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To make the same code work seamlessly on Node. There are 2 optional modules that can be installed along side with the ws module. These modules are binary addons which improve certain operations. The extension is disabled by default on the server and enabled by default on the client. It adds a significant overhead in terms of performance and memory consumption so we suggest to enable it only if it is really needed.
Note that Node. If you intend to use permessage-deflate in production, it is worthwhile to set up a test representative of your workload and ensure Node. Tuning of permessage-deflate can be done via the options defined below. See the docs for more options. The client will only use the extension if it is supported and enabled on the server.
To always disable the extension on the client set the perMessageDeflate option to false. For a full example with a browser client communicating with a ws server, see the examples folder. Sometimes the link between the server and the client can be interrupted in a way that keeps both the server and the client unaware of the broken state of the connection e.
In these cases ping messages can be used as a means to verify that the remote endpoint is still responsive. Just like the server example above your clients might as well lose connection without knowing it. You might want to add a ping listener on your clients to prevent that.
A simple implementation would be:. Use a custom http. Agent implementation like https-proxy-agent or socks-proxy-agent. Comments disabled. I figured out that context manager bug! This was so unexpected that I wondered if the real problem was nondeterministic and if some of the debugging messages had somehow perturbed it. But I removed everything but the context manager change and ran another test, which succeeded. By then I was five and half hours into the debugging and I didn't have any energy left to actually understand what the problem had been.
I still don't know. The problem re-manifested again today, and this time I was able to track it down and fix it. The context manager code I mentioned above was not the issue. That subprocess. Just before the process exits, Greenlight destroys the working tree.
This way, concurrent processes never try to use the same working tree, which would be a mess. Greenlight's main purpose is to track these submission objects, and it has a database of them. Someone would submit a branch, and Greenlight would pickle the submission. Then Greenlight would exit and, just before doing so, it would destroy its temporary working tree. Then later, when someone else wanted to approve the submission for publication, Greenlight would set up a different working tree with its new process ID, and unpickle the submission.
But the submission's git. The context manager was working just fine. Any new submission objects created by Greenlight would have the right path, so Git commands run by fresh submissions also worked properly. Greenlight doesn't always destroy the working tree when it exits. If it exits abnormally, it leaves the working tree intact, for a later autopsy. And the unpickled submission would work perfectly if the working tree still existed, and it would be impossible to reproduce the problem!
I suspect I'm being sabotaged somewhere by Python's weird implicit ideas of scope and variable duration, but I don't know. For the record, then: The issue was indeed one of variable duration. But Python's weird implicit ideas were, in this instance, completely blameless. Necklaces and bracelets There are combinatorial objects called necklaces and bracelets and I can never remember which is which.
Both are finite sequences of things typically symbols where the start point is not important. But which? I have to look it up every time. I have finally thought of a mnemonic. In a necklace, the direction is important, because to reverse an actual necklace you have to pull it off over the wearer's head, turn it over, and put it back on. But in a bracelet the direction is not important, because it could be on either wrist, and a bracelet on the left wrist is the same as the reversed bracelet on the right wrist.
Another day, another bug. It's a Git branch merging service that implements the following workflow:. Multiple instances of Greenlight share a local repository, but to avoid confusion each has its own working tree. When Greenlight needs to run a Git command, it does so like this:. This worked in testing every time. But the first time a beta tester ran the approve command, Greenlight threw a fatal exception. It was trying to run git checkout --quiet --detach , and this was failing, with Git saying.
But in the course of trying to track the problem down, I changed the code above to:. But this revealed a second bug: Greenlight no longer failed in the approval phase. It went ahead and merged the branch, and then tried to publish the merge with git push origin But the push was rejected. This is because the origin repository had an update hook that ran on every push, which performed the same review analysis that Greenlight was performing; one of Greenlight's main purposes is to be a replacement for this hook.
To avoid tying up the main repository for too long, this hook had a two-minute timeout, after which it would die and reject the push. This had only happened very rarely in the past, usually when someone was inadvertently trying to push a malformed branch. For example, they might have rebased all of master onto their topic branch. In this case, however, the branch really was legitimately enormous; it contained over commits. Modifying the hook was easy: I just added:.
