Com S 342 --- Principles of Programming Languages
       DISCUSSION SECTION PRACTICE WITH RECURSION ON FLAT LISTS

0. [list-copy] Write a procedure,

      list-copy : (forall (T) (-> ((list-of T)) (list-of T)))

that takes a list, lst, and returns a new list that is just like lst.
However, do not just return lst, but instead reconstruct a new list
that is like lst and shares all it's top-level elements.  For example:

   (list-copy '(a good egg is fried)) ==> (a good egg is fried)
   (list-copy '(1 1 1 0 1 1 2 1 2)) ==> (1 1 1 0 1 1 2 1 2)
   (list-copy '(a b c d)) ==> (a b c d)
   (list-copy '(b c d)) ==> (b c d)
   (list-copy '()) ==> ()






1. [squares] Write a procedure,

      squares : (-> ((list-of number)) (list-of number))

that takes a list of numbers, lon, and returns a list of all the
squares in lon, in order.  For example:

    (squares '(1 2 3 4)) ==> (1 4 9 16)
    (squares '(2 3 4)) ==> (4 9 16)
    (squares '(3 4)) ==> (9 16)
    (squares '(4)) ==> (16)
    (squares '()) ==> ()
    (squares '(12 12)) ==> (144 144)






2. [product] Write a procedure,

      product : (-> ((list-of number)) number)

that takes a list of numbers, lon, and returns the product of all the
numbers in lon.  For example:

    (product '(1 2 3 4)) ==> 24
    (product '(2 3 4)) ==> 24
    (product '(3 4)) ==> 12
    (product '(4)) ==> 4
    (product '()) ==> 1





3. [some-even?] Write a procedure,

      some-even? : (-> ((list-of number)) boolean)

that takes a list of numbers, lon, and returns true just when some
number in lon is even.  (Hint: Scheme has a predicate even? that tests
to see if a number is even.) For example:

    (some-even? '(1 2 3 4)) ==> #t
    (some-even? '(2 3 4)) ==> #t
    (some-even? '(3 3 5 7 1)) ==> #f
    (some-even? '(10)) ==> #t
    (some-even? '()) ==> #f







4. [delete-even] Write a procedure,

      delete-even : (-> ((list-of number)) (list-of number))

that takes a list of numbers, lon, and returns a list that is just
like lon except that it does not have the even elements of lon. For example:

    (delete-even '(1 2 3 4)) ==> (1 3)
    (delete-even '(2 3 4)) ==> (3)
    (delete-even '()) ==> ()
    (delete-even '(12 6 5 20 12 6 3 10 1 342 541 641 8)) ==> (5 3 1 541 641)








5. [passing] Write a procedure,

      passing: (-> ((list-of (pair-of symbol number))) (list-of symbol))

that takes a list of pairs of symbols and numbers, and returns a list
of the symbols for which the cdr of the pair contains a number that is
strictly greater than 50.  For example:

   (passing '((fred . 51) (mary . 80) (joe . 24) (frank . 50))) ==> (fred mary)
   (passing '((mary . 80) (joe . 24) (frank . 50))) ==> (mary)
   (passing '((joe . 24) (frank . 50))) ==> ()
   (passing '()) ==> ()