Monad transformer

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

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).

Contents 1 Definition 2 Examples 3 See also 4 References 5 External links

[edit] 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:^[1] (the notation `bind` below indicates infix application):
   1. lift . return = return
   2. lift (m `bind` k) = (lift m) `bind` (lift . k)

[edit] Examples

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion.

[edit] See also

• Monads in functional programming
• Natural transformation - a related concept in category theory

[edit] References

[edit] 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

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion.