notion | Tiling tabbed window manager

__init__ should only be used to initialize an existing object. (Though the creation of the object and the call to __init__ usually both happen inside the call to the type itself.)

Use dedicated class methods as alternative constructors (such as copy constructors or constructing an object from another object). For example,

Typeclass laws are not part of the Haskell language, so they are not subject to the same kind of language-theoretic semantic analysis as the language itself.

Instead, these laws are typically presented as an informal mathematical notation. Most presentations do not need a more detailed mathematical exposition, so they do not provide one.

Check the following example and help labels. You can create a datablock and add your labels and plot them rotated and boxed together with your map.

Edit: ...forgot the semitransparent boxes. You need to play with the alpha channel, i.e. 0xAARRGGBB.

Code:

We may use across (if we want to filter the rows when both column conditions are TRUE) or replace across with if_any (if either one of them is TRUE when they are both selected)

Let's ignore the formalised, but incomplete, definitions. We find the actual meaning in the non-normative notes of that section.¹

What is Liveness in JavaScript?

Liveness is the lower bound for guaranteeing which WeakRefs an engine must not empty (note 6). So live (sets of) objects are those that must not be garbage-collected because they still will be used by the program.

However, the liveness of a set of objects does not mean that all the objects in the set must be retained. It means that there are some objects in the set that still will be used by the program, and the live set (as a whole) must not be garbage-collected. This is because the definition is used in its negated form in the garbage collector Execution algorithm²: At any time, if a set of objects S is not live, an ECMAScript implementation may³ […] atomically [remove them]. In other words, if an implementation chooses a non-live set S in which to empty WeakRefs, it must empty WeakRefs for all objects in S simultaneously (note 2).

Looking at individual objects, we can say they are not live (garbage-collectable) if there is at least one non-live set containing them; and conversely we say that an individual object is live if every set of objects containing it is live (note 3). It's a bit weird as a "live set of objects" is basically defined as "a set of objects where any of them is live", however the individual liveness is always "with respect to the set S", i.e. whether these objects can be garbage-collected together.

_{1: This definitely appears to be the section with the highest notes-to-content ratio in the entire spec.
2: emphasis mine
3: From the first paragraph of the objectives: "This specification does not make any guarantees that any object will be garbage collected. Objects which are not live may be released after long periods of time, or never at all. For this reason, this specification uses the term "may" when describing behaviour triggered by garbage collection."}

Now, let's try to understand the definition.

At any point during evaluation, a set of objects S is considered live if either of the following conditions is met:

• Any element in S is included in any agent's [[KeptAlive]] List.
• There exists a valid future hypothetical WeakRef-oblivious execution with respect to S that observes the Object value of any object in S.

The first condition is pretty clear. The [[KeptAlive]] list of an agent is representing the list of objects to be kept alive until the end of the current Job. It is cleared after a synchronous run of execution ends, and the note on WeakRef.prototype.deref⁴ provides further insight on the intention: If [WeakRefDeref] returns a target Object that is not undefined, then this target object should not be garbage collected until the current execution of ECMAScript code has completed.

The second condition however, oh well. It is not well defined what "valid", "future execution" and "observing the Object value" mean. The intuition the second condition above intends to capture is that an object is live if its identity is observable via non-WeakRef means (note 2), aha. From my understanding, "an execution" is the execution of JavaScript code by an agent and the operations occurring during that. It is "valid" if it conforms to the ECMAScript specification. And it is "future" if it starts from the current state of the program.
An object's identity may be observed by observing a strict equality comparison between objects or observing the object being used as key in a Map (note 4), whereby I assume that the note only gives examples and "the Object value" means "identity". What seems to matter is whether the code does or does not care if the particular object is used, and all of that only if the result of the execution is observable (i.e. cannot be optimised away without altering the result/output of the program)⁵.
To determine liveness of objects by these means would require testing all possible future executions until the objects are no longer observable. Therefore, liveness as defined here is undecidable⁶. In practice, engines use conservative approximations such as reachability⁷ (note 6), but notice that research on more advanced garbage-collectors is under way.

