Preconditions and Postconditions

Summary: In the laboratory, you will consider mechanisms for verifying the preconditions of procedures. You will also consider some issues int he documentation of such procedures.

Contents:

• Exercises
  • Exercise 1: Are they all real?
  • Exercise 2: Differentiating Between Errors
  • Exercise 3: When Can You Count Between?
  • Exercise 4: An Odd Factorial
  • Exercise 5: Finding Values
  • Exercise 6: Substitution

Exercises

Exercise 1: Are they all real?

a. Document and write the all-real? procedure described in the accompanying reading.

b. What preconditions should all-real? have?

c. Is it necessary to test those preconditions? Why or why not?

Exercise 2: Differentiating Between Errors

Revise the definition of greatest-of-list given in the corresponding reading so that it prints a different (and appropriate) error message for each error condition.

I'd recommend that you use cond rather than if in writing this revised version.

Exercise 3: When Can You Count Between?

Revise the definition of the count-from procedure presented in the reading on recursion with natural numbers so that it enforces the precondition that its first argument be less than or equal to its second argument.

Exercise 4: An Odd Factorial

Here is a procedure that computes the product of all of the odd natural numbers up to and including number:

(define odd-factorial
  (lambda (number)
    (if (= number 1)
        1
        (* number (odd-factorial (- number 2))))))

a. What precondition or preconditions does odd-factorial impose on its argument?

b. What will happen if these preconditions are not met?

c. Revise the definition of odd-factorial as a husk-and-kernel program in which the husk enforces the precondition.

d. How can we be certain, in this case, that none of the recursive calls we make to the kernel procedure violates the precondition?

Exercise 5: Finding Values

a. Document (using the six-P style), define, and test a procedure named index-of that takes a symbol sym and a list ls of symbols as its arguments and returns the index of sym in ls. You should use 0-based indices, so that the initial value in a list is at index 0. (Note that we defined a similar procedure in a recent homework assignment. I would prefer that you not refer to the answer key in your work here.)

> (index-of 'gamma (list 'alpha 'beta 'gamma 'delta))
2
> (index-of 'easy (list 'easy 'medium 'difficult 'impossible))
0
> (index-of 'the (list 'and 'the 'cat 'sat 'on 'the 'mat))
1

b. Arrange for index-of to signal an error (by invoking the error procedure) if sym does not occur at all as an element of ls.

c. If sym does not occur as an element of ls, is it better to have for index-of to invoke error or return a special value (such as -1 or #f)? Explain your answer.

Exercise 6: Substitution

Document (using the six P style), define, and test a procedure named substitute that takes three arguments -- a symbol new, another symbol old, and a list ls of symbols -- and returns a list just like ls except that every occurrence of old has been replaced with an occurrence of new. Use the husk-and-kernel structure to make sure that new and old are symbols and that ls is a list of symbols before starting into the recursion.

> (substitute 'alpha 'omega (list 'phi 'chi 'psi 'omega 'omega)
(phi chi psi alpha alpha)
> (substitute 'starboard 'port (list 'port 'starboard 'port 'port))
(starboard starboard starboard starboard)
> (substitute 'in 'out null)
()
> (substitute "in" 'out null)
substitute: expected a symbol as first parameter
> (substitute 'in 'out (list 'alpha "beta" 23))
substitute: expected a list of symbols as third parameter