# combinatory logic

(redirected from*Combinatorial logic (mathematics)*)

## combinatory logic

(logic)See combinator.

## Combinatory Logic

a branch of mathematical logic that studies combinators and their properties. The function and the operation of applying a function to an argument are the fundamental concepts in combinatory logic. Members of a certain class of operations on functions that is closed with respect to application are called combinators. The concept of “combinatorily defined function” as formulated using the terms of combinatory logic was one of the first methods of refining the concept of algorithm. The foundations of combinatory logic were worked out by the Soviet mathematician M. I. Sheinfinkel’ (Schönfinkel; 1924). Most of its results belong to the American logician H. Curry. Combinatory logic finds extensive application in the theory of programming languages.

### REFERENCES

Ianovskaia, S. A. “Logika kombinatornaia.” In the book*Filosofskaia entsiklopediia*, vol. 3. Moscow, 1964.

Schönfinkel, M. “Über die Bausteine der mathematischen Logik.”

*Mathematische Annalen*, 1924, vol. 92.

Curry, H. B., and R. Feys.

*Combinatory Logic*. Amsterdam, 1958.

Curry, H. B. “Recent Advances in Combinatory Logic.”

*Bulletin de la Société mathématique de Belgique*, 1968, vol. 20, no. 3.