This didn't work. So I chased that wild goose for a while. Eventually I determined that the key was in the right place, but that the name of the Greenlight identity on the receiving side was not greenlight but bot-greenlight , which I had forgotten. It looks like this:. But wait, why hadn't I noticed this before? Because, apparently, every single person who had alpha-tested Greenlight had had their own credentials stored in ssh-agent , and every single one had had agent-forwarding enabled, so that when Greenlight tried to use ssh to connect to the Git repository, SSH duly forwarded their credentials along and the pushes succeeded.
With these changes, the publication went through. I committed the changes to the SSH credential stuff, and some other unrelated changes, and I looked at what was left to see what had actually fixed the original bug. Every change but one was to add diagnostic messages and logging. The fix for the original bug had been to replace the nested context managers with a single context manager. If you'd like to play along at home, the context manager looks like this, and did not change during the debugging process:.
Rahul Narain referred me to a recent discussion of almost this exact question on Math Stackexchange. Note that the discussion there considers two figures different if they are reflections of one another; I consider them the same. I had said:. I think there are nine shapes but I might have missed one, because I know I kept making mistakes in the enumeration …. I had tried to break them down by the arrangement of the outside ring of edges, which can be described by a composition.
The first two of these have type!! Good call, Mr. On one level it was a mistake, but on a higher and more important level, I did better. Now connect them in a loop: each point should be connected to exactly two others, and each point should be reachable from the others.
How many geometrically distinct shapes can be formed? I phrased this like a geometry problem, but it should be clear it's actually a combinatorics problem. But it's much easier to express as a geometry problem; to talk about the combinatorics I have to ask you to consider a permutation!! But for!! I think there are nine shapes but I might have missed one, because I know I kept making mistakes in the enumeration, and I am not sure they are all corrected:.
It seems like it ought not to be hard to generate and count these, but so far I haven't gotten a good handle on it. I produced the!! But this is fraught with opportunities for mistakes in both directions. I would certainly not trust myself to hand-enumerate the!! Further details. There are no lattice points that are exactly the vertices of an equilateral triangle, but you can come close, and one way to do it is to find integers!!
So okay, we want to find!! The first thing I thought of was that the dot product!! Then I tried something else, using high-school trigonometry. After I got there I realized that my dot product idea had almost worked. To get rid of the troublesome!! Observe that the magnitude of!! Then if we divide, the!! Okay, that's fine. Now we need to find some integers!! So let's look under the next-closest lamppost, and let!! Actually we'll let!! Then, taking!! Each of these gives us a!!
For example, in line 3, we have take!! We still get!! Doing this gives us the two points!! The angle between!! This is exactly the same as in the approximately equilateral!! So the method is a success: I wanted simpler numbers or a better approximation, and I got the same approximation with simpler numbers.
There are some other items in the table for example row 18 gives!! And the chance of finding numbers better than!! So now let's see if we can get the angle closer to exactly!! The next convergents to!! I tried the same procedure for!!
So the points are!! This is as accurate as anyone drawing on graph paper could possibly need; on a circle with a one-mile radius it is an error of 20 inches. Of course, the triangles you get are no longer equilateral, not even close. That first one has sides of!! The slopes of the lines are so simple, it's easy to construct equilateral triangles with a straightedge and a bit of easy measuring.
Let's do it on the!! The straightedge should have slope!! The line won't necessarily intersect!! The point opposite to!! And the segment!! This triangle is geometrically similar to a triangle with vertices at!! I love the dodecahedron I think I forgot to mention that I was looking recently at hamiltonian cycles on a dodecahedron. The dodecahedron has 30 edges and 20 vertices, so a hamiltonian path contains 20 edges and omits It turns out that it is possible to color the edges of the dodecahedron in three colors so that:.
In this presentation, I have taken one of the vertices and sent it away to infinity. The three edges with arrowheads are all attached to that vertex, off at infinity, and the three faces incident to it have been stretched out to cover the rest of the plane.
Every face has five edges and there are only three colors, so the colors can't be distributed evenly around a face. Each face is surrounded by two edges of one color, two of a second color, and only one of the last color. This naturally divides the 12 faces into three classes, depending on which color is assigned to only one edge of that face.
Each class contains two pairs of two adjacent pentagons, and each adjacent pair is adjacent to the four pairs in the other classes but not to the other pair in its own class. Each pair has 8 vertices, of which two are on its hinge, four are adjacent to the hinge, and two are not near of the hinge. These last two vertices are always part of the hinges of the pairs of a different class. I could think about this for a long time, and probably will.
There is plenty more to be seen, but I think there is something else I was supposed to be doing today, let me think…. Oh yes! So I will leave you to go on from here on your own. Then you erect spikes onto the other four of the octahedron's faces. Now you have a stella octangula. So yeah, both. It's both at once. Counting paths through polyhedra A while back someone asked on math stack exchange how many paths there were of length!!
The vertices are distance 5 apart, so for!! This is the kind of thing that the computer answers easily, so that's where I started, and unfortunately that's also where I finished, saying:. I'm still working out a combinatorial method of calculating the answer, and I may not be successful. Another user reminded me of this and I took another whack at it. I couldn't remember what my idea had been last year, but my idea this time around was to think of the dodecahedron as the Cayley graph for a group, and then the paths are expressions that multiply out to a particular group element.
I started by looking at a tetrahedron instead of at a dodecahedron, to see how it would work out. Here's a tetrahedron. Let's say we're counting paths from the center vertex to one of the others, say the one at the top. Tetrahedra don't have opposite vertices, but that's not an important part of the problem. A path is just a list of edges, and each edge is labeled with a letter!! Since each vertex has exactly one edge with each label, every sequence of!!
Which of these paths end at the bottom vertex? The edge labeling I chose here lets us play a wonderful trick. First, since any edge has the same label at both ends, the path!! So if we have a path that ends where we want, we can insert any number of pairs!! But there's an even better trick available. For any starting point, and any letters!! For example, if we start at the middle and follow edge!!
Now suppose we want to find all the paths of length 7 from the middle to the top. Such a path is a sequence of a's, b's, and c's of length 7. Every such sequence specifies a different path out of the middle vertex, but how can we recognize which sequences end at the top vertex?
A complicated-seeming path like abacbcb must go to the same place as!! And since!! Since the paths we want are those that go to the same place as the trivial path!! Any path fitting that description will go to same place as!! It's easy to enumerate such paths:. If we wanted to consider paths of arbitrary length, we could use Burnside's lemma , but I consider the tetrahedron to have been sufficiently well solved by the observations above we counted paths by hand in under 60 seconds and I don't want to belabor the point.
Here we'll consider paths between two antipodal vertices in the upper right and the lower left, which I've colored much darker gray than the other six vertices. The same magic happens as in the tetrahedron. No matter where we start, and no matter what!! So again, if some complicated path gets us where we want to go, we can permute its components into any order and get a different path of the same langth to the same place.
For example, starting from the upper left, bcba , abcb , and abbc all go to the same place. And again, because!! So the three paths in the previous paragraph also go to the same place as ac and ca and also aa bcba bb aa aa aa aa bb cc cc cc bb. We want to count paths from one dark vertex to the other.
Obviously abc is one such, and so too must be bac , cba , acb , and so forth. There are six paths of length 3. To get paths of length 5, we must insert a pair of matching letters into one of the paths of length 3.
Without loss of generality we can assume that we are inserting aa. There are 20 possible orders for aaabc , and three choices about which pair to insert, for a total of 60 paths. To get paths of length 7, we must insert two pairs. If the two pairs are the same, there are!! If the two pairs are different, there are!! Counting the paths of length 9 is almost as easy.
For the general case, again we could use Burnside's lemma, or at this point we could look up the unusual sequence!! So far this technique has worked undeservedly well. The original problem wanted to use it to study paths on a dodecahedron. Where, unfortunately, the magic property!! It is possible to label the edges of the dodecahedron so that every sequence of labels determines a unique path:. Well, nothing exactly like it. I'm not sure that helps.
I will probably need another idea. On an octahedron we need to use four kinds of labels because each vertex has four edges emerging from it:. Here again we don't have!! So it's possible that if I figure out a good way to enumerate paths on the octahedron I may be able to adapt the technique to the dodecahedron. But the octahedron will be!! Viewed as groups, by the way, these path groups are all examples of Coxeter groups. I'm not sure this is actually a useful observation, but I've been wanting to learn about Coxeter groups for a long time and this might be a good enough excuse.
A puzzle about representing numbers as a sum of 3-smooth numbers I think this would be fun for a suitably-minded bright kid of maybe 12—15 years old. Given a number!! For example, one may not represent!! Or, put another way: can we represent any number!! Sadly, the representation is not unique. For example,!! I'm doing more work on matrix functions. A matrix represents a relation, and I am representing a matrix as a [[Integer]]. Except no, that's not right, and this is not a complaint, it's certainly my mistake.
The overloading for liftA2 for lists does not do what I want, which is to apply the operation to each pair of correponding elements. Instead liftA2 lifts an operation to apply to each possible pair of elements, producing [11,21,31,12,22,32,13,23,33]. And the twice-lifted version is similarly not what I want:. No problem, this is what ZipList is for. ZipLists are just regular lists that have a label on them that advises liftA2 to lift an operation to the element-by-element version I want instead of the each-one-by-every-other-one version that is the default.
For instance. The getZipList function turns a ZipList back into a regular list. But my matrices are nested lists, so I need to apply the ZipList marker twice, once to the outer list, and once to each of the inner lists, because I want the element-by-element behavior at both levels.
That's easy enough:. But the matrix and unmatrix pair bugs me a little. This business of changing labels at both levels has happened twice already and I am likely to need it again. So I will turn the two functions into a single higher-order function by abstracting over ZipList. This turns this. The first sign that something is going wrong is that twice does not have the type I wanted.
It is:. Telling GHC explicitly what type I want for twice doesn't work either, so I decide it's time to go to lunch. So now, instead of defining matrix operations, I am looking into the type unification algorithm and trying to figure out why twice doesn't work. And that is yet another reason why I never finish my Haskell programs. We can enumerate the vertices arbitrarily but a convenient way to do it is to assign them the numbers 0 through 7 and then say that vertices!! Ha ha, no it isn't; in Haskell nothing is straightforward.
This produces lines of type whining, followed by a failed compilation. Apparently this is because because 0 and 7 are overloaded, and could mean some weird values in some freakish instance of Num , and then To fix this I have to say explicitly what I mean by 0. I think there must be something really wrong with the language design here. I don't know exactly what it is, but I think someone must have made the wrong tradeoff at some point.
How not to reconfigure your sshd Yesterday I wanted to reconfigure the sshd on a remote machine. Although I'd never done sshd itself, I've done this kind of thing a zillion times before. But this doesn't change the running server; you have to notify the server that it should reread the file. One way would be by killing the server and starting a new one.
This would interrupt service, so instead you can send the server a different signal in this case SIGHUP that tells it to reload its configuration without exiting. Simple enough. It started a shell. Okay, I've never used Match or ForceCommand before, maybe I don't understand how they work, I'll try something simpler.
I added:. Okay, maybe the sshd is not getting the signal, or something? I hunted up the logs, but there was a report like what I expected:. This was a head-scratcher. Was I modifying the wrong file? It semed hardly possible, but I don't administer this machine so who knows? I tried lsof -p to see if maybe sshd had some other config file open, but it doesn't keep the file open after it reads it, so that was no help.
Eventually I hit upon the answer, and I wish I had some useful piece of advice here for my future self about how to figure this out. But I don't because the answer just struck me all of a sudden. It's nice when that happens, but I feel a bit cheated afterward: I solved the problem this time, but I didn't learn anything, so how does it help me for next time? I put in the toil, but I didn't get the full payoff. Normally when you make an ssh connection to a remote machine, it calls up the server, exchanges credentials, each side authenticates the the other, and they negotiate an encryption key.
Then the server forks, the child starts up a login shell and mediates between the shell and the network, encrypting in one direction and decrypting in the other. All that negotiation and authentication takes time. The handshaking process still occurs as usual for the first connection. But once the connection succeeds, there's no need to start all over again to make a second connection. You can tell ssh to multiplex several virtual connections over its one real connection.
To make a new virtual connection, you run ssh in the same way, but instead of contacting the remote server as before, it contacts the local ssh client that's already running and requests a new virtual connection. The client, already connected to the remote server, tells the server to allocate a new virtual connection and to start up a new shell session for it. The server doesn't even have to fork; it just has to allocate another pseudo-tty and run a shell in it.
This is a lot faster. I had my local ssh client configured to use a virtual connection if that was possible. So my subsequent ssh commands weren't going through the reconfigured parent server. They were all going through the child server that had been forked hours before when I started my first connection.
It wasn't affected by reconfiguration of the parent server, from which it was now separate. I verified this by telling ssh to make a new connection without trying to reuse the existing virtual connection:. It occurs to me now that I could have tried to SIGHUP the child server process that my connections were going through, and that would probably have reconfigured any future virtual connections through that process, but I didn't think of it at the time.
Then I went home for the day, feeling pretty darn clever, right up until I discovered, partway through writing this article, that I can't log in because all I get is I like pie! Another trivial utility: git-q One of my favorite programs is a super simple Git utility called git-vee that I just love, and I use fifty times a day. It displays a very simple graph that shows where two branches diverged. For example, my push of master was refused because it was not a fast-forward.
So I used git-vee to investigate, and saw:. The command is called get-vee because the graph is usually V-shaped, and I want to find out where the point of the V is and what is on its two arms. From this V, it appears that what happened was: I pushed fa2ae34 , then amended it to produce a71 , but I have not yet force-pushed the amendment.
I should simply do the force-push now…. Except wait, what if that's not what happened? What if what happened was, a71 was the original commit, and I pushed it, then fetched it on a different machine, amended it to produce fa2ae34 , and force-pushed that? If so, then force-pushing a71 now would overwrite the amendments.
How can I tell what I should do? Formerly I would have used diff and studied the differences, but now I have an easier way to find the answer. I run:. Aha, it was as I originally thought: a71 is five minutes newer. The force-push is the right thing to do this time. Although the commit date is the default output, the git-q command can produce any of the information known to git-log , using the usual escape sequences. The program is in my personal git-util repository but it's totally simple and should be easy to customize the way you want:.
A long story about many bugs Warning : Long and possibly dull. I spent a big chunk of today fixing a bug that should have been easy but that just went deeper and deeper. Unless you're using a small display, where the whole sidebar is suppressed. That menu was at least a year out of date. I wanted to fix it. The blog software I use is the wonderfully terrible Blosxom.
It has a plugin system, and the topic menu was generated by a plugin that I wrote some time ago. When the topic plugin starts up it opens two Berkeley DB files. Each is a simple key-value mapping. One maps topic names to article counts.
The other is just a set of article IDs for the articles that have already been counted. These key-value mappings are exposed in Perl as hash variables. When I regenerate the static site, the topic plugin has a subroutine, story , that is called for each article in each generated page. The business end of the subroutine looks something like this:. The reason the menu wasn't being updated is that at some point in the past, I changed the way story plugins were called.
Out of the box, Blosxom passes story a list of five arguments, like this:. Over the years I had extended this to eight or nine, and I felt it was getting unwieldy, so at some point I changed it to pass a hash, like this:. When I made this conversion, I had to convert all the plugins. I missed converting topic. So instead of getting the eight or nine arguments it expected, it got two: the plugin itself, and the hash.
Then it used the hash as the key into the databases, which by now were full of thousands of entries for things like HASH 0xc1d because that is what Perl silently and uselessly does if you try to use a hash as if it were a string.
Anyway, this was easily fixed, or should have been easily fixed. All I needed to do was convert the plugin to use the new calling convention. Then whenever the plugin has something to announce it just does print F. For example, when the plugin increments the count for a topic, it inserts a message like this:.
