CS 3323 Topics in Programming Languages

1. Write a recursive function maxvec that finds the maximum of a simple list of numbers. [Hint: if the cdr is nil, just return the car, and otherwise return the maximum of the car and of maxvec applied to the cdr. For example, (maxvec '(2 5 6 3)) returns 6.]

2. Try out the function reverse in Lisp:

   (reverse '(a b c))

   (reverse '((a b c)))

   (reverse '(a (b c d) e)).

   Define your own function reverse1 which will behave the same way as reverse, reversing the order of elements of a list at the top level only. [Hint: Invoke reverse1 recursively on the cdr and tack on the car at the end.]

3. Define a function count-atoms that will count the number of atoms in a list, at all levels. For example (count-atoms '(a (b c) (d (e) f))) should return 6. [Hint: Mimic list-atoms from class.]

4. Write a function addvec that takes a single list of numbers as input argument and returns the sum of the numbers. [Assume the input list has only one level. Return 0 for a nil list.]

5. Write a function vecmul that will take as inputs two simple lists of numbers. vecmul should multiply these lists coordinate-wise as one would multiply vectors. If one list is longer than the other, the result should be as if the shorter were padded with ones. [For example, (vecmul '(2 3 4 5) '(1 4 5 2 14)) returns (2*1 3*4 4*5 5*2 1*14) or (2 12 20 10 14).]

6. Use addvec and vecmul to define an inner product function innprod. [For example, (innprod '(1 2 3) '(7 8 9)) returns 1*7 + 2*8 + 3*9 or 50.]

7. Define a function last1 which returns the last element of a list (at the top level) without making use of reverse or last (already built in to Common Lisp.)