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.
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.
A collection of research papers about monads.
Monads in other languages
Implementations of monads in other languages.
- C++, doc
- Clean State monad
- Java (tar.gz)
- LINQ, more, C#, VB
- OCaml, more, also, MetaOcaml
- Perl, Perl6 ?
- Python, and here
- Scala, also continuation monad
- Scheme, also
- The Unix Shell
- Twisted's Deferred
- CML.event ?
And possibly there exist:
- Standard ML (via modules?)
Please add them if you know of other implementations.
A list of monads for various evaluation strategies and games:
- Identity monad
- Optional results
- Random values
- Read only state
- Writable state
- Unique supply
- Undoable state
- Function application
- Atomic memory transactions
- Non-deterministic evaluation
- List monad
- Concurrent threads
- Region allocation
There are many more interesting instance of the monad abstraction out there. Please add them as you come across each species.