Now for the interesting bit: what makes an execution "hypothetical WeakRef-oblivious with respect to a set of object S"? It means an execution under the hypothesis that all WeakRefs to objects in S are already cleared⁸. We assume that during the future execution, the abstract operation WeakRefDeref of a WeakRef whose referent is an element of S always returns undefined (def), and then work back whether it still might observe an element of the set. If none of the objects to be can be observed after all weak references to them are cleared, they may be garbage-collected. Otherwise, S is considered live, the objects cannot be garbage-collected and the weak references to them must not be cleared.

_{4: See the whole note for an example. Interestingly, also the new WeakRef(obj) constructor adds obj to the [[KeptAlive]] list.
5: Unfortunately, "the notion of what constitutes an "observation" is intentionally left vague" according to this very interesting es-discourse thread.
6: While it appears to be useless to specify undecidable properties, it actually isn't. Specifying a worse approximation, e.g. said reachability, would preclude some optimisations that are possible in practice, even if it is impossible to implement a generic 100% optimiser. The case is similar for dead code elimination.
7: Specifying the concept of reachability would actually be much more complicated than describing liveness. See Note 5, which gives examples of structures where objects are reachable through internal slots and specification type fields but should be garbage-collected nonetheless.
8: See also issue 179 in the proposal and the corresponding PR for why sets of objects were introduced.}

Example time!

It is hard to me to recognize how livenesses of several objects may affect each other.

WeakRef-obliviousness, together with liveness, capture[s the notion] that a WeakRef itself does not keep an object alive (note 1). This is pretty much the purpose of a WeakRef, but let's see an example anyway:

(Disclaimer: this answer is based on reading specs and some tests, but not on previous experience.)

First of all, there is an explanation and example code for this exact case (one core writes code for another core to execute) in B2.2.5 of the Architecture Reference Manual (version G.b). The only difference from the examples you've shown is that the final isb needs to be executed in the thread that will execute the new code (which I guess is your "consumer"), after the cache invalidation has finished.

I found it helpful to try to understand the abstract constructs like "inner shareable domain", "point of unification" from the architecture reference in more concrete terms.

Let's think about a system with several cores. Their L1d caches are coherent, but their L1i caches need not be unified with L1d, nor coherent with each other. However, the L2 cache is unified.

The system does not have any way for L1d and L1i to talk to each other directly; the only path between them is through L2. So once we have written our new code to L1d, we have to write it back to L2 (dc cvau), then invalidate L1i (ic ivau) so that it repopulates from the new code in L2.

In this setting, PoU is the L2 cache, and that's exactly where we want to clean / invalidate to.

There's some explanation of these terms in page D4-2646. In particular:

The PoU for an Inner Shareable shareability domain is the point by which the instruction and data caches and the translation table walks of all the PEs in that Inner Shareable shareability domain are guaranteed to see the same copy of a memory location.

Here, the Inner Shareable domain is going to contain all the cores that could run the threads of our program; indeed, it is supposed to contain all the cores running the same kernel as us (page B2-166). And because the memory we are dc cvauing is presumably marked with the Inner Shareable attribute or better, as any reasonable OS should do for us, it cleans to the PoU of the domain, not merely the PoU of our core (PE). So that's just what we want: a cache level that all instruction cache fills from all cores would see.

The Point of Coherency is further down; it is the level that everything on the system sees, including DMA hardware and such. Most likely this is main memory, below all the caches. We don't need to get down to that level; it would just slow everything down for no benefit.

Hopefully that helps with your question 1.

Note that the cache clean and invalidate instructions run "in the background" as it were, so that you can execute a long string of them (like a loop over all affected cache lines) without waiting for them to complete one by one. dsb ish is used once at the end to wait for them all to finish.

Some commentary about dsb, towards your questions #2 and #3. Its main purpose is as a barrier; it makes sure that all the pending data accesses within our core (in store buffers, etc) get flushed out to L1d cache, so that all other cores can see them. This is the kind of barrier you need for general inter-thread memory ordering. (Or for most purposes, the weaker dmb suffices; it enforces ordering but doesn't actually wait for everything to be flushed.) But it doesn't do anything else to the caches themselves, nor say anything about what should happen to that data beyond L1d. So by itself, it would not be anywhere near strong enough for what we need here.

