Higher-Order Procedures

• Exercises
  • Exercise 0: Preparation
  • Exercise 1: Using map
  • Exercise 2: Map with Multiple Lists
  • Exercise 3: Dot-Product
  • Exercise 4: Why Apply?
  • Exercise 5: Tallying
  • Exercise 6: Making Talliers

Exercises

Exercise 0: Preparation

a. If you have not done so already, please scan the corresponding reading on higher-order procedures.

b. Start DrScheme

Exercise 1: Using map

Recall that (map proc lst) builds a list by applying proc to each element of lst in succession.

a. Use map to compute the successors to the squares of the integers between 1 and 10. Your result should be the list (2 5 10 17 26 37 50 65 82 101).

b. Use map to turn a list into an association list by making each value in the first list into a a key. For example, given a list of names, you might produce an association list that associates the grade "A" with that name. Given the list ("William" "Jonathan" "Daniel") you should produce the list (("William" "A") ("Jonathan" "A") ("Daniel A")).

c. Use map to take the last element of each list in a list of lists. The result should be a list of the last elements. For example, given ((1 2 3) (4 5 6) (7 8 9 10) (11 12)) as input, you should produce the list (3 6 10 12).

d. Use apply and map to sum the last elements of each list in a list of lists of numbers. The result should be a number.

Note that you should have written a similar expression for another lab. Your goal here is to see whether you can solve the problem more concisely.

Exercise 2: Map with Multiple Lists

Although we often use the map procedure with only two parameters (a procedure and a list), it can take more than two parameters, as long as the first parameter is a procedure and the remaining parameters are lists.

a. What do you think the value of the following expression will be?
(map (lambda (x y) (+ x y)) (list 1 2 3) (list 4 5 6))

b. Verify your answer through experimentation.

c. What do you think the value of the following expression will be?
(map list (list 1 2 3) (list 4 5 6) (list 7 8 9))

d. Verify your answer through experimentation.

e. What do you think Scheme will do when evaluating the following expression?
(map list (list 1 2 3) (list 4 5))

f. Verify your answer through experimentation.

g. What do you think Scheme will do when evaluating the following expression?
(map (lambda (x y) (+ x y)) (list 1 2) (list 3 4) (list 5 6))

h. Verify your answer through experimentation.

Exercise 3: Dot-Product

Use apply and map to concisely define a procedure, (dot-product list1 list2), that takes as arguments two lists of numbers, equal in length, and returns the sum of the products of corresponding elements of the arguments:

> (dot-product (list 1 2 4 8) (list 11 5 7 3))
73
; ... because (1 x 11) + (2 x 5) + (4 x 7) + (8 x 3) = 11 + 10 + 28 + 24 = 73

> (dot-product null null)
0
; ... because in this case there are no products to add

Exercise 4: Why Apply?

Sarah and Steven Schemer suggest that apply is irrelevant. After all, they say, when you write

(apply proc (arg1 ... argn))

you're just doing the same thing as

(proc arg1 arg2 ... argn)

.

Given your experience in the previous exercise, are they correct? Why or why not?

Exercise 5: Tallying

a. Document and write a procedure, (tally predicate list), that counts the number of values in list for which predicate holds.

b. Demonstrate the procedure by tallying the number of odd values in the list of the first twenty integers.

c. Demonstrate the procedure by tallying the number of multiples of three in the list of the first twenty integers.

Exercise 6: Making Talliers

Document and write a procedure, (make-tallier predicate), that builds a procedure that takes a list as a parameter and tallies the values in the list for which the predicate holds. For example

> (define count-odds (make-tallier odd?))
> (count-odds (list 1 2 3 4 5))
3

You can assume that tally already exists for the purpose of this problem.