A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline
was subsequently termed combinatory logic by Curry and "
-conversion" or "lambda
calculus" by Church. The system of combinatory logic is extremely fundamental,
in that there are a relatively small finite numbers of atoms, axioms, and elementary
rules. Despite the fact that the system contains no formal variables, it can be used
for doing anything that can be done with variables in more usual systems (Curry
1977, p. 119).
Combinatory Logic
See also
Combinator, Lambda CalculusExplore with Wolfram|Alpha
References
Curry, H. B. "Combinatory Logic." §3D5 in Foundations of Mathematical Logic. New York: Dover, pp. 117-119, 1977.Curry, H. and Feys, R. Combinatory Logic, Vol. 1. Amsterdam, Netherlands: North-Holland, 1958.Hindley, J. R.; Lercher, B.; Seldin, J. P. Introduction to Combinatory Logic. London: Cambridge University Press, 1972.Hindley, J. R. and Seldin, J. P. Introduction to Combinators and lambda-Calculus. Cambridge, England: Cambridge University Press, 1986.Holmes, M. R. "Systems of Combinatory Logic Related to Quine's 'New Foundations.' " Annals Pure Appl. Logic 53, 103-133, 1991.Seldin, J. P. and Hindley, J. R. (Eds.). To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. New York: Academic Press, 1980.Schönfinkel, M. "Über die Bausteine der mathematischen Logik." Math. Ann. 92, 305-316, 1924.Schönfinkel, M. "Sur les éléments de construction de la logique mathématique." Math. Inform. Sci. Humaines, No. 112, 5-26 and 59, 1990. [French translation with commentary.]Referenced on Wolfram|Alpha
Combinatory LogicCite this as:
Weisstein, Eric W. "Combinatory Logic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CombinatoryLogic.html