Control.Proxy.Trans.Tutorial

This module provides the tutorial for the Control.Proxy.Trans hierarchy

Motivation

In a Session, all composed proxies share effects within the base monad. To see how, consider the following simple Session:

client1 :: () -> Client () () (StateT Int IO) r
client1 () = forever $ do
    s <- lift get
    lift $ lift $ putStrLn $ "Client: " ++ show s
    lift $ put (s + 1)
    request ()

server1 :: () -> Server () () (StateT Int IO) r
server1 () = forever $ do
    s <- lift get
    lift $ lift $ putStrLn $ "Server: " ++ show s
    lift $ put (s + 1)
    respond ()

>>> execWriterT $ runProxy $ client1 <-< server1
Client: 0
Server: 1
Client: 2
Server: 3
Client: 4
Server: 5
...

The client and server share the same state, which is sometimes not what we want. We can easily solve this by running each Proxy with its own local state by changing the order of the Proxy and StateT monad transformers:

client2 :: () -> StateT Int (Client () () IO) r
client2 () = forever $ do
    s <- get
    lift $ lift $ putStrLn $ "Client: " ++ show s
    put (s + 1)
    lift $ request ()

server2 :: () -> StateT Int (Server () () IO) r
server2 () = forever $ do
    s <- get
    lift $ lift $ putStrLn $ "Server: " ++ show s
    put (s + 1)
    lift $ respond ()

... but then we can no longer compose them directly. We have to first unwrap each one with evalStateT before composing:

>>> runProxy $ (`evalStateT` 0) . client2 <-< (`evalStateT` 0) . server2
Client: 0
Server: 0
Client: 1
Server: 1
Client: 2
Server: 2
...

Here's another example: suppose we want to handle errors within proxies. We could try adding EitherT to the base monad like so:

import Control.Error

client3 :: () -> Client () () (EitherT String IO) ()
client3 () = forM_ [1..] $ \i -> do
    lift $ lift $ print i
    request ()

server3 :: (Monad m) => () -> Server () () (EitherT String m) r
server3 () = lift $ left "ERROR"

>>> runEithert $ runProxy $ client2 <-< server2
1
Left "ERROR"

Unfortunately, we can't modify server2 to catchT that error because we cannot access the inner EitherT monad transformer until we run the Session. We'd really prefer to place the EitherT monad transformer outside the Proxy monad transformer so that we can catch and handle errors locally within a Proxy without disturbing other proxies:

client4 :: () -> EitherT String (Client () () IO) ()
client4 () = forM_ [1..] $ \i -> do
    lift $ lift $ print i
    lift $ request ()

server4 :: () -> EitherT String (Server () () IO) ()
server4 () = (forever $ do
    lift $ respond ()
    throwT "Error" )
  `catchT` (\str -> do
        lift $ lift $ putStrLn $ "Caught: " ++ str
        server4 () )

However, this solution similarly requires unwrapping the client and server using runEitherT before composing them:

>>> runProxy $ runEitherT . client4 <-< runEitherT . server4
1
Caught: Error
2
Caught: Error
3
Caught: Error
...

Proxy Transformers

We need some way to layer monad transformers outside the proxy type without interfering with Proxy composition. To do this, we overload Proxy composition using the Channel type class from Control.Proxy.Class:

class Channel p where
    idT :: (Monad) m => a' -> p a' a a' a m r
    (>->)
     :: (Monad m)
     => (b' -> p a' a b' b m r)
     -> (c' -> p b' b c' c m r)
     -> (c' -> p a' a c' c m r)

Obviously, Proxy implements this class:

instance Channel Proxy where ...

... but we would also like our monad transformers layered outside the Proxy type to also implement the Channel class so that we could compose them directly without unwrapping. Unfortunately, these monad transformers do not fit the signature of the Channel class.

Fortunately, the Control.Proxy.Trans hierarchy provides several common monad transformers which have been upgraded to fit the Channel type class. I call these "proxy transformers".

For example, Control.Proxy.Trans.State provides a proxy transformer equivalent to Control.Monad.Trans.State. Similarly, Control.Proxy.Trans.Either provides a proxy transformer equivalent to Control.Monad.Trans.Either.

Let's use a working code example to demonstrate how to use them:

import Control.Proxy.Trans.State

client5 :: () -> StateP Int Proxy () () () C IO r
client5 () = forever $ do
    s <- get
    liftP $ lift $ putStrLn $ "Client: " ++ show s
    put (s + 1)
    liftP $ request ()

server5 :: () -> StateP Int Proxy C () () () IO r
server5 () = forever $ do
    s <- get
    liftP $ lift $ putStrLn $ "Server: " ++ show s
    put (s + 1)
    liftP $ respond ()

You'll see that our type signatures changed. Now we use StateP instead of StateT. However, StateP does not transform monads, but instead transforms proxies.

To see this, let's first study the kind of StateT. If we first define:

kind MonadKind = * -> *

Then StateT s takes a monad, and returns a new monad:

StateT s :: MonadKind -> MonadKind

Now consider the kind of a Proxy-like type constructor suitable for the Channel type class:

kind ProxyKind = * -> * -> * -> * -> (* -> *) -> * -> *

Then StateP s takes a Proxy-like and returns a new Proxy-like type:

StateP s :: ProxyKind -> ProxyKind

This is why I call these "proxy transformers" and not monad transformers. They all take some Proxy-like type that implements Channel and transform it into a new Proxy-like type that also implements Channel. For example, StateP implement the following instance:

instance (Channel p) => Channel (StateP s p) where ...

All proxy transformers guarantee that if the base proxy implements the Channel type class, then the transformed proxy also implements the Channel type class. This means that you can build a proxy transformer stack, just like you might build a monad transformer stack.

Unfortunately, in order to use proxy transformers, you must expand out the Client and Server type synonyms, which are not compatible with proxy transformers. Sorry! This is why there are no Server or Client type synonyms in the types of our new client and server and I had to write out all the inputs and outputs.

Notice how the outermost lift statements in our client and server have changed to liftP. liftP replaces lift for proxy transformers, and it lifts any action in the base proxy to an action in the transformed proxy. In the previous example, the base proxy was Proxy and the transformed proxy was StateP s Proxy, so liftPs type got specialized to:

liftP :: Proxy a' a b' b m r -> StateP s Proxy a' a b' b m r

The ProxyTrans class defines liftP, and all proxy transformers implement the ProxyTrans class. Since proxies are still monads, liftP must behave just like lift and obey the monad transformer laws:

(liftP .) return = return

(liftP .) (f >=> g) = (liftP .) f >=> (liftP .) g

But, unlike lift, liftP obeys one extra set of laws that guarantee it also lifts composition sensibly:

(liftP .) idT = idT

(liftP .) (f >-> g) = (liftP .) f >-> (liftP .) g

In fact, this (liftP .) pattern is so ubiquitous, that the ProxyTrans class provides the additional mapP method for convenience:

mapP = (liftP .)

Proxy transformers automatically derive how to lift composition correctly and also guarantee that the derived composition obeys the category laws if the base composition obeyed the category laws. Since Proxy composition obeys the category laws, any proxy transformer stack built on top of it automatically derives a composition operation that is correct by construction.

Let's prove this by directly composing our StateP-extended proxies without unwrapping them:

:t client5 <-< server5 :: () -> StateP Int Proxy C () () C IO r

However, we still have to unwrap the final StateP Session before we can pass it to runProxy. We use runStateK for this purpose:

>>> runProxy $ runStateK 0 $ client5 <-< server5
Client: 0
Server: 0
Client: 1
Server: 1
Client: 2
Server: 2
Client: 3
Server: 3
...

Keep in mind that runStateK takes the initial state as its first argument, unlike runStateT. I break from the transformers convention for syntactic convenience.

We can similarly fix our EitherT example, using EitherP from Control.Proxy.Trans.Either:

import Control.Proxy.Trans.Either as E

client6 :: () -> EitherP String Proxy () () () C IO ()
client6 () = forM_ [1..] $ \i -> do
    liftP $ lift $ print i
    liftP $ request ()

server6 :: () -> EitherP String Proxy C () () () IO ()
server6 () = (forever $ do
    liftP $ respond ()
    E.throw "Error" )
  `E.catch` (\str -> do
        liftP $ lift $ putStrLn $ "Caught: " ++ str
        server6 () )

>>> runProxy $ runEitherK $ client6 <-< server6
1
Caught: Error
2
Caught: Error
3
Caught: Error
...

Compatibility

Proxy transformers do more than just lift composition. They automatically promote proxies written in the base monad. For example, what if I wanted to use the takeB_ proxy from Control.Proxy.Prelude.Base to cap the number of results? I can't compose it directly because it uses the Proxy type:

takeB_ :: (Monad m) => Int -> a' -> Proxy a' a a' a m ()

... whereas client6 and server6 use EitherP String Proxy. However, this doesn't matter because we can automatically lift takeB_ to be compatible with them using mapP:

>>> runProxy $ runEitherK $ client6 <-< mapP (takeB_ 2) <-< server6
1
Caught: Error
2
Caught:Error

mapP promotes any proxy written using the base proxy type to automatically be compatible with proxies written using the extended proxy type. This means you can safely write utility proxies using the smallest feature set they require and promote them as necessary to work with more extended feature sets. This ensures that any proxies you write always remain forwards-compatible as people write new extensions.

Proxy Transformer Stacks

You can stack proxy transformers to combine their effects, such as in the following example, which combines everything we've used so far:

client7 :: () -> EitherP String (StateP Int Proxy) () Int () C IO r
client7 () = do
    n <- liftP get
    liftP $ liftP $ lift $ print n
    n' <- liftP $ liftP $ request ()
    liftP $ put n'
    E.throw "ERROR"

>>> runProxy $ runStateK 0 $ runEitherK $ client7 <-< mapP (mapP (enumFromS 1))
0
(Left "Error", 1)

But that's still not the full story! For calls to the base monad (i.e. IO in this case), you don't need to precede them with all those liftPs. Every proxy transformer also correctly derives MonadTrans, so you can dig straight to the base monad by just calling lift at the outer-most level:

client7 :: () -> EitherP String (StateP Int Proxy) () Int () C IO r
client7 () = do
    n <- liftP get
    lift $ print n  -- Much better!
    n' <- liftP $ liftP $ request ()
    liftP $ put n'
    E.throw "ERROR"

Also, you can combine multiple proxy transformers into a single proxy transformer, just like you would with monad transformers:

newtype BothP e s p a' a b' b m r =
    BothP { unBothP :: EitherP e (StateP s p) a' a b' b m r }
    deriving (Functor, Applicative, Monad, MonadTrans, Channel)

instance ProxyTrans (BothP e s) where
    liftP = BothP . liftP . liftP

runBoth
 :: (Monad m)
 => s
 -> (b' -> BothP e s p a' a b' b m r)
 -> (b' -> p a' a b' b m (Either e r, s))
runBoth s = runStateK s . runEitherK . fmap unBothP

get' :: (Monad (p a' a b' b m), Channel p)
     => BothP e s p a' a b' b m s
get' = BothP $ liftP get

put' :: (Monad (p a' a b' b m), Channel p)
     => s -> BothP e s p a' a b' b m ()
put' x = BothP $ liftP $ put x

throw' :: (Monad (p a' a b' b m), Channel p)
       => e -> BothP e s p a' a b' b m r
throw' e = BothP $ E.throw e

Then we can write proxies using this new proxy transformer of ours:

client8 :: () -> BothP String Int Proxy () Int () C IO r
client8 () = do
    n <- get'
    lift $ print n
    n' <- liftP $ request ()
    put' n'
    throw' "ERROR"

>>> runProxy $ runBoth 0 $ client8 <-< mapP (enumFromS 1)
0
(Left "ERROR",1)

Note that request and respond are not automatically liftable, because of technical limitations with Haskell type classes. When I resolve these issues they will also be automatically promoted by proxy transformers. For now, you must lift them manually using liftP:

request = (liftP .) request
respond = (liftP .) respond

The left request and respond in the above equations are what the lifted definitions would be for each proxy transformer if Haskell's type class system didn't get in my way.