The Universe of Discourse

Haskell type checker complaint 184 of 698

I want to build an adjacency matrix for the vertices of a cube; this is a matrix that has m[a][b] = 1 exactly when vertices a and b share an edge. 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 !!a!! and !!b!! are adjacent if, regarded as binary numerals, they differ in exactly one bit, so:

   import Data.Bits
   a `adj` b = if (elem (xor a b) [1, 2, 4]) then 1 else 0         

This compiles and GHC infers the type

   adj :: (Bits a, Num a, Num t) => a -> a -> t 

Fine.

Now I want to build the adjacency matrix, which is completely straightforward:

    cube = [ [a `adj` b | b <- [0 .. 7] ] | a <- [0 .. 7] ]  where
      a `adj` b = if (elem (xor a b) [1, 2, 4]) then 1 else 0

Ha ha, no it isn't; in Haskell nothing is straightforward. This produces 106 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 0 .. 7 might generate an infinite list of 1-graded torsion rings or something.

To fix this I have to say explicitly what I mean by 0. “Oh, yeah, by the way, that there zero is intended to denote the integer zero, and not the 1-graded torsion ring with no elements.”

        cube = [ [a `adj` b | b <- [0 :: Integer .. 7] ] | a <- [0 .. 7] ]  where
          a `adj` b = if (elem (xor a b) [1, 2, 4]) then 1 else 0

Here's another way I could accomplish this:

        zero_i_really_mean_it = 0 :: Integer
        cube = [ [a `adj` b | b <- [zero_i_really_mean_it .. 7] ] | a <- [0 .. 7] ] where       
          a `adj` b = if (elem (xor a b) [1, 2, 4]) then 1 else 0

Or how about this?

        cube = [ [a `adj` b | b <- numbers_dammit [0 .. 7] ] | a <- [0 .. 7] ] where
          p `adj` q = if (elem (xor p q) [1, 2, 4]) then 1 else 0
          numbers_dammit = id :: [Integer] -> [Integer] 

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.

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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. It looks like this: there is a configuration file (in this case /etc/ssh/sshd-config) that you modify. 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.

Except, it didn't work. I added:

 Match User mjd
   ForceCommand echo "I like pie!"

and signalled the server, then made a new connection to see if it would print I like pie! instead of starting a shell. 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:

    PrintMotd yes

which seemed straightforward enough, and I put some text into /etc/motd, but when I connected it didn't print the motd.

I tried a couple of other things but none of them seemed to work.

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:

   sshd[1210]: Received SIGHUP; restarting.

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 1210 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.)

“Aha,” I said. “I bet it's because my connection is multiplexed.”

Normally when you make an ssh connection to a remote machine, it calls up the server, exchanges credentials, each side authenticates 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.

There is a “multiplexing” option you can use instead. 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:

   ssh -o ControlPath=none -o ControlMaster=no ...

This time I saw the MOTD and when I reinstated that Match command I got I like pie! instead of a shell.

(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! instead of a shell.

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