Combinator definition

Combinator





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1 definition found

From The Free On-line Dictionary of Computing (27 SEP 03) [foldoc]:

  combinator
       
           A function with no {free variables}.  A term is
          either a constant, a variable or of the form A B denoting the
          {application} of term A (a function of one argument) to term
          B.  {Juxtaposition} associates to the left in the absence of


          parentheses.  All combinators can be defined from two basic
          combinators - S and K.  These two and a third, I, are defined
          thus:
       
          	S f g x	= f x (g x)
          	K x y	= x
          	I x	= x		= S K K x
       
          There is a simple translation between {combinatory logic} and
          {lambda-calculus}.  The size of equivalent expressions in the
          two languages are of the same order.
       
          Other combinators were added by {David Turner} in 1979 when he
          used combinators to implement {SASL}:
       
          	B f g x = f (g x)
          	C f g x = f x g
          	S' c f g x = c (f x) (g x)
          	B* c f g x = c (f (g x))
          	C' c f g x = c (f x) g
       
          See {fixed point combinator}, {curried function},
          {supercombinator}s.
       
          (2002-11-03)
       
       

















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