When I'm debugging a plugin, I can open an Emacs buffer on this file and put it in auto-revert mode so that Emacs always displays the current contents of the file. Blosxom has an option to generate pages on demand for a web browser, and I use this for testing. I should have seen it inserting a lot of HASH 0xc1d garbage:. I didn't see this. I saw the startup message and nothing else. I did a bunch of very typical debugging, such as having the plugin print a message every time story was called:.
But I knew that story was being called. Was I maybe editing the wrong file on disk? No, because I could introduce a syntax error and the browser would happily report the resulting Server Error. Fortunately, somewhere along the way I changed. But why was the plugin being run twice?
This took quite a while to track down. At first I suspected that Blosxom was doing it, either on purpose or by accident. My instance of Blosxom is a hideous Frankenstein monster that has been cut up and reassembled and hacked and patched dozens of times since and it is full of unpleasant surprises. But the problem turned out to be quite different. Looking at the Apache server logs I saw that the browser was actually making two requests, not one:.
Since the second request was for a nonexistent article, the story callback wasn't invoked in the second run. So I would see the startup message, but I didn't see any messages from the story callback. They had been there in the first run for the first request, but that output was immediately overwritten on the second request. This expansion is done by a different plugin, called path2 , and apparently in this case it wasn't being expanded.
The place it was being used was easy enough to find; it looked like this:. This took a very long time to track down, and I think it was totally not my fault. When I first wrote path2 I just had it do a straight text substitution. This would parse the article body and return a tree of HTML::Element objects, which the plugin would then filter, looking for img and a elements.
The plugin would look for the magic tags and replace them with the right URLs. This magic tag was not in an img or an a element, so the plugin wasn't finding it. I needed to tell the plugin to look in source elements also. Easy fix! Except it didn't work. It took a long time because I'm good at debugging. The downside of this is that when the wallet is in an unlikely place it takes a really long time to find it.
The end result this time was that it wasn't in any of the usual places. For some reason it completely ignores source elements:. No trace of the source element. I reported the bug, commented out the source element in the article, and moved on. The article was unpublished, in part because I could never get the video to play properly in the browser. I had been tearing my hair about over it, but now I knew why!
Because of a bug in the HTML parser! With that fixed I went back to finish the work on the topic plugin. I did, and I fixed that. Then I expected the 'article' is article 17 in topic prog lines to go away. But no, every article on the page, every article from , was being processed every time I rebuilt the page. And the topic counts were going up, up, up.
This also took a long time to track down, because again the cause was so unlikely. I must have been desperate because I finally found it by doing something like this:. Yep, it died. Both of them are ancient, and this kind of shocking bug should have been shaken out 20 years go. WTF, indeed,. I fixed this by discarding the entire database and rebuilding it.
I needed to clean out the HASH 0xc1d crap anyway. I am sick of DB files. I am never using them again. I have been bitten too many times. From now on I am doing the smart thing, by which I mean the dumb thing, the worse-is-better thing: I will read a plain text file into memory, modify it, and write out the modified version whem I am done. It will be simple to debug the code and simple to modify the database.
Well, that sucked. It has a list of valid HTML4 tags and by default it ignores any element that isn't one. The maintainer won't change the default to HTML5 because that might break backward compatibility for people who are depending on this behavior. More about auto-generated switch-cases Yesterday I described what I thought was a cool hack I had seen in rsync , to try several possible methods and then remember which one worked so as to skip the others on future attempts.
This was abetted by a different hack, for automatically generating the case labels for the switch , which I thought was less cool. Simon Tatham wrote to me with a technique for compile-time generation of case labels that I liked better. Recall that the context is:. The case labels are no longer consecutive, but that doesn't matter; all that is needed is for them to be distinct.
Nobody is ever going to see them except the compiler. But it was new to me. One possible drawback of this method is that if the file contains more than lines, the case labels will not fit in a single byte. The ultimate effect of this depends on how the compiler handles switch.
It might be compiled into a jump table with!! Or it might be compiled to an if-else tree, or something else we don't want. Still, it seems like a reasonable bet. You could use case 0: at the beginning instead of default: , but that's not as much fun. Tatham observes that it's one of very few situations in which it makes sense not to put default: last. He says this is the only other one he knows:.
