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. |