## Turing published the first Fixed Point Combinator > Incidentally, in the course of his doctoral work Turing gave the first published > fixed-point combinator, \[Turing, 1937b, term Θ\]. This was seen as only having minor > interest at that time, but in view of the later importance given to such combinators > (see §8.1.2 below), we digress here to discuss them. > A fixed-point combinator is any closed term Y such that Yx converts to x(Yx). > Turing’s was > > (λxy.y(xxy)) (λxy.y(xxy)). > > The next one to appear was in \[Rosenbloom, 1950, pp.130-131, Exs. 3e, 5f\]. > It was λx. W(Bx)(W(Bx)), which is convertible to λx. (λy.x(yy))(λy.x(yy)). > The latter has often been called Curry’s Y; in fact Curry gave no explicit > fixed-point combinator before \[Curry and Feys, 1958, §5G\], but the accounts > of Russell’s paradox in \[Church, 1932, p.347\] and \[Curry, 1934a, §5\] both > mentioned (λy.N (yy))(λy.N (yy)), where N represented negation, and Curry’s > use of the latter term dated back to a letter to Hilbert in 1929. > > -From Hindley 2006 The History of Lambda Calculus and Combinatory Logic