Difference between revisions of "Monad"
DonStewart (talk | contribs) (a list of known monads) |
DonStewart (talk | contribs) (reorder) |
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* [http://haskell.org/ghc/docs/latest/html/libraries/mtl/Control-Monad-Identity.html Identity monad] |
* [http://haskell.org/ghc/docs/latest/html/libraries/mtl/Control-Monad-Identity.html Identity monad] |
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* [http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Maybe.html Optional results] |
* [http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Maybe.html Optional results] |
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* [http://haskell.org/haskellwiki/New_monads/MonadRandom Random values] |
* [http://haskell.org/haskellwiki/New_monads/MonadRandom Random values] |
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* [http://haskell.org/ghc/docs/latest/html/libraries/mtl/Control-Monad-Reader.html Read only state] |
* [http://haskell.org/ghc/docs/latest/html/libraries/mtl/Control-Monad-Reader.html Read only state] |
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* [http://haskell.org/ghc/docs/latest/html/libraries/base/System-IO.html#t%3AIO IO] |
* [http://haskell.org/ghc/docs/latest/html/libraries/base/System-IO.html#t%3AIO IO] |
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* [http://www.haskell.org/haskellwiki/SudokuNon deterministic evaluation] |
* [http://www.haskell.org/haskellwiki/SudokuNon deterministic evaluation] |
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* [http://logic.csci.unt.edu/tarau/research/PapersHTML/monadic.html Backtracking] |
* [http://logic.csci.unt.edu/tarau/research/PapersHTML/monadic.html Backtracking] |
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* [http://www.cs.cornell.edu/people/fluet/research/rgn-monad/index.html Region allocation] |
* [http://www.cs.cornell.edu/people/fluet/research/rgn-monad/index.html Region allocation] |
Revision as of 04:19, 2 November 2006
import Control.Monad |
The Monad class is 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
All instances of Monad should obey:
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.
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.
- Monads as containers
- All About Monads
- Simple monad examples
- Of monads and space suits
- You could have invented monads
- Meet Bob The Monadic Lover, or the slightly more serious The Monadic Way
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.
Monads in other languages
Implementations of monads in other languages.
And possibly there exist:
- Perl
- Ruby
- Python
- ML
- Clean
- Java
Please add them if you know of other implementations.
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
- STM
- continuations
- IO
- deterministic evaluation
- List monad
- Backtracking
- Region allocation
There are many more interesting instance of the monad abstraction out there. Please add them as you come across each species.