Standard monad transformers

• The MonadTrans and MonadIO classes
• Transformer versions of standard monads

Haskell's base libraries provide support for monad transformers in the form of classes which represent monad transformers and special transformer versions of standard monads.

The MonadTrans class is defined in Control.Monad.Trans and provides the single function lift. The lift function lifts a monadic computation in the inner monad into the combined monad.

class MonadTrans t where
    lift :: (Monad m) => m a -> t m a

Monads which provide optimized support for lifting IO operations are defined as members of the MonadIO class, which defines the liftIO function.

class (Monad m) => MonadIO m where
    liftIO :: IO a -> m a

The standard monads of the monad template library all have transformer versions which are defined consistently with their non-transformer versions. However, it is not the case the all monad transformers apply the same transformation. We have seen that the ContT transformer turns continuations of the form (a->r)->r into continuations of the form (a->m r)->m r. The StateT transformer is different. It turns state transformer functions of the form s->(a,s) into state transformer functions of the form s->m (a,s). In general, there is no magic formula to create a transformer version of a monad — the form of each transformer depends on what makes sense in the context of its non-transformer type.

Order is important when combining monads. StateT s (Error e) is different than ErrorT e (State s). The first produces a combined type of s -> Error e (a,s), in which the computation can either return a new state or generate an error. The second combination produces a combined type of s -> (Error e a,s), in which the computation always returns a new state, and the value can be an error or a normal value.