\documentclass{rtaloop}
\rtalabel{universal}


\begin{document}
\begin{problem}{Richard Statman}{}{June 1993}

\begin{abstract}
In combinatory logic, is there a \emph{uniform universal generator}?
\end{abstract}

Recall that $M$ is a {\em universal generator\/} if each combinator
$P$ has a superterm $Q$ such that $M \rightarrow^* Q$. 
Call $M$ a {\em uniform universal generator\/} if there exists a context
$C[\cdot]$ such that, for each combinator $P$, we have $M \rightarrow^* C[P]$.
Is there a uniform universal generator? 
(For Combinatory Logic, if we restrict the context $C[\cdot]$
to be of the form $(N \cdot)$, no such term exists \cite{S92:inria}.)

\end{problem}
\end{document}
