When we design recursive functions, we don’t think about the context of their use. Whether they are applied for the first time or whether they are called for the hundredth time in a recursive manner doesn’t matter. They are to work according to their purpose statement, and that’s all we need to know as we design the bodies of the functions.
Altough this principle of context-independence greatly facilitates the development of functions, it also causes occasional problems. In this section, we illustrate the most important problem with two examples. Both concern the loss of knowledge that occurs during a recursive evaluation. The first subsection shows how this loss makes a structurally recursive function more complicated and less efficient than necessary; the second one shows how the loss of knowledge causes a fatal flaw in an algorithm.
The rest of this chapter is under development. Use HtDP/1e in the meantime.