Recall [[the recent homework assignment|/exercises/assignment12]] where you solved the same-fringe problem with a `make_fringe_enumerator` function, or in the Scheme version using streams instead of zippers, with a `lazy-flatten` function.
-The technique illustrated in those solutions is a powerful and important one. It's an example of what's sometimes called **cooperative threading**. A "thread" is a subprogram that the main computation spawns off. Threads are called "cooperative" when the code of the main computation and the thread fixes when control passes back and forth between them. (When the code doesn't control this---for example, it's determined by the operating system or the hardware in ways that the programmer can't predict---that's called "preemptive threading.") Cooperative threads are also sometimes called *coroutines* or *generators*.
+The technique illustrated in those solutions is a powerful and important one. It's an example of what's sometimes called **cooperative threading**. A "thread" is a subprogram that the main computation spawns off. Threads are called "cooperative" when the code of the main computation and the thread fixes when control passes back and forth between them. (When the code doesn't control this --- for example, it's determined by the operating system or the hardware in ways that the programmer can't predict --- that's called "preemptive threading.") Cooperative threads are also sometimes called *coroutines* or *generators*.
With cooperative threads, one typically yields control to the thread, and then back again to the main program, multiple times. Here's the pattern in which that happens in our `same_fringe` function:
start next1
(paused) starting
(paused) calculate first leaf
- (paused) <--- return it
+ (paused) <-- return it
start next2 (paused) starting
(paused) (paused) calculate first leaf
(paused) (paused) <-- return it
{left = {left = {leaf=1}, right = {leaf=2}}, right = {leaf=3}} )
true
-We're going to think about the underlying principles to this execution pattern, and instead learn how to implement it from scratch---without necessarily having zippers or dedicated native syntax to rely on.
+We're going to think about the underlying principles to this execution pattern, and instead learn how to implement it from scratch --- without necessarily having zippers or dedicated native syntax to rely on.
##Exceptions and Aborts##
OK, now this exception-handling apparatus does exemplify the second execution pattern we want to focus on. But it may bring it into clearer focus if we **simplify the pattern** even more. Imagine we could write code like this instead:
- # let foo x =
- try begin
- (if x = 1 then 10
- else abort 20
- ) + 100
- end
- ;;
+ let foo x =
+ try begin
+ (if x = 1 then 10
+ else abort 20
+ ) + 100
+ end
then if we called `foo 1`, we'd get the result `110`. If we called `foo 2`, on the other hand, we'd get `20` (note, not `120`). This exemplifies the same interesting "jump out of this part of the code" behavior that the `try ... raise ... with ...` code does, but without the details of matching which exception was raised, and handling the exception to produce a new result.
-Many programming languages have this simplified exceution pattern, either instead of or alongside a `try ... with ...`-like pattern. In Lua and many other languages, `abort` is instead called `return`. In Lua, the preceding example would be written:
+> If we had to write that using `try...with...`, it'd look something like this:
+
+> exception Abort of int;; (* declare a new type of exception that can carry an int parameter *)
+> let foo x =
+> try
+> (if x = 1 then 10
+> else raise (Abort 20)
+> ) + 100
+> with Abort n -> n
+
+Many programming languages have this simplified execution pattern, either instead of or alongside a `try ... with ...`-like pattern. In Lua and many other languages, `abort` is instead called `return`. In Lua, the preceding example would be written:
> function foo(x)
local value
else abort 20
) + 100
end
- in (foo 2) + 1;; (* this line is new *)
+ in (foo 2) + 1000;; (* this line is new *)
we can imagine a box:
That function is our "snapshot". Normally what happens is that code *inside* the box delivers up a value, and that value gets supplied as an argument to the snapshot-function just described. That is, our code is essentially working like this:
let x = 2
- in let snapshot = fun box ->
+ in let outer_snapshot = fun box ->
let foo_result = box
in (foo_result) + 1000
in let foo_applied_to_x =
(if x = 1 then 10
else ... (* we'll come back to this part *)
) + 100
- in shapshot foo_applied_to_x;;
+ in outer_snapshot foo_applied_to_x;;
But now how should the `abort 20` part, that we ellided here, work? What should happen when we try to evaluate that?
-Well, that's when we use the snapshot code in an unusual way. If we encounter an `abort 20`, we should abandon the code we're currently executing, and instead just supply `20` to the snapshot we saved when we entered the box. That is, something like this:
+Well, that's when we use the `outer_snapshot` code in an unusual way. If we encounter an `abort 20`, we should abandon the code we're currently executing, and instead just supply `20` to the snapshot we saved when we entered the box. That is, something like this:
let x = 2
- in let snapshot = fun box ->
+ in let outer_snapshot = fun box ->
let foo_result = box
in (foo_result) + 1000
in let foo_applied_to_x =
(if x = 1 then 10
- else snapshot 20
+ else outer_snapshot 20
) + 100
- in shapshot foo_applied_to_x;;
+ in outer_snapshot foo_applied_to_x;;
-Except that isn't quite right, yet---in this fragment, after the `snapshot 20` code is finished, we'd pick up again inside `let foo_applied_to_x = (...) + 100 in snapshot foo_applied_to_x`. That's not what we want. We don't want to pick up again there. We want instead to do this:
+Except that isn't quite right, yet --- in this fragment, after the `outer_snapshot 20` code is finished, we'd pick up again inside `let foo_applied_to_x = (...) + 100 in outer_snapshot foo_applied_to_x`. That's not what we want. We don't want to pick up again there. We want instead to do this:
let x = 2
- in let snapshot = fun box ->
+ in let outer_snapshot = fun box ->
let foo_result = box
in (foo_result) + 1000
in let foo_applied_to_x =
(if x = 1 then 10
- else snapshot 20 THEN STOP
+ else outer_snapshot 20 THEN STOP
) + 100
- in shapshot foo_applied_to_x;;
+ in outer_snapshot foo_applied_to_x;;
We can get that by some further rearranging of the code:
let x = 2
- in let snapshot = fun box ->
+ in let outer_snapshot = fun box ->
let foo_result = box
in (foo_result) + 1000
- in let continue_foo_normally = fun from_value ->
+ in let continue_foo_snapshot = fun from_value ->
let value = from_value + 100
- in snapshot value
+ in outer_snapshot value
in (* start of foo_applied_to_x *)
- if x = 1 then continue_foo_normally 10
- else snapshot 20;;
+ if x = 1 then continue_foo_snapshot 10
+ else outer_snapshot 20;;
And this is indeed what is happening, at a fundamental level, when you use an expression like `abort 20`. Here is the original code for comparison:
These snapshots are called **continuations** because they represent how the computation will "continue" once some target code (in our example, the code in the box) delivers up a value.
-You can think of them as functions that represent "how the rest of the computation proposes to continue." Except that, once we're able to get our hands on those functions, we can do exotic and unwholesome things with them. Like use them to suspend and resume a thread. Or to abort from deep inside a sub-computation: one function might pass the command to abort *it* to a subfunction, so that the subfunction has the power to jump directly to the outside caller. Or a function might *return* its continuation function to the outside caller, giving *the outside caller* the ability to "abort" the function (the function that has already returned its value---so what should happen then?) Or we may call the same continuation function *multiple times* (what should happen then?). All of these weird and wonderful possibilities await us.
+You can think of them as functions that represent "how the rest of the computation proposes to continue." Except that, once we're able to get our hands on those functions, we can do exotic and unwholesome things with them. Like use them to suspend and resume a thread. Or to abort from deep inside a sub-computation: one function might pass the command to abort *it* to a subfunction, so that the subfunction has the power to jump directly to the outside caller. Or a function might *return* its continuation function to the outside caller, giving *the outside caller* the ability to "abort" the function (the function that has already returned its value --- so what should happen then?) Or we may call the same continuation function *multiple times* (what should happen then?). All of these weird and wonderful possibilities await us.
-The key idea behind working with continuations is that we're *inverting control*. In the fragment above, the code `(if x = 1 then ... else snapshot 20) + 100`---which is written as if it were to supply a value to the outside context that we snapshotted---itself *makes non-trivial use of* that snapshot. So it has to be able to refer to that snapshot; the snapshot has to somehow be available to our inside-the-box code as an *argument* or bound variable. That is: the code that is *written* like it's supplying an argument to the outside context is instead *getting that context as its own argument*. He who is written as value-supplying slave is instead become the outer context's master.
+The key idea behind working with continuations is that we're *inverting control*. In the fragment above, the code `(if x = 1 then ... else outer_snapshot 20) + 100` --- which is written as if it were to supply a value to the outside context that we snapshotted --- itself *makes non-trivial use of* that snapshot. So it has to be able to refer to that snapshot; the snapshot has to somehow be available to our inside-the-box code as an *argument* or bound variable. That is: the code that is *written* like it's supplying an argument to the outside context is instead *getting that context as its own argument*. He who is written as value-supplying slave is instead become the outer context's master.
-In fact you've already seen this several times this semester---recall how in our implementation of pairs in the untyped lambda-calculus, the handler who wanted to use the pair's components had *in the first place to be supplied to the pair as an argument*. So the exotica from the end of the seminar was already on the scene in some of our earliest steps. Recall also what we did with our [[abortable list traversals|/topics/week12_abortable_traversals]].
+In fact you've already seen this several times this semester --- recall how in our implementation of pairs in the untyped lambda-calculus, the handler who wanted to use the pair's components had *in the first place to be supplied to the pair as an argument*. So the exotica from the end of the seminar was already on the scene in some of our earliest steps. Recall also what we did with our [[abortable list traversals|/topics/week12_abortable_traversals]]. (The `outer_snapshot` corresponds to the "done" handler in those traversals; and the `continue_foo_snapshot` to the "keep_going" handler.)
This inversion of control should also remind you of Montague's treatment of determiner phrases in ["The Proper Treatment of Quantification in Ordinary English"](http://www.blackwellpublishing.com/content/BPL_Images/Content_store/Sample_chapter/0631215417%5CPortner.pdf) (PTQ).
-A naive semantics for atomic sentences will say the subject term is of type `e`, and the predicate of type `e -> t`, and that the subject provides an argument to the function expressed by the predicate.
+> A naive semantics for atomic sentences will say the subject term is of type `e`, and the predicate of type `e -> t`, and that the subject provides an argument to the function expressed by the predicate.
-Monatague proposed we instead take the subject term to be of type `(e -> t) -> t`, and that now it'd be the predicate (still of type `e -> t`) that provides an argument to the function expressed by the subject.
+> Monatague proposed we instead take the subject term to be of type `(e -> t) -> t`, and that now it'd be the predicate (still of type `e -> t`) that provides an argument to the function expressed by the subject.
-If all the subject did then was supply an `e` to the `e -> t` it receives as an argument, we wouldn't have gained anything we weren't already able to do. But of course, there are other things the subject can do with the `e -> t` it receives as an argument. For instance, it can check whether anything in the domain satisfies that `e -> t`; or whether most things do; and so on.
+> If all the subject did then was supply an `e` to the `e -> t` it receives as an argument, we wouldn't have gained anything we weren't already able to do. But of course, there are other things the subject can do with the `e -> t` it receives as an argument. For instance, it can check whether anything in the domain satisfies that `e -> t`; or whether most things do; and so on.
This inversion of who is the argument and who is the function receiving the argument is paradigmatic of working with continuations.
