Preconditions and Postconditions

Exercises

Exercise 0: Preparation

If you have not done so already, scan the reading on preconditions and postconditions

Exercise 1: Are they all real?

a. 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 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`.

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 does `odd-factorial` impose on its argument?

b. What will happen if this precondition is 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 calls we make to the kernel procedure violates the precondition?

Exercise 5: Finding values

a. Define and test a procedure named `index` that takes a symbol `sym` and a list `ls` of symbols as its arguments and returns the number of list elements that precede the first occurrence of `sym` in `ls`:

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

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

Exercise 6: Substitution

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)
> (substitution 'in 'out null)
()
```

History

Friday, 15 September 2000

Monday, 18 September 2000

• Fixed some formatting.
• Rearranged the first two problems.

Disclaimer Often, these pages were created "on the fly" with little, if any, proofreading. Any or all of the information on the pages may be incorrect. Please contact me if you notice errors.