\include{6001mac}
\begin{document}
\psetheader{IAP 2005}{Lecture 3}

\section*{Scheme}
\begin{enumerate}
\item {\bf Special Forms}
  \begin{enumerate}
  \item {\large {\it begin}} - {\tt (begin {\it exps})}\\ Evaluate each
  expression in order and return the value of the last expression.
  \vspace{.5in}
  \end{enumerate}
\end{enumerate}

\section*{Problems}

\begin{enumerate}
\item Write {\tt abs}, a function that returns the absolute value of
its input.

\begin{verbatim}
(abs 5)
;Value: 5
(abs -5)
;Value: 5

(define abs
  (lambda (val)
\end{verbatim}
\vspace{1in}

\item Write {\tt sum-to-n} which sums the numbers from 1 to n
inclusive.

\begin{verbatim}
(define sum-to-n
  (lambda (n)
\end{verbatim}
\vspace{1in}
Alter the procedure to sum the squares of the numbers.

\item Write a procedure that computes $e$.
\vspace{1.5in}

\item Write a procedure that runs forever.  (Remember that C-c, C-c stops evaluation)
\vspace{1in}

\item Using {\tt string-append}, write a procedure {\tt pad}, which
takes a string and a number, that returns the string with
that number of spaces added to the end.

\begin{verbatim}
(pad "yay" 0)
;Value: "yay"
(pad "yay" 1)
;Value: "yay "
(pad "yay" 3)
;Value: "yay   "

(define pad
\end{verbatim}
\vspace{1in}

\item Write a procedure that uses Euclid's algorithm to compute the GCD of
two numbers.  Euclid's algorithm (according to Knuth it's the oldest
known algorithm) goes as follows: if r is the remainder of a divided
by b, then the common divisors of a and b are the same as those of b
and r.  Additionally, the gcd of a number and 0 is the number.

\begin{verbatim}
(gcd 206 40)
;Value: 2

(define gcd
  (lambda (a b)
\end{verbatim}
\end{enumerate}

\section*{Tower of Hanoi}

\vspace{2in}

\section*{Scheme}

\begin{enumerate}
\item {\bf Special Forms}
  \begin{enumerate}
  \item {\large {\it define} (sugared form)} - {\tt (define ({\it
    name parameters}) {\it expressions})}\\ This form is equivalent to
    {\tt (define {\it name} (lambda ({\it parameters}) {\it
    expressions}))}.
    \vspace{.5in}
  \item {\large {\it let}} - {\tt (let {\it bindings body})}\\ Binds the
    given bindings for the duration of the body.  The bindings is a
    list of {\tt ({\it name value})} pairs.  The body consists of one
    or more expressions which are evaluated in order and the value of
    last is returned.
    \vspace{1in}
  \end{enumerate}
\end{enumerate}

\section*{Problems}

\begin{enumerate}
\setcounter{enumi}{6}
\item Guess the value, then evaluate the expression in scheme.  If
your guess differs from the actual output, try desugaring any relevant
expressions.

\begin{verbatim}
(define (foo x)
  (+ x 3))

foo

(foo 5)

(define bar 5)

(define (baz) 5)

bar

baz

(bar)

(baz)

(let ((a 3)
      (b 5))
  (+ a b))

(let ((+ *)
      (* +))
  (+ 3 (* 4 5)))

(define m 3)
(let ((m (+ m 1)))
  (+ m 1))

(define n 4)
(let ((n 12)
      (o (+ n 2)))
  (* n o))

\end{verbatim}

\end{enumerate}

\section*{Guessing Game}

\end{document}