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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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