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Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the...

Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments. Combinatory logic was originally intended as a 'pre-logic' that would clarify the role of quantified variables in logic, essentially by eliminating them. Another way of eliminating quantified variables is Quine's predicate functor logic. While the expressive power of combinatory logic typically exceeds that of first-order logic, the expressive power of predicate functor logic is identical to that of first order logic (Quine 1960, 1966, 1976). The original inventor of combinatory logic, Moses Schönfinkel, published nothing on combinatory logic after his original 1924 paper, and largely ceased to publish after Stalin consolidated his power in 1929. Curry rediscovered the combinators while working as an instructor