Lambda the Ultimate

Recently Rys McCusker and I started talking about continuations, in another node where that was probably off topic. The link if you want to read it is http://lambda-the-ultimate.org/node/5082.

The ability to directly refer to continuations is supposed to be something like an "ultimate" control structure, or "goto with its context intact," which all other control structures are trivially implementable with.

But because it does a lot more than "goto" in order to preserve that context, there can be some serious problems if that extra stuff it does is irrelevant, wasteful, or harmful. And I have experienced that some kinds of continuations are just plain worse than others. But let me explain what I mean by kinds of continuations. Most languages that have them at all have only one kind, so the fact that there are different kinds is something that people who only program in one language tend never to notice.

There are a bunch of different things that can be called continuations. I think of them as being divided along four axes. First, there is delimited versus reified. Second, there is lexical-capturing versus dynamic-capturing (or both, or neither). Third there is winding/unwinding versus raw. And fourth there is mutable vs. immutable capture.

Delimited or "one-shot" continuations are delimited in dynamic extent; You can store them in values or pass them to subroutines or whatever, but having called a function, you can its continuation to return from that function exactly once, and that only if you haven't already returned from the function in some other way first. With delimited continuations you can reorder the sequence in which functions return, making it not equal to the usual standard of being the reverse of sequence in which they were called. You can even "delay" some of the function returns until after the program halts (ie, never) by just never using them, or by having your function just skip the returns of its callees by telling them to call its own continuation directly. These are mostly no problem in my experience.

Reified continuations can do the same kind of things that you can do with delimited continuations in terms of returning from the function or passing one to a called function or reordering function returns, but reified continuations have an additional property: having captured a reified continuation and stored it as a value in some variable that persists beyond the dynamic extent of the function (ie, after the function has already returned) you can call it and simulate that function returning, with the same environment (that may include the environments of other functions that have already returned) AGAIN, even though the function whose return you are simulating has not been called a second time. This sounds like a good idea, but experience has taught me that it is deeply problematic.

Lexical-capture vs. Dynamic-capture is whether your continuations capture the lexical environment (ie, the bindings within the lexical scope of the function whose continuation is taken) or the dynamic environment (ie, the bindings within the dynamic extent of the function whose continuation is taken). Usually, programming languages use scope, which is called lexical scope, or extent, which is called dynamic scope, but rarely both. In those two cases this is a trivial choice because your continuations will capture the same environment whose bindings are extended by your function calls (it could be done the other way but that would be insane). However, if your language has both lexically scoped and dynamically scoped variables, this distinction can become crucially important. Usually continuations that capture the lexical environment will allow the dynamic environment to be inherited from wherever the continuation is called, rather than from where the continuation is taken. You can make powerful arguments on both sides of the question of whether continuations that capture the lexical environment should or should not also capture the dynamic environment. Semantically it's nicer if they do, but in terms of implementation that doubles the branchiness of your environment tree and can become very expensive very fast if people use it a lot. In Common Lisp version 1, before they switched to lexical scope by default, there were (delimited) continuations that captured the dynamic environment but not the lexical environment. I guess there is actually a fourth subcategory here: "goto" is a sort of continuation that captures neither lexical nor dynamic environment.

Winding and Unwinding is another important distinction, and another controversy. If your continuations wind and unwind, it means that you can arrange for code to be called when a given scope (or extent) is entered or left, including entering or leaving that scope by means of a continuation. A classic example would be releasing a resource when you escape from a function that needs that resource, and then locking the resource again when re-entering that function. With raw continuations, it's a lot more like just a jump; you don't get to call set-up and shut-down code. In some ways winding and unwinding continuations are more orderly, but once again the devil is in the implementation; this renders continuations nearly useless for mechanisms like lightweight context switches between green threads.

And finally we get to the last category; is the captured environment mutable or immutable after capture? An implementation of continuations could copy the stack, and then treat the copied value as immutable. If the bindings visible in the stack were then mutated before the continuation were called, the stack from the continuation (including the former values) would be copied back into the working stack, undoing the mutations. This type of continuation is called a "restart" and is very rare because it is highly expensive in memory costs. In the usual case, the captured environment is mutable - ie, the implementation records only pointers to the stack frames where the variables are found, not the variables themselves. So if code after the continuation is captured mutates the values of those variables, the continuation when invoked will not overwrite the mutated values.

And I think that is an exhaustive taxonomy of all the things that have been called "continuations." Doubtless I've missed something.

Continuations are used to implement:
control structures - for example if you want to roll your own do-while loops, no environment capture is needed.
nonlocal flow of control - for example if you want to roll your own try/catch and exception handlers.
variable scoping - using the winding/unwinding variety, you can simulate dynamic variables in lexically scoped languages or vice versa.
green threads - if you want to roll your own cooperative multitasking.
session management - you can represent the session of visitor #1392 to your website (or whatever) as a continuation.
type system extensions - using winding/unwinding continuations can allow you to add typechecking code on entry and exit to functions, even for types the native language could not define. The drawback is that these are runtime rather than compile time typechecks.
and many other things.

Many of these things can't be done within the (other) tools a well-defined language can give you to work with. So, yay.

But many of these are BAD uses for continuations, in that continuations are a BAD way to implement these things. So, boo.

Many of these things cannot coexist in the same program because different uses of continuations would force stack captures that can never be recovered by garbage collection, or otherwise interfere with each other. This is especially true of reified continuations. So, boo some more.

Many of these different "continuations" have very fundamental semantic differences, in terms of composability and tractability for combinations.

And now that I've written half a book here, you guys can tell me what I missed or what it means. ;-)