\begin{frame}
 \frametitle{Fixed-point Combinators}

  \begin{definition}
  A \structure{fixed-point combinator} {$Y$} is any closed 
  CL-term for which there
  is a conversion
  \[
  Yx \fromto^* x(Yx)
  \]
  \vspace{-3ex}
  \end{definition}
  \pause
  \vspace{5ex}
  
  Many fixed-point combinators exist in CL.
  \bigskip
  
  The  most famous one is Curry's:
  \emph{paradoxical combinator}
  $$Y_C = SSI(SB(KD))$$
\end{frame}