# Difference between revisions of "Monad"

Monads in Haskell are structures used to supplement pure computations with features like state, common environment or I/O. Even though Haskell is a purely-functional language, side-effects can be conveniently simulated using monads.

Because they are very useful in practice but rather mind-twisting for the beginners, numerous tutorials that deal exclusively with monads were created (see monad tutorials).

Most common applications of monads include:

• Representing failure using `Maybe` monad
• Non-determinism using `List` monad
• State using `State` monad
• Read-only environment using `Reader` monad
• I/O using `IO` monad

All common monads are members of Monad class defined like this:

```class Monad m where
(>>=) :: m a -> (a -> m b) -> m b
(>>) :: m a -> m b -> m b
return :: a -> m a
fail :: String -> m a
```

In addition to implementing the class functions, all instances of Monad should obey following equations:

```return a >>= k  =  k a
m >>= return  =  m
m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h
```

See this intuitive explanation of why they should obey the Monad laws.

Any Monad can be made a Functor by defining

```fmap ab ma = ma >>= (return . ab)
```

However, the Functor class is not a superclass of the Monad class. See Functor hierarchy proposal.

## Special notation

In order to improve the look of code that uses monads Haskell provides a special syntactic sugar called `do`-notation. For example, following expression:

```thing1 >>= (\x -> func1 x >>= (\y -> thing2 >>= (\_ -> func2 y (\z -> return z))))
```

which can be written more clearly by breaking it into several lines and omitting parentheses:

```thing1 >>= \x ->
func1 x >>= \y ->
thing2 >>= \_ ->
func2 y >>= \z ->
return z
```

can be also written using the `do`-notation as follows:

```do
x <- thing1
y <- func1 x
thing2
z <- func2 y
return z
```

Code written using the `do`-notation is transformed by the compiler to ordinary expressions that use `Monad` class functions.

When using the `do`-notation and a monad like `State` or `IO` programs look very much like programs written in an imperative language as each line contains a statement that can change the simulated global state of the program and optionally binds a (local) variable that can be used by the statements later in the code block.

It is possible to intermix the `do`-notation with regular notation.

More on the `do`-notation can be found in a section of Monads as computation and in other tutorials.

Monads are known for being deeply confusing to lots of people, so there are plenty of tutorials specifically related to monads. Each takes a different approach to Monads, and hopefully everyone will find something useful.

## Monad reference guides

An explanation of the basic Monad functions, with examples, can be found in the reference guide A tour of the Haskell Monad functions, by Henk-Jan van Tuyl.

A collection of research papers about monads.

## Monads in other languages

Implementations of monads in other languages.

Unfinished:

And possibly there exist:

• Standard ML (via modules?)

Please add them if you know of other implementations.