Source : Webster's Revised Unabridged Dictionary (1913)

Monad \Mon"ad\, n. [L. monas, -adis, a unit, Gr. ?, ?, fr. ?
   alone.]
   1. An ultimate atom, or simple, unextended point; something
      ultimate and indivisible.

   2. (Philos. of Leibnitz) The elementary and indestructible
      units which were conceived of as endowed with the power to
      produce all the changes they undergo, and thus determine
      all physical and spiritual phenomena.

   3. (Zo["o]l.) One of the smallest flangellate Infusoria;
      esp., the species of the genus Monas, and allied genera.

   4. (Biol.) A simple, minute organism; a primary cell, germ,
      or plastid.

   5. (Chem.) An atom or radical whose valence is one, or which
      can combine with, be replaced by, or exchanged for, one
      atom of hydrogen.

   {Monad deme} (Biol.), in tectology, a unit of the first order
      of individuality.

Source : WordNet®

monad
     n 1: an atom having a valence of one
     2: a singular metaphysical entity from which material
        properties are said to derive [syn: {monas}]
     [also: {monades} (pl)]

Source : Free On-Line Dictionary of Computing

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} notaion):
     
        	unitM :: a -> M a
        	bindM :: M a -> (a -> M b) -> M b
     
        I.e. unitM converts an ordinary value of type a in to monadic
        form and bindM applies a function to a monadic value after
        de-monadising it.  E.g. a state transformer monad:
     
        	type S a = State -> (a, State)
        	unitS a  = \ s0 -> (a, s0)
        	m `bindS` k = \ s0 -> let (a,s1) = m s0
        			      in k a s1
     
        Here unitS adds some initial state to an ordinary value and
        bindS applies function k to a value m.  (`fun` is Haskell
        notation for using a function as an {infix} operator).  Both m
        and k take a state as input and return a new state as part of
        their output.  The construction
     
        	m `bindS` k
     
        composes these two state transformers into one while also
        passing the value of m to k.
     
        Monads are a powerful tool in {functional programming}.  If a
        program is written using a monad to pass around a variable
        (like the state in the example above) then it is easy to
        change what is passed around simply by changing the monad.
        Only the parts of the program which deal directly with the
        quantity concerned need be altered, parts which merely pass it
        on unchanged will stay the same.
     
        In functional programming, unitM is often called initM or
        returnM and bindM is called thenM.  A third function, mapM is
        frequently defined in terms of then and return.  This applies
        a given function to a list of monadic values, threading some
        variable (e.g. state) through the applications:
     
        	mapM :: (a -> M b) -> [a] -> M [b]
        	mapM f []     = returnM []
        	mapM f (x:xs) = f x		   `thenM` ( \ x2 ->
        	                mapM f xs          `thenM` ( \ xs2 ->
        	    		returnM (x2 : xs2)         ))
     
        (2000-03-09)