Note to self on constructing a monad transformer. In a way this follows on from the earlier post Applicatives compose, monads do not. Literate Haskell source for this post is available here: https://github.com/carlohamalainen/playground/tree/master/haskell/transformers.

A Reader is a data type that encapsulates an environment. The runReader function takes an environment (a Reader) and runs it, producing the result of type a.

Note that with record syntax, the type of runReader is actually

Reader that increments its environment value, returning the same type:

Reader that converts its environment value into a string:

“Run” the reader using runReader:

ghci> runReader reader1 100
101


There’s nothing magic about runReader; it is just taking the function out of the data type. We can do it manually ourselves:

ghci> runReader' reader1 100
101


Next, make Reader an instance of Monad:

The definition of >>= is relatively easy to work out using hole driven development.

Example usage:

Or in the more readable do notation:

ghci> runReader eg1' 100
"hey, 100"


Note that we use id to produce a Reader that just passes its environment argument along as the output. See readerAsk later for the equivalent situation which uses return for MonadReader.

Since [] is an instance of Monad we can also do things like this:

ghci> runReader eg1'' 100
"hey, [100]"


We’d like to use the Reader in conjunction with other monads, for example running IO actions but having access to the reader’s environment. To do this we create a transformer, which we’ll call ReaderT:

The r parameter is the reader environment as before, m is the monad (for example IO), and a is the result type, as before. Again, note the actual type of runReaderT:

It takes a ReaderT and provides us with a function that takes a reader environment of type r and produces a monadic value. Following from the Monad instance declaration for Reader it is straightforward to write the definition for ReaderT.

With a ReaderT as the outer monad, we would like to “lift” a monadic computation into the reader. A monadic action doesn’t know anything about the reader environment, so to lift the monadic value we just create a ReaderT with a function that ignores the environment:

Example usage:

Note the type of return on the first line of egLift. In this context, return :: a -> m a is the equivalent of id :: a -> a from the earlier Reader example.

ghci> runReaderT egLift 100
"boo"
"value of e: 100"


More generally, let’s name the ask function:

If we want to modify the environment, we use withReaderT which takes as its first parameter a function to modify the environment. Note that the result is of type ReaderT r' m a so the function is of type r' -> r which modifies the supplied reader of type ReaderT r m a.

Lastly, it is convenient to apply a function to the current environment.

This is almost the same as readerAsk except that we create a reader that returns f r instead of f. In other words:

Finally, we collect the functions readerAsk, withReader, and readerReader in a type class MonadReader and give them more general names:

An instance declaration for our ReaderT type:

Now we can write fairly succinct code as follows. Use the IO monad as the inner monad in a ReaderT, with an Int environment and String result type.

ghci> result <- runReaderT eg2 100
"I'm in the eg2 function and the environment is: 100"

ghci> result
"returned value: 100"


The State monad encapsulates a modifiable state. It has a transformer StateT as one would expect. Yet we are able to call ask inside a StateT monad. Here is an example (the raw code is here):

The function inside0 has the IO monad nested inside a Reader, while inside1 has a StateT with the ReaderT inside. Yet in both we can write e <- ask.

Inspecting the types using ghcmod-vim we find that

so there must be a type class that provides the ask function for StateT.

First, inspect the type of ask using ghci (here we are using the definitions from Control.Monad.Reader and Control.Monad.State, not the implementation in this file).

ghci> :t ask


So StateT must have a MonadReader instance. Confirm this with :i:

ghci> :i StateT
(lots of stuff)
-- Defined in Control.Monad.Reader.Class'
(lots of stuff)


The lift function comes from Monad.Trans.Class, and looking there we see:

So actually we are after the MonaTrans type class. Again looking at :i on StateT we see:

ghci> :i StateT
(lots of stuff)
(lots of stuff)


So off we go to Control.Monad.Trans.State.Lazy where we finally get the answer:

This shows that for StateT, the lift function takes a monadic action and produces a state transformer that takes the current state, runs the action, and returns the result of the action along with the unmodified state. This makes sense in that the underlying action should not modify the state. (There are some laws that monad transformers must satisfy.)

If we did not have the MonadTrans type class then we would have to embed the ask call manually:

Obviously this is laborious and error-prone. In this case, Haskell’s type class system lets us implement a few classes so that ask, get, put, etc, can be used seamlessly no matter which monad transformer we are in.

The downside is that reading Haskell code can be nontrivial. In our case we had to follow a trail through a few files to see where ask was actually implemented, and finding the right definition relied on us being able to infer the correct types of certain sub-expressions.

Personally I am finding more and more that plain vim and ghci does not cut it for Haskell development, and something richer like ghcmod-vim is a real necessity. Shameless self plug: ghc-imported-from is also very useful :-)