# SICP Solutions

### Section - 2.5 - Systems with Generic Operations

#### Exercise 2.77

The expression (magnitude z) fails initially because it results in a call to apply-generic. As per figure(mentioned in question), z is tagged with complex, thus apply-generic will lookup in the data directed table using get. Since magnitude is not stored in the table corresponding to complex, it results in error - “no method for the operation magnitude on the types (complex)”.

After adding the put statements, the error disappears because it adds magnitude to the table.

Now after the first call to apply-generic, it will result in (magnitude zz) where zz is (content z). Thus zz is of type ‘rectangular as can be seen form the figure.

Now this will again invoke apply-generic which will invoke magnitude from the rectangular package. And which will finally return the magnitude.

Thus there are two invocations of apply-generic`.