Fall 2007 LISP Written Assignment #2 CMSC 420
Hanan Samet
The following exercises are designed to test your understanding of recursion. The functions
are defined using a variant of LISP known as meta-LISP. In order to aid your understanding, the
function defined in problem 1 is identical to the one below:
drop(x) = if null x then nil
else (car x) cons drop(cdr x)
The idea is that
a x =car x
d x =cdr x
n x =null x
at x =atom x
a.b =a cons b
<a> =a cons nil = a list whose single element is a
a*b = concatenate lists aand b(i.e. append list bto list a)
reverse[x] = reverses the top level list x. For example reverse[(A B C)] =(C B A). But
reverse[((A B C)(D E))] =((D E)(A B C)).
1. Consider the function drop defined by
drop[x] โif n x then nil else [a x].drop[d x].
Compute (by hand) drop[(A B C)]. What does drop do to lists in general?
2. What does the function
r2[x] โif n x then nil else reverse[a x].r2[d x]
do to lists of lists? How about
r3[x] โif at x then x else reverse[r4[x]]
r4[x] โif n x then nil else r3[a x].r4[d x]?
3. Compare the following function with the function r3 of the preceding example:
r3โ[x] โif at x then x else r3โ[d x]*<r3โ[a x]>
4. Consider r5 defined by
r5[x] โif n x โจn d x then x
else [a r5[d x]] . r5[a x . r5[d r5[d x]]].
Compute r5[(A B C D)]. What does r5 do in general. Needless to say, this is not a good
way of computing this function even though it involves no auxiliary functions.
1