# Compose

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− | This one's easy. We fold over the list using [[ | + | This one's easy. We fold over the list using [[Function composition|composition]] as our combinator to join items. We flip it, though, because we want a value to be fed into the first function in the list first, but <hask>f . g</hask> applies <hask>g</hask> before <hask>f</hask>. |

We use <hask>id</hask> as the starting value, as <hask>id</hask> is an identity for composition. | We use <hask>id</hask> as the starting value, as <hask>id</hask> is an identity for composition. |

## Revision as of 16:24, 10 October 2006

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 |

## 1 The Sane Solution

compose :: [a -> a] -> a -> a compose fs v = foldl (flip (.)) id fs $ v

## 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 do-block: 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.

## 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)

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.

## 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)

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## 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.

## 6 References

Mainly see All About Monads, specifically chapter two, which has overviews and examples for all the major monads.

## 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 -}