Monad

Monad class (base)

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
• Computational monads part 1 and part 2.
• Three kind of monads : sequencing, side effects or containers
• More tutorials on monads
• Even more tutorials on monads..

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
• JavaScript
• Java (tar.gz)
• Joy
• LINQ, more, C#, VB
• Lisp
• Miranda
• OCaml, more, also, MetaOcaml
• Perl, Perl6 ?
• Prolog
• Python, and here, and Twisted's Deferred
• Ruby, and other implementation
• Scala, also continuation monad
• Scheme, also
• Tcl
• The Unix Shell
• More monads by Oleg

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

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