isomorphism.hs

{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleInstances #-}

{-# LANGUAGE FlexibleContexts #-}

import Control.Monad.Reader

class Iso a b where
    isoFrom :: a -> b
    isoTo :: b -> a

instance Iso a a where
    isoFrom = id
    isoTo = id

-- real-life sample
type MyState = Int
type Callback = MyState -> MyState

testCallback :: MyState -> Callback -> MyState
testCallback myState cb = cb myState

testCallbackGeneric :: Iso Callback a => MyState -> a -> MyState
testCallbackGeneric myState cb = (isoTo cb) myState

callbackFunction :: Callback
callbackFunction s = s + 10

-- we need a proof of isomorphism
{-
instance Iso Callback (Reader MyState MyState) where
    isoFrom cb = reader cb
    isoTo m = runReader m 
-}

-- a more generic version, proving my point
instance Iso (a -> b) (Reader a b) where
    isoFrom f = reader f
    isoTo m = runReader m 

callbackMonad :: Reader MyState MyState
callbackMonad = do
    x <- ask
    return $ x - 10

main :: IO ()
main = do
    let myState = 42
    
    let myStateA = testCallback myState callbackFunction
    -- let myStateB = testCallback myState callbackMonad -- won't work, obviously
    let myStateC = testCallbackGeneric myState callbackFunction
    let myStateD = testCallbackGeneric myState callbackMonad

    print myStateA
    --print myStateB
    print myStateC
    print myStateD