Title: Lisp Macros.

Instructions: Study the short chapter on writing Lisp macros. Try performing the MACROEXPAND operation on various calls to built-in macros. Then do the following problems.

• 1. Write a macro ZERO-IT that sets the value of its argument (which must be an unquoted symbol) to 0. For example, we might have:

  > (zero-it x)
  0
  > x
  0
  

• 2. Write a macro ZERO-THEM which takes any number of unquoted symbols as arguments and sets them all to 0. For example:

  > (zero-them x y z)
  0
  > x
  0
  > y
  0
  > z
  0
  

• 3. Write a macro THRICE-EACH that takes any number of forms as arguments and evaluates the first one three times, the second one three times, etc., in that order. At the end, it returns the result of the last evaluation of the last form.

  > (thrice-each 
  >   (setq x 0)(incf x)(print x)(setq x (* x 2))(print x) )
  3
  3
  3
  24
  24
  24
  24
  

• 4. Now let's take a brief break from writing macros in order to get familiar with the manipulation of ordered pairs (which are used in exercise 5, which involves writing a macro again.) Write a function ORDERED-PAIRS that takes a list of elements and returns a new list containing all ordered pairs of the elements.

  > (ordered-pairs '(a b c))
  ((a a)(a b)(a c)(b a)(b b)(b c)(c a)(c b)(c c))
  

• 5. Write a macro FOR-ALL-UNORDERED-PAIRS that will take a list of two symbols, a list of 1 or more values, and then any number of forms, and it will repeatedly execute the sequence of forms, once for each "unordered" pair of the values, with the two values bound to the two variables. After doing that processing, it will return NIL. For example, the following call would work as shown:

  > (for-all-unordered-pairs (x y) '(1 2 3 4)
  >    (print (cons x y))
  >    (print (* x y)) )
  (1 . 1)
  1
  (1 . 2)
  2
  (1 . 3)
  3
  (1 . 4)
  4
  (2 . 2)
  4
  (2 . 3)
  6
  (2 . 4)
  8
  (3 . 3)
  9
  (3 . 4)
  12
  (4 . 4)
  16
  NIL
  

  By unordered, we mean that reversing the order of two values does not lead to another iteration in the loop. For example, (3 . 4) gets printed in one of the iterations, but (4 . 3) never gets printed, because it's considered equivalent to the (3 . 4).
   
• 6. Write a macro FOR-ALL-UNORDERED-PAIRS-LIST that takes similar arguments and behaves similarly to FOR-ALL-UNORDERED-PAIRS, but rather than return NIL, it returns a list of all the values, from each iteration, of the last form, If it were used in the example above, it would return

  (1 2 3 4 4 6 8 9 12 16)
  

  
   

  Individual Work:  This assignment requires individual work.  Do NOT work in teams on this assignment..