Section~#secloss#40607> illustrated with two examples the need for
accumulating extra knowledge. In some cases, the accumulation makes it
easier to understand a function, in others it is necessary for the function
to work properly. In both cases, however, we first chose one of the
available design recipes, inspected the function, and then revised or fixed
it. Put more generally, adding an <#67491#><#40608#>ACCUMULATOR<#40608#><#67491#>, that is, a
parameter that accumulates knowledge, is something that we add to a function
after we have designed a function, not before.
The keys to the development of an accumulator-style function are:
The first two subsections address these two questions. Because the second
one is a difficult topic, the third subsection illustrates how to formulate
precise claims about accumulators. More concretely, in this section, we
transform several standard recursive functions into functions that use
auxiliary functions with accumulators.
- to recognize that the function benefits from, or needs, an accumulator;
- to understand what the accumulator represents.