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Definition

The ``Y-combinator'', which is sometimes also called fixpoint combinator, was discovered by H. Curry. With its help it is possible to handle recursive functions in the Lambda Calculus.

In many programming languages it is possible to simply refer to the name of a function within the function itself. This is called implicit recursion, which is not possible in the Lambda Calculus because all lambda abstractions are by definition `anonymous functions'.

\fbox{ \parbox{12.5cm}{ {\sc Definition 5 (Y-Combinator)} \\ The Y-Combinator ... ... (x\hspace{0.25em} x))) (\lambda x.(f (x\hspace{0.25em} x))))$ \end{center} } }

Georg P. Loczewski 2004-03-05

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