I = λx . x
K = λx . λy . x
S = λx . λy . λz . x(z)(y(z))
Y = λf . (λu . f(u(u))) (λu . f(u(u)))
The combinators I, K, and S were introduced by Schönfinkel and Curry, who showed that any λ-expression can essentially be formed by combining them. More recently combinators have been applied to the design of implementations for functional languages. In particular Y (also called the paradoxical combinator) can be seen as producing fixed points, since Y(f) reduces to f(Y(f)).
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