<logic> A system for reducing the operational notation of logic, mathematics or a functional language to a sequence of modifications to the input data structure. First introduced in the 1920's by Schoenfinkel. Re-introduced independently by Haskell Curry in the late 1920's (who quickly learned of Schoenfinkel's work after he had the idea). Curry is really responsible for most of the development, at least up until work with Feys in 1958. See combinator. (1995-01-05)

Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel Translated by Stefan Bauer-Mengelberg as "On the building blocks of mathematical logic" in Jean van Heijenoort, 1967.

<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 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)