So far in this course, we have used accumulators as tools to implement functions which are tail recursive, by storing our intermediate computations in an extra argument to the function in question, as we recurse.

Continuation-passing style is a natural extension of accumulation, where instead of using an accumulator of a type like int, the accumulator is a function which represents the work left to do by the function. This allows us to store computations in our accumulator argument, called the continuation, and discharge them all at a later time.

Philosophically, continuation-passing style can be seen as contrasting to direct-style recursion by noting down instructions of what instructions to execute, rather than executing instructions themselves and storing the results in the accumulator. These end up being spiritually the same information, but having slightly different implications for implementation.

We saw that we could use continuation-passing style to make the control flow of our programs extremely clear, and implement backtracking and doubly-recursing functions easily via using them. Written in such a way, these programs have a more explicit evaluation order, and rely less on implicit evaluation rules.