Design Pattern for Recursive Functions

A design pattern is an abstracted way of writing programs of a certain kind. By learning design patterns, you can write programs faster and with fewer errors.

A design pattern for recursive functions is:

(defun myfun (arg)
         (if (basecase? arg)
                 (baseanswer arg)
                 (combine arg (myfun (smaller arg)))))

In this pattern,

• (basecase? arg) is a test to determine whether arg is a base case for which the answer is known at once.

• (baseanswer arg) is the known answer for the base case.

• (combine arg (myfun (smaller arg))) computes the answer in terms of the current argument arg and the result of calling the function recursively on (smaller arg), a reduced version of the argument.

Exercise: Show how the factorial function corresponds to this design pattern.