' [(*2), (+1), \n > (n  5) * 4]  again, this is entirely equivalent to the following: fs' = local (*2) $ local (+1) $ local (\n > (n  5) * 4) ask
Once this composition has been built up, we run it, starting off with an environment of the starting value.
[edit] 4 Using Writer
composeWriter :: [a > a] > a > a composeWriter fs v = (execWriter $ compose' fs) v where compose' [] = return id compose' (f:fs) = censor (. f) (compose' fs)  compose' = foldr (censor . flip (.)) (return id)
Once this computation has been built up, we extract this long composition chain, and apply it to our starting value.
Also interesting to note is that this method is really equivalent to the "Sane method" described above. We just iterate along the list, accumulating a composition chain. The only difference here is that we're using some of[edit] 5 Using Cont
The getCC :: MonadCont m => m (m a) getCC = callCC (\c > let x = c x in return x) getCC' :: MonadCont m => a > m (a, a > m b) getCC' x0 = callCC (\c > let f x = c (x, f) in return (x0, f)
do stuff; boing < getCC moreStuff; boing;
x `modulo` m = (`runContT` return) $ do (u, jump) < getCC' x lift $ print u case u of _  u < 0 > jump (u + m)  u >= m > jump (u  m)  otherwise > return u
composeCont :: [a > a] > a > a composeCont fs = runCont compose' id where compose' = do ((gs,f), jump) < getCC' (fs,id) case gs of [] > return f (g:gs') > jump (gs', g . f)
composeCont :: [a > a] > a > a composeCont fs x = runCont compose' id where compose' = do ((gs,y), jump) < getCC' (fs,x) case gs of [] > return y (g:gs') > jump (gs', g y)
Thanks to Cale Gibbard for providing this example.
[edit] 6 References
Mainly see All About Monads, specifically chapter two, which has overviews and examples for all the major monads.
[edit] 7 The whole code
In case you wish to run this code, here it is in its entirety:
 Thread a value through a list of function applications module Compose where import Control.Monad.Writer import Control.Monad.Reader import Control.Monad.State import Control.Monad.Cont compose :: [a > a] > a > a compose fs v = foldl (flip (.)) id fs $ v composeState :: [a > a] > a > a composeState = execState . mapM modify composeReader :: [a > a] > a > a composeReader fs v = runReader (compose' fs) v where compose' [] = ask compose' (f:fs) = local f (compose' fs) composeWriter :: [a > a] > a > a composeWriter fs v = (execWriter $ compose' fs) v where compose' [] = return id compose' (f:fs) = censor (. f) (compose' fs) getCC :: MonadCont m => m (m a) getCC = callCC (\c > let x = c x in return x) getCC' :: MonadCont m => a > m (a, a > m b) getCC' x0 = callCC (\c > let f x = c (x, f) in return (x0, f)) composeCont :: [a > a] > a > a composeCont fs = runCont compose' id where compose' = do ((gs,f), jump) < getCC' (fs,id) case gs of [] > return f (g:gs') > jump (gs',g . f) main = do let fs = [(+1), (*2), \n > (n  5) * 4] v = 3 putStrLn $ "compose: " ++ (show $ compose fs v) putStrLn $ "compostState: " ++ (show $ composeState fs v) putStrLn $ "composeReader: " ++ (show $ composeReader fs v) putStrLn $ "composeWriter: " ++ (show $ composeWriter fs v) putStrLn $ "composeCont: " ++ (show $ composeCont fs v) { *Compose> main compose: 12 compostState: 12 composeReader: 12 composeWriter: 12 composeCont: 12 }