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<*theory*> 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 xThere 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) gSee fixed point combinator, curried function, supercombinators.

(2002-11-03)

Nearby terms: com « COMAL « combination « **combinator** » combinatory logic » Comdex » COME FROM

FOLDOC, Topics, A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, ?, ALL