Archive for the ‘ai’ Category

A tic-tac-toe implementation using haskell

March 30, 2008

After about half a year, I can finally say that I am comfortable using haskell as a language. Dealing with the functional part, the biggest stumbling block for me were the Data types, just because you cannot declare Data types in other languages as you do in haskell. In languages like Java or Python you can’t really really declare your own Data types. You can create classes, but that is different since they may not be just containers, they may change the outside world somehow. In haskell, a Data type is just that, a container, kind of like a slot for some value. That value may be restricted to a certain subset, or it may be a special kind of slot (for instance, a tree), but it cannot be executed to change some state outside of itself. The other thing that I haven’t seen before anywhere else is the use of higher-order functions, and mainly being able to pass a function as a parameter to another function. I have never seen this property in math either, but I’m sure it exists, I just haven’t taken such advanced courses yet. That leads me to my topic, which is an AI agent for a tic-tac-toe implementation that I made using haskell. It is available at hackage if anyone wants to try it out. I used two references when I was coding the project, Principles of Artificial Intelligence by Nils Nilsson, and the paper Why Functional Programming Matters by John Hughes. Both of these were excellent references, especially the paper. The program makes extensive use of higher-order functions and function composition. It uses minimax and alpha-beta pruning for its algorithm. Using these functions, I could test out certain functionalities one by one. What I used to do before in imperative languages was print statements, which would get very messy. Here I can just test the input of a function, and as long as it returns the desired output for all my tests, I don’t have to worry about that function at all. That lets me concentrate on one problem, without thinking about other functions introducing some errors. I also used maps and zips in a nice way. I first made a function that given a board, returns a list of all the possibilities of that board, calling it moves. After that, I made a recursive function reptree that in this case takes moves (a function!) as parameter, and a Tree with only one root, mainly the board that we wanted to pass into moves. The reptree function constructs another tree with the board as root, and since the children of the root is a list, it maps reptree moves over the list generated by moves called with the root board as parameter. Therefore, it becomes a recursive function that given a certain board as parameter, can generate a tree of all the possible possibilities ever to occur! OK, that however generates only the board moves, what I really want the actual values of the moves. Therefore I have a function getValue, that for a certain board, outputs a number and that’s all it does. How it actually generates this number is explained in the comments of the source code. All I do then is map the function getValue over the tree that I generated and I get as output a tree of the values. I can then just simply feed that output to maximise which would return to me the most advantageous value. One thing that the paper doesn’t mention and something I didn’t find anywhere is how to get the actual board, since you get a value from maximise but you can’t really do anything with it, all it tells you is the value of the best move, but the actual move is lost. Therefore, I just made a tree zipper that zips the two trees together and returns a tree of tuples consisting of the value and the actual board. We then feed the tuple to maximise, with it only looking at the first value, but actually returning a tuple of the value and the best move. That gives you a best move that the agent should make some time in the future however, considering both the player and the enemy play optimally. We need the best move right for the next move that we need to make, not the move a couple of plies down the line. It’s good thing that I provide a list of history that tells us what moves the board has already generated, so I just backtrack to one move after the current move and I have my best move for the next ply. My code is still not as pretty as I would like it to be, due to a couple of hacks I had to make, but it is a lot better than what I would have had to go through if I wrote this in an imperative language.