##### Views

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).

## Contents

Most common applications of monads include:

• Representing failure using
Maybe
• Nondeterminism through backtracking using
List
• State using
State
• I/O using
IO

(>>=) :: 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.

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

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

## 3 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
class functions. When using the
do
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.

Commutative monads are monads for which the order of actions makes no difference (they commute), that is when following code:

do
a <- f x
b <- g y
m a b

is the same as:

do
b <- g y
a <- f x
m a b

Examples of commutative include:

• Maybe

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.

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.

## 8 Monads in other languages

Implementations of monads in other languages.

Unfinished:

And possibly there exist:

• Standard ML (via modules?)