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In this (very simplistic) example, the programmer saves the operation of actually writing the file into a continuation (which can potentially be a very complex operation with many details to write out), and then passes that continuation (i.e, as a first-class closure) to another operator which does some more processing, and then calls it if necessary. (I use this design pattern a lot in actual GUI programming, either because it saves me lines of code or, more importantly, to wait for GUI events and then execute saved continuations repeatedly)

In this (very simplistic) example, the programmer saves the operation of actually writing the file into a continuation (which can potentially be a very complex operation with many details to write out), and then passes that continuation (i.e, as a first-class closure) to another operator which does some more processing, and then calls it if necessary. (I use this design pattern a lot in actual GUI programming, either because it saves me lines of code or, more importantly, to manage control flow after GUI events trigger)

In continuation passing style (CPS), continuations are just normal (only in languages where functions are first class) which the programmer explicitly manages and passes around to subroutines. In this style, program state is represented by closures (and the variables that happen to be encoded in them) rather than variables that reside somewhere on the stack. Functions that manage control flow accept continuation as arguments (in some variations of CPS, functions may accept multiple continuations) and manipulate control flow by invoking them by simply calling them and returning afterwards.

In continuation passing style (CPS), continuations are just normal functions (only in languages where functions are first class) which the programmer explicitly manages and passes around to subroutines. In this style, program state is represented by closures (and the variables that happen to be encoded in them) rather than variables that reside somewhere on the stack. Functions that manage control flow accept continuation as arguments (in some variations of CPS, functions may accept multiple continuations) and manipulate control flow by invoking them by simply calling them and returning afterwards. A very simple example of continuation passing style is as follows:

def save_file(filename):
  def write_file_continuation():
    write_stuff_to_file(filename)

  check_if_file_exists_and_user_wants_to_overwrite( write_file_continuation )

In this (very simplistic) example, the programmer saves the operation of actually writing the file into a continuation (which can potentially be a very complex operation with many details to write out), and then passes that continuation (i.e, as a first-class closure) to another operator which does some more processing, and then calls it if necessary. (I use this design pattern a lot in actual GUI programming, either because it saves me lines of code or, more importantly, to wait for GUI events and then execute saved continuations repeatedly)

This is clearly a reasonable iterable and the behavior of this generator -- returning 4 forever -- makes perfect sense. But it isn't probably the prototypical type of iterable that come to mind when thinking of iterators (i.e., for x in collection: do_something(x)).

To reiterate the last point: Continuations can save the state of a program's stack and generators can save the state of iteration. This means that continuations are more a lot powerful than generators, but also that generators are a lot, lot easier. They are easier for the language designer to implement, and they are easier for the programmer to use (if you have some time to burn, try to read and understand this page about continuations and call/cc).

This is clearly a reasonable iterable whose behavior is well defined -- each time the generator iterates over it, it returns 4 (and does so forever). But it isn't probably the prototypical type of iterable that comes to mind when thinking of iterators (i.e., for x in collection: do_something(x)). This example illustrates the power of generators: if anything is an iterator, a generator can save the state of its iteration.

To reiterate: Continuations can save the state of a program's stack and generators can save the state of iteration. This means that continuations are more a lot powerful than generators, but also that generators are a lot, lot easier. They are easier for the language designer to implement, and they are easier for the programmer to use (if you have some time to burn, try to read and understand this page about continuations and call/cc).