/ | \
leaf 1 leaf 2 leaf 3
-We'll call this new untargetted tree `node 20`. The result of moving upward from our previous targetter tree, targetted on `leaf 1`, would be the outermost `parent` element of that targetted tree, with `node 20` being the subtree that fills that parent's target position `*`:
+We'll call this new untargetted tree `node 20`. The result of moving upward from our previous targetted tree, targetted on `leaf 1`, would be the outermost `parent` element of that targetted tree, with `node 20` being the subtree that fills that parent's target position `*`:
{
parent = ...;
you won't move upwards at the same steps. Keep comparing "the next leafs" until they are different, or you exhaust the leafs of only one of the trees (then again the trees have different fringes), or you exhaust the leafs of both trees at the same time, without having found leafs with different labels. In this last case, the trees have the same fringe.
-If your trees are very big---say, millions of leaves---you can imagine how this would be quicker and more memory-efficient than traversing each tree to construct a list of its fringe, and then comparing the two lists so built to see if they're equal. For one thing, the zipper method can abort early if the fringes diverge early, without needing to traverse or built a list containing the rest of each tree's fringe.
+If your trees are very big---say, millions of leaves---you can imagine how this would be quicker and more memory-efficient than traversing each tree to construct a list of its fringe, and then comparing the two lists so built to see if they're equal. For one thing, the zipper method can abort early if the fringes diverge early, without needing to traverse or build a list containing the rest of each tree's fringe.
Let's sketch the implementation of this. We won't provide all the details for an implementation of the tree zipper, but we will sketch an interface for it.
# type blah_record = { height : int; weight : int; char_tester : char -> bool };;
# let b2 = { height = 1; weight = 2; char_tester = fun c -> c = 'M' };;
val b2 : blah_record = {height = 1; weight = 2; char_tester = <fun>}
+ # let b3 = { height = 1; char_tester = (fun c -> c = 'K'); weight = 3 };; (* also works *)
+ val b3 : blah_record = {height = 1; weight = 3; char_tester = <fun>}
These were the strategies to extract the components of an unlabeled tuple:
The auxiliary `loop` function will keep calling itself recursively until a difference in the fringes has manifested itself---either because one fringe is exhausted before the other, or because the next leaves in the two fringes have different labels. If we get to the end of both fringes at the same time (`next1 (), next2 ()` matches the pattern `None, None`) then we've established that the trees do have the same fringe.
-The technique illustrated here with our fringe enumerators 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.") 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:
+The technique illustrated here with our fringe enumerators 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:
main program next1 thread next2 thread
------------ ------------ ------------
(paused) <-- return it (paused)
... and so on ...
+If you want to read more about these kinds of threads, here are some links:
+
+<!-- * [[!wikipedia Computer_multitasking]]
+* [[!wikipedia Thread_(computer_science)]] -->
+* [[!wikipedia Coroutine]]
+* [[!wikipedia Iterator]]
+* [[!wikipedia Generator_(computer_science)]]
+* [[!wikipedia Fiber_(computer_science)]]
+<!-- * [[!wikipedia Green_threads]]
+* [[!wikipedia Protothreads]] -->
+
The way we built cooperative threads here crucially relied on two heavyweight tools. First, it relied on our having a data structure (the tree zipper) capable of being a static snapshot of where we left off in the tree whose fringe we're enumerating. Second, it relied on our using mutable reference cells so that we could update what the current snapshot (that is, tree zipper) was, so that the next invocation of the `next_leaf` function could start up again where the previous invocation left off.
In coming weeks, we'll learn about a different way to create threads, that relies on **continuations** rather than on those two tools. All of these tools are inter-related. As Oleg says, "Zipper can be viewed as a delimited continuation reified as a data structure." These different tools are also inter-related with monads. Many of these tools can be used to define the others. We'll explore some of the connections between them in the remaining weeks, but we encourage you to explore more.