As far as I can tell, the "wait for cache maintenance to complete" effect is a sort of bonus feature of dsb ish. It seems orthogonal to the instruction's main purpose, and I'm not sure why they didn't provide a separate wcm instruction instead. But anyway, it is only dsb ish that has this bonus functionality; dsb ishst does not. D4-2658: "In all cases, where the text in this section refers to a DMB or a DSB, this means a DMB or DSB whose required access type is both loads and stores".

I ran some tests of this on a Cortex A-72. Omitting either of the dc cvau or ic ivau usually results in the stale code being executed, even if dsb ish is done instead. On the other hand, doing dc cvau ; ic ivau without any dsb ish, I didn't observe any failures; but that could be luck or a quirk of this implementation.

To your #4, the sequence we've been discussing (dc cvau ; dsb ish ; ci ivau ; dsb ish ; isb) is intended for the case when you will run the code on the same core that wrote it. But it actually shouldn't matter which thread does the dc cvau ; dsb ish ; ci ivau ; dsb ish sequence, since the cache maintenance instructions cause all the cores to clean / invalidate as instructed; not just this one. See table D4-6. (But if the dc cvau is in a different thread than the writer, maybe the writer has to have completed a dsb ish beforehand, so that the written data really is in L1d and not still in the writer's store buffer? Not sure about that.)

The part that does matter is isb. After ci ivau is complete, the L1i caches are cleared of stale code, and further instruction fetches by any core will see the new code. However, the runner core might previously have fetched the old code from L1i, and still be holding it internally (decoded and in the pipeline, uop cache, speculative execution, etc). isb flushes these CPU-internal mechanisms, ensuring that all further instructions to be executed have actually been fetched from the L1i cache after it was invalidated.

Thus, the isb needs to be executed in the thread that is going to run the newly written code. And moreover you need to make sure that it is done after all the cache maintenance has fully completed; maybe by having the writer thread notify it via condition variable or the like.

I tested this too. If all the cache maintenance instructions, plus an isb, are done by the writer, but the runner doesn't isb, then once again it can execute the stale code. I was only able to reproduce this in a test where the writer patches an instruction in a loop that the runner is executing concurrently, which probably ensures that the runner had already fetched it. This is legal provided that the old and new instruction are, say, a branch and a nop respectively (see B2.2.5), which is what I did. (But it is not guaranteed to work for arbitrary old and new instructions.)

I tried some other tests to try to arrange it so that the instruction wasn't actually executed until it was patched, yet it was the target of a branch that should have been predicted taken, in hopes that this would get it prefetched; but I couldn't get the stale version to execute in that case.

One thing I wasn't quite sure about is this. A typical modern OS may well have W^X, where no virtual page can be simultaneously writable and executable. If after writing the code, you call the equivalent of mprotect to make the page executable, then most likely the OS is going to take care of all the cache maintenance and synchronization for you (but I guess it doesn't hurt to do it yourself too).

But another way to do it would be with an alias: you map the memory writable at one virtual address, and executable at another. The writer writes at the former address, and the runner jumps to the latter. In that case, I think you would simply dc cvau the writable address, and ic ivau the executable one, but I couldn't find confirmation of that. But I tested it, and it worked no matter which alias was passed to which cache maintenance instruction, while it failed if either instruction was omitted altogether. So it appears that the cache maintenance is done by physical address underneath.

It's called binomial coefficient, or "nCk" or "n Choose k".

The formula is

Here n is the size of the set, and k = 2 is the number of elements to select, so that e.g. sets {3, 6} and {6,3} taken are considered equal.

AFAIK, the standard notation in combinatorics is as shown above and spelled "n choose k", where as C(...) is non-standard requiring clarification when first introduced.

That's because every struct has fields, and hence this pattern will work for any struct, but will not compile with an enum:

The "trick" is here: