Using monad-control with monad transformers

Posted by John Wiegley
on September 21, 2013 with labels:haskell

This article assumes familiarity with monads and monad transformers. If you’ve never had an occasion to use lift
yet, you may want to come back to it later. It is also available on the School of Haskell:

The Problem

What is the problem that monad-control
aims to solve? To answer that, let’s back up a bit. We know that a monad represents some kind of “computational context”. The question is, can we separate this context from the monad, and reconstitute it later? If we know the monadic types involved, then for some monads we can. Consider the State
monad: it’s essentially a function from an existing state, to a pair of some new state and a value. It’s fairly easy then to extract its state and later use it to “resume” that monad:

import Control.Applicative
import Control.Monad.Trans.State

main = do
    let f = do { modify (+1); show  get } :: StateT Int IO String
    (x,y) <- runStateT f 0
    print $ "x = " ++ show x   -- x = "1"
    (x',y') <- runStateT f y
    print $ "x = " ++ show x'  -- x = "2"

In this way, we interleave between StateT Int IO
and IO
, by completing the StateT
invocation, obtaining its state as a value, and starting a new StateT
block from the prior state. We’ve effectively resumed the earlier StateT

Nesting calls to the base monad

But what if we didn’t, or couldn’t, exit the StateT
block to run our IO
computation? In that case we’d need to use liftIO
to enter IO
and make a nested call to runStateT
inside that IO
block. Further, we’d want to restore any changes made to the inner StateT
within the outer StateT
, after returning from the IO

import Control.Applicative
import Control.Monad.Trans.State
import Control.Monad.IO.Class

main = do
    let f = do { modify (+1); show  get } :: StateT Int IO String

    flip runStateT 0 $ do
        x <- f
        y <- get
        y' <- liftIO $ do
            print $ "x = " ++ show x   -- x = "1"

            (x',y') <- runStateT f y
            print $ "x = " ++ show x'  -- x = "2"
            return y'
        put y'

A generic solution

This works fine for StateT
, but how can we write it so that it works for any monad tranformer over IO? We’d need a function that might look like this:

foo :: MonadIO m => m String -> m String
foo f = do
    x <- f
    y <- getTheState
    y' <- liftIO $ do
        print $ "x = " ++ show x

        (x',y') <- runTheMonad f y
        print $ "x = " ++ show x'
        return y'
    putTheState y'

But this is impossible, since we only know that m
is a Monad
. Even with a MonadState
constraint, we would not know about a function like runTheMonad
. This indicates we need a type class with at least three capabilities: getting the current monad tranformer’s state, executing a new transformer within the base monad, and restoring the enclosing transformer’s state upon returning from the base monad. This is exactly what MonadBaseControl
provides, from monad-control

class MonadBase b m => MonadBaseControl b m | m -> b where
    data StM m :: * -> *
    liftBaseWith :: (RunInBase m b -> b a) -> m a
    restoreM :: StM m a -> m a

Taking this definition apart piece by piece:

  1. The MonadBase
    constraint exists so that MonadBaseControl
    can be used over multiple base monads: IO
    , ST
    , STM
    , etc.

  2. liftBaseWith
    combines three things from our last example into one: it gets the current state from the monad transformer, wraps it an StM
    type, lifts the given action into the base monad, and provides that action with a function which can be used to resume the enclosing monad within the base monad. When such a function exits, it returns a new StM

  3. restoreM
    takes the encapsulated tranformer state as an StM
    value, and applies it to the parent monad transformer so that any changes which may have occurred within the “inner” transformer are propagated out. (This also has the effect that later, repeated calls to restoreM
    can “reset” the transformer state back to what it was previously.)

Using monad-control and liftBaseWith

With that said, here’s the same example from above, but now generic for any transformer supporting MonadBaseControl IO

{-# LANGUAGE FlexibleContexts #-}

import Control.Applicative
import Control.Monad.Trans.State
import Control.Monad.Trans.Control

foo :: MonadBaseControl IO m => m String -> m String
foo f = do
    x <- f
    y'  do
        print $ "x = " ++ show x   -- x = "1"

        x' <- runInIO f
        -- print $ "x = " ++ show x'

        return x'
    restoreM y'

main = do
    let f = do { modify (+1); show  get } :: StateT Int IO String

    (x',y') <- flip runStateT 0 $ foo f
    print $ "x = " ++ show x'   -- x = "2"

One notable difference in this example is that the second print
statement in foo
becomes impossible, since the “monadic value” returned from the inner call to f
must be restored and executed within the outer monad. That is, runInIO f
is executed in IO, but it’s result is an StM m String
rather than IO String
, since the computation carries monadic context from the inner transformer. Converting this to a plain IO
computation would require calling a function like runStateT
, which we cannot do without knowing which transformer is being used.

As a convenience, since calling restoreM
after exiting liftBaseWith
is so common, you can use control
instead of restoreM =<< liftBaseWith

y' <- restoreM =< runInIO f)

-- becomes...
y'  runInIO f

Another common pattern is when you don’t need to restore the inner transformer’s state to the outer transformer, you just want to pass it down as an argument to some function in the base monad:

foo :: MonadBaseControl IO m => m String -> m String
foo f = do
    x <- f
    liftBaseDiscard forkIO $ f

In this example, the first call to f
affects the state of m
, while the inner call to f
, though inheriting the state of m
in the new thread, but does not restore its effects to the parent monad transformer when it returns.

Now that we have this machinery, we can use it to make any function in IO
directly usable from any supporting transformer. Take catch
for example:

catch :: Exception e => IO a -> (e -> IO a) -> IO a

What we’d like is a function that works for any MonadBaseControl IO m
, rather than just IO
. With the control
function this is easy:

catch :: (MonadBaseControl IO m, Exception e) => m a -> (e -> m a) -> m a
catch f h = control $ runInIO -> catch (runInIO f) (runInIO . h)

You can find many function which are generalized like this in the packages lifted-base
and lifted-async

稿源:Lost in Technopolis (源链) | 关于 | 阅读提示

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