Monad
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 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
Common monads
Most common applications of monads include:
- Representing failure using
Maybe
monad - Nondeterminism through backtracking using
List
monad - State using
State
monad - Read-only environment using
Reader
monad - I/O using
IO
monad
Monad class
Monads can be viewed as a standard programming interface to various data or control structures, which is captured by the Monad
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.
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
monadMaybe
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 Henk-Jan 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
- Clojure
- 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 first-order 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
- Non-deterministic 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 read-only and write-only 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.