Continuations come in many varieties. There are **undelimited continuations**, expressed in Scheme via `(call/cc (lambda (k) ...))` or the shorthand `(let/cc k ...)`. (`call/cc` is itself shorthand for `call-with-current-continuation`.) These capture "the entire rest of the computation." There are also **delimited continuations**, expressed in Scheme via `(reset ... (shift k ...) ...)` or `(prompt ... (control k ...) ...)` or any of several other operations. There are subtle differences between those that we won't be exploring in the seminar. Ken Shan has done terrific work exploring the relations of these operations to each other.
-When working with continuations, it's easiest in the first place to write them out explicitly, the way that we explicitly wrote out the `snapshot` continuation when we transformed this:
+When working with continuations, it's easiest in the beginning to write them out explicitly, the way that we explicitly wrote out the "snapshot" continuations when we transformed this:
let foo x =
+---try begin----------------+
into this:
let x = 2
- in let snapshot = fun box ->
+ in let outer_snapshot = fun box ->
let foo_result = box
in (foo_result) + 1000
- in let continue_foo_normally = fun from_value ->
+ in let continue_foo_snapshot = fun from_value ->
let value = from_value + 100
- in snapshot value
+ in outer_snapshot value
in (* start of foo_applied_to_x *)
- if x = 1 then continue_foo_normally 10
- else snapshot 20;;
+ if x = 1 then continue_foo_snapshot 10
+ else outer_snapshot 20;;
Code written in the latter form is said to be written in **explicit continuation-passing style** or CPS. Later we'll talk about algorithms that mechanically convert an entire program into CPS.
(shift k
(if (eqv? x 1) (k 10) 20))
100)))])
- (+ (foo 1) 1000))
+ (+ (foo 2) 1000))
<!--
# open Delimcc;;
# let reset body = let p = new_prompt () in push_prompt p (body p);;
# let test_cps x =
- let snapshot = fun box ->
+ let outer_snapshot = fun box ->
let foo_result = box
in (foo_result) + 1000
- in let continue_foo_normally = fun from_value ->
+ in let continue_foo_snapshot = fun from_value ->
let value = from_value + 100
- in snapshot value
- in if x = 1 then continue_foo_normally 10
- else snapshot 20;;
+ in outer_snapshot value
+ in if x = 1 then continue_foo_snapshot 10
+ else outer_snapshot 20;;
# let test_shift x =
let foo x = reset(fun p () ->
-->
-Various of the tools we've been introducing over the past weeks are inter-related. We saw coroutines implemented first with zippers; here we've talked in the abstract about their being implemented with continuations. Oleg says that "Zipper can be viewed as a delimited continuation reified as a data structure." Ken expresses the same idea in terms of a zipper being a "defunctionalized" continuation---that is, take something implemented as a function (a continuation) and implement the same thing as an inert data structure (a zipper).
+Various of the tools we've been introducing over the past weeks are inter-related. We saw coroutines implemented first with zippers; here we've talked in the abstract about their being implemented with continuations. Oleg says that "Zipper can be viewed as a delimited continuation reified as a data structure." Ken expresses the same idea in terms of a zipper being a "defunctionalized" continuation --- that is, take something implemented as a function (a continuation) and implement the same thing as an inert data structure (a zipper).
Mutation, delimited continuations, and monads can also be defined in terms of each other in various ways. We find these connections fascinating but the seminar won't be able to explore them very far.
-We recommend reading [the Yet Another Haskell Tutorial on Continuation Passing Style](http://en.wikibooks.org/wiki/Haskell/YAHT/Type_basics#Continuation_Passing_Style)---though the target language is Haskell, this discussion is especially close to material we're discussing in the seminar.
+We recommend reading [the Yet Another Haskell Tutorial on Continuation Passing Style](http://en.wikibooks.org/wiki/Haskell/YAHT/Type_basics#Continuation_Passing_Style) --- though the target language is Haskell, this discussion is especially close to material we're discussing in the seminar.