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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,

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