# Compose

### From HaskellWiki

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 build up, we extract this long composition chain, and apply it to our starting value.

## 5 Using Cont

I'm pretty sure this could be done, but I don't have a clue how! If you know ## 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 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) 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) {- *Compose> main compose: 12 compostState: 12 composeReader: 12 composeWriter: 12 -}