SICP Exercise 2.77

Question

Louis Reasoner tries to evaluate the expression (magnitude z) where z is the object shown in Figure 2.24. To his surprise, instead of the answer 5 he gets an error message from apply-generic, saying there is no method for the operation magnitude on the types (complex). He shows this interaction to Alyssa P. Hacker, who says “The problem is that the complex-number selectors were never defined for complex numbers, just for polar and rectangular numbers. All you have to do to make this work is add the following to the complex package:”

copy(put 'real-part '(complex) real-part)
(put 'imag-part '(complex) imag-part)
(put 'magnitude '(complex) magnitude)
(put 'angle '(complex) angle)

Describe in detail why this works. As an example, trace through all the procedures called in evaluating the expression (magnitude z) where z is the object shown in Figure 2.24. In particular, how many times is apply-generic invoked? What procedure is dispatched to in each case?

Answer

As Alyssa P. Hacker correctly states, the reason why the program did not work in the first place was because there simply was no stored function with an op of 'magnitude and a type of '(complex).

After adding it to the installation package, if (magnitude z) is called, apply-generic is first called using these values: op is magnitude and type-tags is '(complex). It is then called a second time with a type-tags of '(rectangular). This then calls the internal magnitude method.