Personal tools


From HaskellWiki

(Difference between revisions)
Jump to: navigation, search

Revision as of 12:58, 9 June 2010

Monad class (base)
import Control.Monad

Monads in Haskell can be thought of as composable computation descriptions. The essence of monad is thus separation of composition timeline from the composed computation's execution timeline, which lends monads to supplementing pure calculations with features like state, common environment or I/O.

Even though Haskell is a purely-functional language, side effects that would be performed by the final computation (when and if run) can be dealt with and combined purely at the monad's composition time. The combined computation doesn't have to be impure and can be pure itself as well.

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).


1 Common monads

Most common applications of monads include:

  • Representing failure using
  • Nondeterminism through backtracking using
  • State using
  • Read-only environment using
  • I/O using

2 Monad class

Monads can be viewed as a standard programming interface to various data or control structures, which is captured by the
class. All common monads are members of it:
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 the 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.

3 Special notation

In order to improve the look of code that uses monads Haskell provides a special syntactic sugar called
-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
-notation as follows:
  x <- thing1
  y <- func1 x
  z <- func2 y
  return z
Code written using the
-notation is transformed by the compiler to ordinary expressions that use
class functions. When using the
-notation and a monad like
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
-notation with regular notation. More on the
-notation can be found in a section of Monads as computation and in other tutorials.

4 Commutative monads

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

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

is the same as:

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

Examples of commutative include:

  • Reader
  • Maybe

5 Monad 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.

See Monad tutorials.

6 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.

7 Monad research

A collection of research papers about monads.

8 Monads in other languages

Implementations of monads in other languages.


And possibly there exist:

  • Standard ML (via modules?)

Please add them if you know of other implementations.

Collection of links to monad implementations in various languages. on Lambda The Ultimate.

9 Interesting monads

A list of monads for various evaluation strategies and games:

There are many more interesting instance of the monad abstraction out there. Please add them as you come across each species.

10 Fun