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\markright{\footnotesize CS 451 Programming Paradigms, Spring 2001}

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\section*{Homework set 15: Larger programs in the $\lambda$-calculus --- due Thursday 5 April}

Total number of points available on this homework is 100. Full credit
is equivalent to 100 points.


Use your $\lambda$-calculus evaluator to test the programs you develop here.
Report how fast the evaluator works for different inputs or input sizes. (Take
into account that with a unary representation, different numbers have
different sizes.)

\begin{enumerate}

\item   (30 pts.)
Implement the factorial function over Church numerals. (Use the
$\textsf{\textbf{Y}}$ combinator.)


\item   (70 pts.)
Implement a list merge-sort algorithm. It should be a direct translation
of the ML program \texttt{mergeSort} from Ullman, page~83 (also see
\texttt{merge}, page~68). Sort some lists of Church numerals.



\end{enumerate}


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