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more about monad
## monad |

4 definitions found From Webster's Revised Unabridged Dictionary (1913) [web1913]: 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. From WordNet r 1.6 [wn]: 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}] From The Free On-line Dictionary of Computing (13 Mar 01) [foldoc]: monadfunctional programming> /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) From THE DEVIL'S DICTIONARY ((C)1911 Released April 15 1993) [devils]: MONAD, n. The ultimate, indivisible unit of matter. (See _Molecule_.) According to Leibnitz, as nearly as he seems willing to be understood, the monad has body without bulk, and mind without manifestation -- Leibnitz knows him by the innate power of considering. He has founded upon him a theory of the universe, which the creature bears without resentment, for the monad is a gentlmean. Small as he is the monad contains all the powers and possibilities needful to his evolution into a German philosopher of the first class -- altogether a very capable little fellow. He is not to be confounded with the microbe, or bacillus; by its inability to discern him a good microscope shows him to be of an entirely distinct species.

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