6 Structuring programs with monad transformers

We’ve seen many monads already. We know that every monad specifies a way to combine two computations in a sequence by implementing the >>= operator. We also know that in a monadic setting we have a result of a computation with some additional effects: computations may fail (as in the Maybe monad) or give an opportunity to communicate with the real world by doing input and otput (as in the IO monad), we may mutate state or consult an environment in some other effectful computations. There are many other monads but we already know what all of them share in common.

In this chapter, we discuss one simple question: how to express computations that need to use more than one monadic effect at the same time? We start with exploring the problem. We solve a problem in one monad, find some flaws in that solution, and try to fix them. In Haskell it is often the case that there is a monad for that. But we have a monad already so the problem now is how to add another monad to a solution. Let’s see.

6.1  The problem of combining monads

6.1.1  Evaluating expressions in the reversed polish notation

6.1.2  Introducing monad transformers and monad stacks

6.2  IO-based monad transformer stacks

6.2.1  Describing monad stack

6.2.2  Exploiting a monad stack functionality

6.2.3  Running an application

6.2.4  Can we do it without RWST?

6.3  What is a monad transformer

6.3.1  Step 0: defining a type for a transformer

6.3.2  Step 1: turning a monad stack into a monad

6.3.3  Step 2: implementing the full monad stack functionality

6.3.4  Step 3: supplying additional functionality

6.3.5  Using a transformer

6.4  Monad transformers in the Haskell libraries

6.4.1  Identity is where it all starts

6.4.2  An overview of the most common monad transformers

6.5  Summary