Monad transformer

In functional programming, a monad transformer is essentially a type constructor which takes a monad as an argument, and returns a monad.

Monad transformers can be used to compose features encapsulated by monads - such as state, exception handling, and I/O - in a modular way. Typically, a monad transformer is created by generalising an existing monad; applying the resulting monad transformer to the identity monad yields a monad which is equivalent to the original monad (ignoring any necessary boxing and unboxing).

Definition

A monad transformer consists of:

1. A type constructor t of kind (* -> *) -> * -> *
2. Monad operations return and bind (or an equivalent formulation) for all t m where m is a monad, satisfying the monad laws
3. An additional operation, lift :: m a -> t m a, satisfying the following laws: (the notation `bind` below indicates infix application):
   1. lift . return = return
   2. lift (m `bind` k) = (lift m) `bind` (lift k)

External links

• [1] - a highly technical blog post briefly reviewing some of the literature on monad transformers and related concepts, with a focus on categorical-theoretic treatment