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 Definitions for combinator: The Free On-line Dictionary of Computing (27 SEP 03)
:
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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