CS 314	Prof Steinberg	Fall 2005

Exercise Set 3

  In all of the following use recursion and binding, not iteration and
  assignment.

1.  Write a scheme function filter-evens which takes a list of numbers as its
    argument and returns a a new list containing only the even numbers in the
    input list.  E.g., (filter-evens '(23 33 44 2 1 8)) returns (44 2 8).
    use even? to test if a number is even.

2.  Write a scheme function sep-lines that prints the elements of a
    list, starting each on a new line.  E.g. (sep-lines '((a b) c d (e g g)))
    prints:
    (a b)
    c
    d
    (e f g)

    Use (display #\newline) to print a new line character.

3.  Write a scheme function mtable that prints a multiplication table.
    E.g. (mtable 6) prints
    1 2 3 4 5 6
    2 4 6 8 10 12
    3 6 9 12 15 18
    4 8 12 16 20 24
    5 10 15 20 25 30
    6 12 18 24 30 36

4.  Write a scheme function deep-reverse which reverses all levels of
    list in its argument.  E.g.,  (deep-reverse '((a b c) d (e (f g))))
    returns (((g f) e) d (c b a))

5.  Write a scheme function square-all which takes a list of numbers and
    returns a list of their squares.  E.g., (square-all '(3 5 2)) returns
    (9 25 4). Use map to do so.

6.  Write a scheme function (assoc-all lst a-list)  where lst is a list of
    symbols and a-list is an assoc-list.  assoc-all returns a list of
    the data associated with elements of lst by assoc-list.  E.g.,
    (assoc-all '(a d c) '((a apple)(b boy)(c cat)(d dog))) returns
    (apple dog cat).  Use map.  Note that you can't simply use assoc as
    one of the arguments to map. You need a lambda.