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1. The Free On-line Dictionary of Computing (30 December 2018)
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,
   supercombinators.

   (2002-11-03)


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