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monadmore 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]: 
 
  monad 
 
  functional  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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