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There are certainly laws as to what goes on when you do various things with IO values. The relevant point, though, was that access to IO means there are few (any?) laws restricting what is actually going on when that integer is generated.

Actually, I kind of wish IO was split up a bit... I have been meaning to play with rolling some typeclasses (with an IO instance and a testing instance) that wrap up IO of various types, so I define my functions in terms of these and spot what kind of IO various functions might do - I'm not yet sure how much of a win it will be, but it seems like something to explore.




I've seen them created a few times. I'm pretty sure there are at least a few implementations in Hackage of such divided IO monads. More generally, the haute method for solving this would be to use Operational or Free monads to create your restricted monad type and then interpret it into IO.

http://www.haskellforall.com/2012/07/purify-code-using-free-...

http://www.haskellforall.com/2012/06/you-could-have-invented...

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I think optimally, with a set of typeclasses, one could define instances for IO and just use things with no interpretation or build a datastructure with free monads to perform whatever other inspections or manipulations you want. There could be some incompatability between the two notions that I'm missing, though...

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I think I've seen the typeclass route as well before. It may have just been a blog post and not a library implementation, though. The two methods have different epistemological ideas, but could be combined. For instance:

    {-# LANGUAGE DeriveFunctor, GeneralizedNewtypeDeriving, FlexibleInstances #-}
    module CrWr where
    
    import Control.Monad.Free
    import Data.IORef
    
    data RWRefF t a = NewRef t (IORef t -> a) | PeekRef (IORef t) (t -> a) | PutRef (IORef t) t a
                    deriving Functor
    newtype RWRef t a = RWRef (Free (RWRefF t) a) deriving Monad
    
    newRef :: t -> RWRef t (IORef t)
    newRef t = RWRef $ liftF $ NewRef t id
    peekRef :: IORef t -> RWRef t t
    peekRef r = RWRef $  liftF $ PeekRef r id
    putRef :: IORef t -> t -> RWRef t ()
    putRef r t = RWRef $ liftF $ PutRef r t ()
    
    interpret :: RWRef t a -> IO a
    interpret (RWRef (Pure a)) = return a
    interpret (RWRef (Free (NewRef t f))) = newIORef t >>= interpret . RWRef . f
    interpret (RWRef (Free (PeekRef r f))) = readIORef r >>= interpret . RWRef . f
    interpret (RWRef (Free (PutRef r t next))) = writeIORef r t >> interpret (RWRef next)
    
    -- Highly specialized class of IO monads
    class Monad m => RWIntRefMonad m where
      new  :: Int -> m (IORef Int)
      peek :: IORef Int -> m Int
      put  :: IORef Int -> Int -> m ()
      toIO :: m a -> IO a
    
    instance RWIntRefMonad (RWRef Int) where
      new = newRef
      peek = peekRef
      put = putRef
      toIO = interpret
    
    incr :: RWIntRefMonad m => IORef Int -> m ()
    incr r = peek r >>= put r . (+1)
    
    main = do r <- newIORef 0
              -- We need to specialize before the m gets erased
              toIO (incr r :: RWRef Int ())
              readIORef r >>= print

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> Actually, I kind of wish IO was split up a bit... I have been meaning to play with rolling some typeclasses (with an IO instance and a testing instance) that wrap up IO of various types, so I define my functions in terms of these and spot what kind of IO various functions might do - I'm not yet sure how much of a win it will be, but it seems like something to explore.

There's a section on this practice in Real World Haskell: http://book.realworldhaskell.org/read/programming-with-monad...

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Right, that's very much what I had in mind - I might very well have got it from there and forgotten; I've read much if not all of RWH at one point or another.

I would point out that in addition to the mentioned testing use (itself not to be underestimated - QuickCheck is amazing and making more things tractable to QuickCheck is great), there's also some other big potential wins. If I have a function that deals with local files in a monad that's an instance of MonadHandle, I can write an instance for a RemoteIO type that performs file operations on a remote system through a network connection, and suddenly the function that was local also works remotely.

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OH! That's where I saw it. I couldn't remember, but I know the idea has been floating around for a long while.

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