Monad

5 definitions found

From The Collaborative International Dictionary of English v.0.48 [gcide]:

  Monad \Mon"ad\, n. [L. monas, -adis, a unit, Gr. ?, ?, fr.
     mo`nos alone.]
     1. An ultimate atom, or simple, unextended point; something
        ultimate and indivisible.
        [1913 Webster]
  


     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.
        [1913 Webster]
  
     3. (Zool.) One of the smallest flagellate Infusoria; esp.,
        the species of the genus {Monas}, and allied genera.
        [1913 Webster]
  
     4. (Biol.) A simple, minute organism; a primary cell, germ,
        or plastid.
        [1913 Webster]
  
     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.
        [1913 Webster]
  
     {Monad deme} (Biol.), in tectology, a unit of the first order
        of individuality.
        [1913 Webster]

From WordNet (r) 2.0 [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}]
       [also: {monades} (pl)]

From Moby Thesaurus II by Grady Ward, 1.0 [moby-thes]:

  63 Moby Thesaurus words for "monad":
     I, ace, air, an existence, atom, atomic particles, being, body,
     brute matter, building block, chemical element, component,
     constituent, creature, critter, earth, electron, element,
     elementary particle, elementary unit, entelechy, entity, fire,
     fundamental particle, hyle, hypostasis, individual, ion, life,
     material, material world, materiality, matter, meson, molecule,
     natural world, nature, no other, none else, nothing else,
     nought beside, nuclear particle, object, one, one and only,
     organism, person, persona, personality, physical world, plenum,
     proton, quark, something, soul, stuff, substance, substratum,
     the four elements, thing, unit, unit of being, water
  
  

From The Free On-line Dictionary of Computing (27 SEP 03) [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} 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.