Monads

Definition of monads

Monads are versatile functors built on top of polymorphic concepts, and complete a genealogy of type-classes. The versatility of monads is such that they allow programmers to write context-rich maps. With a monad, it is possible to compose branching logic (like that seen in the Maybe and Either sum types), computations (I/O-bound and CPU-bound code), and effects (the integer residue of a print call for instance). Like functors, monads follow the laws of the calculus from which they originate. The cornerstone monad principles are the mathematical forms of associativity, left-identity, and right-identity. They are as follows:

Law	Mathematical Representation
Left identity	$return \space x >>= f = f \circ x$
Right identity	$m>>=re$

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