Addendum Several people have asked for an explanation of why the default is in the middle of the last switch. It follows the pattern of a very well-known mnemonic poem that goes. A fun optimization trick from rsync I was looking at the rsync source code today and I saw a neat trick I'd never seen before. It wants to try to set the mtime on a file, and there are several methods that might work, but it doesn't know which.
So it tries them in sequence, and then it remembers which one worked and uses that method on subsequent calls:. The first time the function is called, its value is 0 and the switch starts at case 0. The actual code is a little more sophisticated than this. The list of cases is built depending on the setting of several compile-time config flags, so that the code that is compiled only includes the methods that are actually callable.
Calling one of the methods can produce three distinguishable results: success, real failure because of permission problems or some such , or a sort of fake failure ENOSYS that only means that the underlying syscall is unimplemented. This third type of result is the one where it makes sense to try another method. So the cases actually look like this:. On top of this there's another trick: since the various cases are conditionally compiled depending on the config flags, we don't know ahead of time which ones will be included.
So the case labels themselves are generated at compile time this way:. Unfortunately you can only use this trick one switch per file. A snide addendum about implicit typeclass instances In an earlier article I demanded:.
Maybe someone can explain to me why this is a useful behavior, and then explain why it is so useful that it should happen automatically …. That doesn't happen in the second example. Yeah, yeah, I know that. Hey, you know what else is a functor? The identity functor. I understand this is a terrible idea. To be clear, what I want is for it to collapse on the divan for both expressions. Pearl-clutching is Haskell's finest feature and greatest strength, and it should do it whenever possible.
Hangman's Wages A few years back I asked on history stackexchange :. Wikipedia's article on the Halifax Gibbet says, with several citations:. I've met this guy and probably you have too: he knows everything worth knowing, and therefore what he doesn't know must be completely beyond the reach of mortal ken. But that doesn't mean he will shrug and leave it at that, oh no. Having said nobody could possibly know, he will nevertheless ramble for six or seven decreasingly relevant paragraphs, as he did here.
According to William Hone, it has a Scottish origin , being two-thirds of the Scottish pound, as the mark was two-thirds of the English pound. The same value was proposed as coinage for South Carolina in This answer makes me happy in several ways, most of them positive. And I'm glad to be introduced to the bizarre world of pre-union Scottish currency, which, in addition to the loonslate , includes the bawbee , the unicorn , the hardhead , the bodle , and the plack.
My pleasure has a bit of evil spice in it too. Brick's slam-dunk put it right where it deserved. I'm still not completely satisfied. Or would it? I may dig into this some more. I may not find out what I want to know, but I will probably find out something.
In some type classes, you get a choice about what to define, and then the rest of the functions are built from the ones you provided. But both of these problems can be worked around. If I have a Monad instance, it seems to work just fine if I say:. I suppose these might faul foul of whatever problem is being described in the documents I linked above.
But I'll either find out, or I won't, and either way is a good outcome. Applicative WTF? While I was writing up last week's long article about Traversable , I wrote this stuff about Applicative also. This is a disorganized collection of loosely-related paragraphs on that topic. I need some function for making Tree s that isn't too simple or too complicated, and I went with:.
Now I wanted to traverse h [1,2,3] but I couldn't do that because I didn't have an Applicative instance for Tree. I had been putting off dealing with this, but since Traversable doesn't really make sense without Applicative I thought the day of reckoning would come. Here it was. Now is when I learn how to fix all my broken monads. What the hell does that mean? Well, I can kinda make sense of it. If I apply one function to a tree of inputs, that's straightforward, it's just fmap , and I get a tree of results.
Suppose I have a tree of functions, and I replace the function at each leaf with the tree of its function's results. Then I have a tree of trees. But a tree that has trees at its leaves is just a tree. So I could write some tree-flattening function that builds the tree of trees, then flattens out the type. In fact this is just join that I already know from Monad world. The corresponding operation for lists takes a list of lists and flattens them into a single list.
