Difference between revisions of "Monad"
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{{Standard classMonadmodule=Control.Monadmoduledoc=ControlMonadpackage=base}} 

−  '''Monads''' in Haskell are structures used to supplement pure computations with features like state, common environment or I/O. Even though Haskell is a purelyfunctional language, side 
+  '''Monads''' in Haskell are structures used to supplement pure computations with features like state, common environment or I/O. Even though Haskell is a purelyfunctional language, side effects can be conveniently simulated using monads. 
Because they are very useful in practice but rather mindtwisting for the beginners, numerous tutorials that deal exclusively with monads were created (see [[Monad#Monad tutorialsmonad tutorials]]). 
Because they are very useful in practice but rather mindtwisting for the beginners, numerous tutorials that deal exclusively with monads were created (see [[Monad#Monad tutorialsmonad tutorials]]). 
Revision as of 17:02, 1 February 2008
import Control.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 purelyfunctional language, side effects can be conveniently simulated using monads.
Because they are very useful in practice but rather mindtwisting for the beginners, numerous tutorials that deal exclusively with monads were created (see monad tutorials).
Contents
Common monads
Most common applications of monads include:
 Representing failure using
Maybe
monad  Nondeterminism through backtracking using
List
monad  State using
State
monad  Readonly environment using
Reader
monad  I/O using
IO
monad
Monad class
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 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.
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.
Commutative monads
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:

Reader
monad 
Maybe
monad
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.
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 HenkJan van Tuyl.
Monad research
A collection of research papers about monads.
Monads in other languages
Implementations of monads in other languages.
 C
 C++, doc
 CML.event ?
 Clean State monad
 JavaScript
 Java (tar.gz)
 Joy
 LINQ, more, C#, VB
 Lisp
 Miranda
 OCaml:
 Perl
 Perl6 ?
 Prolog
 Python
 Python
 here
 Twisted's Deferred monad
 Ruby:
 Scala:
 Scheme:
 Tcl
 The Unix Shell
 More monads by Oleg
 CLL: a concurrent language based on a firstorder intuitionistic linear logic where all right synchronous connectives are restricted to a monad.
Unfinished:
 Slate
 Parsing, Maybe and Error in Tcl
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.
Interesting monads
A list of monads for various evaluation strategies and games:
 Identity monad
 Optional results
 Random values
 Read only state
 Writable state
 Unique supply
 ST
 State
 Undoable state
 Function application
 Error
 Atomic memory transactions
 Continuations
 IO
 Nondeterministic evaluation
 List monad
 Concurrent threads
 Backtracking
 Region allocation
 LogicT: backtracking monad transformer with fair operations and pruning
 Pi calculus as a monad
 Halfs, uses a readonly and writeonly monad for filesystem work.
 House's H monad for safe hardware access
 Commutable monads for parallel programming
There are many more interesting instance of the monad abstraction out there. Please add them as you come across each species.
Fun
 If you are tired of monads, you can easily get rid of them.