Monadic programming is a way to write functional programs. It forms a separate paradigm from classic FunctionalProgramming, because it provides a different way of structuring programs.
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In plain terms, a monad is a set of rules that enforce regular behavior but broad enough to allow most computational processes to be expressed as a monad.
The wikipedia entry: http://en.wikipedia.org/wiki/Monads_in_functional_programming
See OnMonads and MonadTransformer. Also see ProgrammingParadigm.
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