Flattening a tree is quite easy to do:. Haskell makes this a pain. It should be able to infer the Applicative from this, and I wasn't clever enough to do it myself. This gets back to my original complaint: Haskell now wants every Monad instance to be an instance of Applicative , but if I give it the fmap and the join and the return it ought to be able to figure out the Applicative instance itself instead of refusing to compile my program. Okay, fine, whatever.
Haskell's gonna Hask. I sought one but did not find any. One can eliminate the do notation to obtain the expression:. I was not able to do this, and the automatic pointfree converter produced. When the tree of functions is Con f it's a single function and we can just use fmap to map it over the input tree:.
Once this is written it seemed a little embarrassing that it took me so long to figure out what it meant but this kind of thing always seems easier from the far side of the fence. It's hard to understand until you understand it. Say we have a tree of functions and a tree of arguments. The code I showed earlier does the second of those. You can see it from the fmap f tv expression, which takes a single function and maps it over a whole tree of values. I had actually wanted the other one, but there isn't anything quite like fmap for that.
I was busy trying to understand Applicative and I was afraid if I got distracted trying to invent a reverse fmap I might lose the thread. This happens to me a lot with Haskell. I did eventually go back and figure it out. The reverse fmap is. Now there's a simple answer to this which occurs to me now that I didn't think of before, but I'm going to proceed with how I planned to do it before, with pamf. This is an interesting example: usually the base case is trivial and the recursive clause is harder to write, but this time it's the base case that's not perfectly straightforward.
Anyway, this worked, but there was an easier solution at hand. The difference between the first version and the second is exactly the same as the difference between. Digging deeper into why this worked this way was interesting, but it's bed time, so I'm going to cut the scroll here. I struggle to understand Traversable Haskell evolved a lot since the last time I seriously wrote any Haskell code, so much so that all my old programs broke.
My Monad instances don't compile any more because I'm no longer allowed to have a monad which isn't also an instance of Applicative. Last time I used Haskell, Applicative wasn't even a thing. I had read the McBride and Paterson paper that introduced applicative functors, but that was years ago, and I didn't remember any of the details.
In fact, while writing this article, I realized that the paper I read was a preprint, and I probably read it before it was published, in It was a very annoying experience. Anyway I got that more or less under control maybe I'll publish a writeup of that later and moved on to Traversable which, I hadn't realized before, was also introduced in that same paper. In the prepublication version, Traversable was been given the unmemorable name IFunctor.
I had casually looked into this several times in the last few years but I never found anything enlightening. A Traversable is a functor which must also implement Foldable , but let's pass over that for now, no pun intended that implements a traverse method with the following signature:. The traversable functor itself here is t. The f thing is an appurtenance. The first thing to try here is to make it less abstract. I was thinking about Traversable this time because I thought I might want it for a certain type of tree structure I was working with.
So I defined an even simpler tree structure:. Defining a bunch of other cases wouldn't add anything to my understanding, and it would make it take longer to try stuff, so I really want to use the simplest possible example here. And this is it: one base case, one recursive case. Then I tried to make this type it into a Traversable instance. First we need it to be a Functor , which is totally straightforward:. Then we need it to be a Foldable , which means it needs to provide a version of foldr.
The old-fashioned foldr was. The idea is that foldr fn collapses a list of a s into a single b value by feeding in the a s one at a time. Each time, foldr takes the previous b and the current a and constructs a new b. The second argument is the initial value of b. Another way to think about it is that every list has the form. The Con clause says to take the constant value and combine it with the default total. The Add clause says to first fold up the left-side subtree x to a single value, then use that as the initial value for folding up the right-side subtree y , so everything gets all folded up together.
We could of course do the right subtree before the left; the results would be different but just as good. We can only use it recursively via foldr. It turns out it is easier and more straightforward to write foldMap instead, but I didn't know that at the time. I won't go into it further because I have already digressed enough. The preliminaries are done, we can finally get on to the thing I wanted, the Traversable :. What is this supposed to actually do? For our Tree functor it has this signature:.
The answer is that the secret sauce is in the Applicative , but I didn't understand that yet. I scratched my head and read a bunch of different explanations and none of them helped. All the descriptions I found were in either prose or mathematics and I still couldn't figure out what it was for. Finally I just wrote a bunch of examples and at last the light came on.
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