Yesterday’s challenge from Programming Praxis challenges us to rebuild a data structure near and dear to any Lisper’s/Schemer’s/Racketer’s1/functional programmer’s heart: lists. The idea presented in their sample solution uses two element vectors, directly mimicking the general internal structure of Scheme’s lists. How about we do something a bit stranger? 😄
On Monday we laid out a framework for converting structures into bytes. On Wednesday, we used that to enhance Racket’s UDP and DNS capabilities. Today, we’re going to take that all one step further and scan large portions of the Internet. The end goal will be to look for DNS-based on a worldwide scale.
As I mentioned on Monday, I wrote my DNS-based censorship around the world–and to do that, I need a fair bit of control over the DNS packets that I’m sending back and over parsing the ones that I get back.
Keen eyed observers may have noticed that last Friday when I posted about converting my various Racket libraries to Planet 2 packages, that there was a new package there I haven’t otherwise talked about: bit-struct. Today seems like a good time to talk about that. Theoretically, I’ll also have another post or two this week showing exactly what I’m doing with it (spoilers: it involves sending on the order of billions of DNS requests1).
Over the last few years, I’ve managed to write a fair bit of Racket code. It’s a lovely language and an even better ecosystem for writing quick/clean code (batteries included!
). Several times throughout that, I’ve written code that I thought could be useful to others, including several libraries that I used to write my Racket Roguelike and code that I’ve used working with the C211 class at Indiana University. I’ve always said that I should turn these into packages that others can use and… I’ve finally figured it out.
Another post from Programming Praxis, from this past Tuesday:
The smallest pair of consecutive natural numbers that each have two distinct prime factors are 14 = 2 * 7 and 15 = 3 * 5. The smallest triplet of consecutive natural numbers that each have three distinct prime factors are 644 = 2^2 * 7 * 23, 645 = 3 * 5 * 43 and 646 = 2 * 17 * 19. What is the smallest set of four consecutive natural numbers that each have four distinct prime factors?
Today we’re going to be talking about cryptography, specifically Diffie-Hellman key exchange1. The basic idea isn’t necessarily to communicate in secret, but rather to establish the information that makes doing so much easier.
I’m a bit behind the times, but this post from Programming Praxis intrigued me enough that I kept it in my todo list for rather a while. So let’s get around to it.
I’ll just copy the description straight from the Programming Praxis website (although there are at least two previous version:[1][2]):
There is a monkey which can walk around on a planar grid. The monkey can move one space at a time left, right, up or down. That is, from (x, y) the monkey can go to (x+1, y), (x-1, y), (x, y+1), and (x, y-1). Points where the sum of the digits of the absolute value of the x coordinate plus the sum of the digits of the absolute value of the y coordinate are lesser than or equal to 19 are accessible to the monkey. For example, the point (59, 79) is inaccessible because 5 + 9 + 7 + 9 = 30, which is greater than 19. Another example: the point (-5, -7) is accessible because abs(-5) + abs(-7) = 5 + 7 = 12, which is less than 19. How many points can the monkey access if it starts at (0, 0), including (0, 0) itself?
Something was bugging me about my proof from yesterday. If we take another tack on proving Turing completeness, all we would have to prove is that we can simulate SUBLEQ. Since SUBLEQ is Turing complete, that’s all we need–just convert each SUBLEQ into a SUB, JZ, and a JLS. So that means that Tiny as written should be Turing complete.
So how does that work?
Today’s challenge at /r/dailyprogrammer asks to implement an assembler for a small virtual machine. It has only 16 mnemonics which in unique opcodes (each instruction can have multiple forms for if they’re accessing memory or literals), so it’s a simple virtual machine indeed. As a challenge, you’re supposed to write an interesting program (I actually wrote a virtual machine as well to test them). As an even better challenge, we’re supposed to prove that Tiny is Turing complete. Well, let’s get to it!