Combinatory Logic
Combinatory Logic
A branch of mathematical logic, which has been extensively investigated by Curry, and which is concerned with analysis of processes of substitution, of the use of variables generally, and of the notion of a function. The program calls, in particular, for a system of logic in which variables are altogether eliminated, their place being taken by the presence in the system of certain kinds of function symbols. For a more detailed and exact account, reference must be made to the papers cited below. — A.C.
M. Schnfinkel,
ber die Bausteine der mathematischen Logik, Mathematische Annalen, vol. 92 (1924), pp. 305-316.
H. B. Curry,
Grundlagen der kombmatorischen Logik, American Journal of Mathematics, vol. 52 (1930), pp. 509-536, 789-834.
H. B. Curry,
The universal quantifier in combinatory logic, Annals of Mathematics, ser. 2, vol. 32 (1931), pp. 154-180.
H. B. Curry,
Apparent variables from the standpoint of combinatory logic, Annals of Mathematics, ser. 2, vol 34 (1933), pp. 381-404.
H. B. Curry,
Functionality in combinatory logic, Proceedings of the National Academy of Sciences, vol. 20 (1934), pp. 584-590.
J. B. Rosser,
A mathematical logic without variables, Annals of Mathematics, ser. 2, vol. 36 (1935), pp 127-150, and Duke Mathematical Journal, vol. 1 (1935), pp. 328-355.
H. B. Curry,
A revision of the fundamental rules of combinatory logic, The Journal of Symbolic Logic, vol. 6 (1941), pp. 41-53.
H. B. Curry,
Consistency and completeness of the theory of combinators, ibid , pp. 54-61.