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monad
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monad : FOLDOC
monad
/mo'nad/ A technique from {category theory} which has been adopted as a way of dealing with state in functional programming languages in such a way that the details of the state are hidden or abstracted out of code that merely passes it on unchanged.
A monad has three components: a means of augmenting an existing type, a means of creating a default value of this new type from a value of the original type, and a replacement for the basic application operator for the old type that works with the new type.
The alternative to passing state via a monad is to add an extra argument and return value to many functions which have no interest in that state. Monads can encapsulate state, side effects, exception handling, global data, etc. in a purely lazily functional way.
A monad can be expressed as the triple, (M, unitM, bindM) where M is a function on types and (using Haskell notation):
unitM :: a -> M a
bindM :: M a -> (a -> M b) -> M b

I.e.


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