Homework 14: Tallying

Assigned: Tuesday, April 17, 2007
Due: Friday, April 20, 2007
No extensions!

Summary: In this assignment, you will write your own higher-order procedure.

Purposes: To help you think about higher-order procedures and how they might help with control.

Expected Time: One to two hours.

Collaboration: You may work in a group of any size between one and four, inclusive. You may consult others outside your group, provided you cite those others. You need only submit one assignment per group.

Submitting: Email me your work, using a subject of CSC151 Homework 14.

Warning: So that this exercise is a learning assignment for everyone, I may spend class time publicly critiquing your work.

Background

As you've seen in our discussions this past week, one of the key ideas in functional programming is that you can factor out common control structures. We've seen it possible to factor out the process of building a new list by recursing over the list with map and to factor out the process of checking all the values in a list with list-of?.

Here's another common task: Counting values that match some predicate. We've written procedures that count the number of symbols in a list and that count the number of odd numbers in a list of numbers.

(define tally-symbols
  (lambda (lst)
    (cond
      ((null? lst) 0)
      ((symbol? (car lst)) (+ 1 (tally-symbols (cdr lst))))
      (else (tally-symbols (cdr lst))))))
(define tally-odds
  (lambda (lst)
    (cond
      ((null? lst) 0)
      ((odd? (car lst)) (+ 1 (tally-odds (cdr lst))))
      (else (tally-odds (cdr lst))))))

Assignment

a. Write a procedure, (tally pred? lst), that counts the number of values in lst for which pred? holds.

b. Rewrite tally-symbols and tally-odds using tally. That is, your definitions should look something like the following:

(define tally-symbols
  (lambda (lst)
    (tally ...)))

c. Write a procedure, tally-as, which takes a list of integers (representing grades) as a parameter and returns the number of values that are 90 and above. You should not verify the preconditions of the procedure (that is, do not check that it's a list of integers).

d. Write a procedure better-tally-odds, which takes a list of arbitrary Scheme values as a parameter and returns a count of the number of times an odd integer appears in the list.

> (tally-odds (list 'a 'b 3))
odd?: expects argument of type *lt;integer>; given a
> (better-tally-odds (list 'a 'b 3 "hello" list -1))
2

You should write better-tally-odds so that its body is a call to tally with an appropriate predicate as the parameter.

e. [Optional] Write tally-odds without using a lambda. Hint: You might want to use left-section, right-section, or compose.