Combinatory logic is a notation to eliminate the need for
quantified variables in
mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
. It was introduced by
Moses Schönfinkel
Moses Ilyich Schönfinkel (russian: Моисей Исаевич Шейнфинкель, translit=Moisei Isai'evich Sheinfinkel; 29 September 1888 – 1942) was a logician and mathematician, known for the invention of combinatory logic.
Life
Mos ...
and
Haskell Curry, and has more recently been used in
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includin ...
as a theoretical
model of computation
In computer science, and more specifically in computability theory and computational complexity theory, a model of computation is a model which describes how an output of a mathematical function is computed given an input. A model describes h ...
and also as a basis for the design of
functional programming languages. It is based on combinators, which were introduced by
Schönfinkel Schönfinkel ( yi, שײנפֿינק(ע)ל ''Sheynfinkel'', russian: Шейнфинкель ''Šejnfinkeľ''):
* Moses (Ilyich) Schönfinkel, born ''Moisei (Moshe) Isai'evich Sheinfinkel'' (1889, Ekaterinoslav - 1942, Moscow)
** The Bernays–Schö ...
in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in
predicate logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quanti ...
. A combinator is a
higher-order function that uses only
function application and earlier defined combinators to define a result from its arguments.
In mathematics
Combinatory logic was originally intended as a 'pre-logic' that would clarify the role of
quantified v