Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and 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, which were introduced by Schönfinkel 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. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.
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Combinatory logic in the context of Curry's paradox
Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F". The paradox requires only a few apparently-innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.
The paradox is named after the logician Haskell Curry, who wrote about it in 1942. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.
View the full Wikipedia page for Curry's paradoxCombinatory logic in the context of Haskell Curry
Haskell Brooks Curry (/ˈhæskəl/ HAS-kəl; September 12, 1900 – September 1, 1982) was an American mathematician, logician and computer scientist. Curry is best known for his work in combinatory logic, whose initial concept is based on a paper by Moses Schönfinkel, for which Curry did much of the development. Curry is also known for Curry's paradox and the Curry–Howard correspondence. Named for him are three programming languages: Haskell, Brook, and Curry, and the concept of currying, a method to transform functions, used in mathematics and computer science.
View the full Wikipedia page for Haskell CurryCombinatory logic in the context of Moses Schönfinkel
Moses Ilyich Schönfinkel (Russian: Моисей Эльевич Шейнфинкель, romanized: Moisei El'evich Sheinfinkel; 29 September 1888 – 1942) was a logician and mathematician, known for the invention of combinatory logic.
View the full Wikipedia page for Moses Schönfinkel