This assignment is due on Monday, January 31; deposit your assignment in the locking drop box in room CS 189. Try to finish the assignment by Friday morning so you can ask questions about it in discussion.

Summary: In the last lab, you became comfortable (or at least conversant) with the Scheme interpreter, with Scheme syntax, and with the recursive style of list processing. In this assignment you will work with list structures and explore some programming techniques using higher-order functions.

(a) Draw box-and-pointer diagrams (as shown on page 579 of Sebesta) for the following expressions. For the empty list, use an empty cell (rather than a cell pointing to the symbol NIL, as Sebesta does).

   * (Franz () Klefstad)

   * ((Pratt Mehrotra Baldi))

   * ((Pratt Gennari) (Venkatasubramanian Mehrotra) (Mark Kobsa))

   * (Ackerman (King (Grudin (Kling))))

   * (define fact (lambda (x) (if (<= 0 x) 1 (* x (fact (- x 1))))))

(b) Write the Scheme expression that corresponds to each of the two box-and-pointer diagrams below.

(c) Sebesta defines the function mapcar, more commonly called map:

   * (map action list), which returns a list, each of whose elements is the result of applying action (a function) to the corresponding element of list.

Another function that takes another function as an argument is filter:

   * (filter test? list), which returns a list of those elements in list that satisfy test? (which is a predicate--a function that returns true or false, given an element of list.)

Write a definition of filter. Check the Notes on Scheme handout, which contains a function that does the same task.

Now look at this third function:

   * (accumulate action initial-value list), which is defined as follows:
(define accumulate
   (lambda (action initial-value list)
       ((null? list) initial-value)
       (else (action (first list)
             (accumulate action initial-value (rest list)))))))

(c.1) What is the result of evaluating each of these expressions? Try them by hand before typing them in to check your answer; you won't have a Scheme interpreter on the exams.

   * (accumulate + 0 '(1 2 3 4 5))

   * (accumulate (lambda (a b) (+ b (if (even? a) a 0))) 0 '(1 2 3 4 5))

   * (accumulate cons '() '(Huey Dewey Louie))

   * (accumulate max -1 '(1953 1956 1949 1991 1964))

(c.2) Assume you have a function (interval a b) that returns a list of all the integers between a and b, inclusive (so that (interval 5 10) would return (5 6 7 8 9 10)). (Re-)write the function factorial using accumulate (and interval), without any explicit recursion.

(c.3) Now, think back to the restaurant database and assume we have a standard Lisp list (called RL) of the restaurant objects as we described. For each of the following expressions, describe in one English sentence what value it returns. Don't just say, "It does an accumulate of plus and zero to a map of ... ;" give a description of what the expression means, something you could put in a software catalog so that a prospective buyer could find what he or she wanted.

   * (accumulate + 0 (map (lambda (R) 1) RL))

   * (filter (lambda (R)(equal? 'Ethiopian (rest-cuisine R))) RL)

   * (/ (accumulate + 0 (map (lambda (R) (rest-price R)) RL))
     (accumulate + 0 (map (lambda (R) 1) RL)))

   * (let ((PRL (filter (lambda (R) (equal? 'pizza (rest-dish R))) RL)))
     (/ (accumulate + 0
  (map (lambda (R) (rest-price R)) PRL))
  (accumulate + 0 (map (lambda (R) 1) PRL))))

(c.4) Using map, filter, and accumulate, write an expression to return each of the following values without using explicit recursion:

   * a list of all the French and Italian restaurants in RL

   * a list of all the names of the French and Italian restaurants in RL

   * a list of all the restaurants in RL whose best dish costs between $10.00 and $20.00 (inclusive).

   * the name of the lowest-priced French restaurant in RL

   * (extra credit) a list of all the restaurants in RL, where every French restaurant whose best dish's price is less than the average (price of best dishes at French restaurants) has its price changed to that average price.

You aren't required to code up and run the solutions to this problem; you can do them with pencil and paper. However, coding them up is good practice, it can help you verify that your solutions are right, and it might earn you a bit of extra credit.