I want to make a Java program to help people with basic discrete mathematics (that is to say, checking the truth values of statements). To do this, I need to be able to detect how many variables the user inputs, what operators there are, and what quantifiers there are, if any (∃ and ∀). Is there a good algorithm for being able to do all these things?
Just so you know, I don't just want a result; I want full control over their input, so I can show them the logical proof. (so doing something like passing it to JavaScript won't work).
Okay, so, your question is a bit vague, but I think I understand what you'd like to do: an educational aid that processes first-order logic formulas, showing the user step by step how to work with such formulas, right? I think the idea has merit, and it's perfectly doable, even as a one-man project, but it's not terribly easily, and you'll have to learn a lot of new things -- but they're all very interesting things, so even if nothing at all comes out of it, you'd certainly get yourself some valuable knowledge.
I'd suggest you to start small. I'd start by building a recursive descent parser to recognize zero-order logic formulas (a machine that would decide if a formula is valid, i.e. it'd accept "A ^ B" but it'd reject "^ A ^"). Next up you'd have to devise a way to store the formula, and then you'd be able to actually work on it. Then again, start small: a little machine that accepts valid zero-order logic formulas like TRUE AND NOT (TRUE AND FALSE), and successfully reduces it step by step to true is already something that people can learn from, and it's not too hard to write. If you're feeling adventurous, add variables and make equations: A AND TRUE = TRUE -- it's easy to work these out with reductions and truth tables.
Things get tricky with quantifiers that bind variables, that's where the Automated theorem proving may come into play; but then, it all depends on exactly what you'd like to do: implementing transformations into the various normal forms, and showing the process step by step to the student would be fairly easy, and rather useful.
At any rate, I think it's a decent personal project, and you could learn a lot from it. If you're in a university, you could even get some credit for it eventually.
The technique I have used is to parse the input string using a context free grammar. There are many frameworks to help you do this, I have personally used ANTLR in the past to parse an input string into a descrete logic tree. ANTLR allows you to define a CFG which you can map to Java types. This allows you to map to a data structure to store and evaluate the truth value of the expression. Of course, you would also be able to pull out the variables contained in the data structure.
Related
Some information (don't want to confuse you with a lot of shitty code):
I've done a pretty large console programm (my largest project so far) which helps me a lot with managing some accounts / assets and more. I'm constantly adding more features but at the same time I reshape the code to work on my shitty coding style.
The console program has a lot of commands the user can type and for every command different methods get called / objects get created / manipulated and so on.
My keywords which are saved in an ArrayList<String> and my commands have this type: [keyword] [...n more Strings]
DESIGN PROBLEM 1:
I have a method cmdProcessor(String[] arguments) which handles the input (command) of the user, and the [keyword] is always the first argument arguments[0]. That means I have a large number of if-statements of this type:
if(arguments[0].equalsIgnoreCase("keyword") callMethod(argmts); where in the String[] argmts the remaining arguments[1] ... [n] are.
Is this a good way to handle this or should I go with switch-case?
Or something else (what?)? Is it better to save the keywords in a HashMap<String, Method>?
DESIGN PROBLEM 2:
The methods (see above callMethod(argmts) ), which are triggered by the entered keyword look even more chaotic. Since the same method can have different numbers and forms of arguments saved in the String[] argmts the method is full of if(argmts.length == ...) to check length, and every of these if-blocks has a bunch of switch-case options which also have a lot of ifs and so on. The last else and the default-case in switch-case I always use for error-handling (throwing error codes and and explanation why the pattern doesn't match and so on).
Is this good or are there better ways?
I thought about using lots of submethods, which would also blow up
my program and cost a lot of time but maybe improve readability / overview. Is this okay, or what is the best
option in such cases (lots of ifs and switch-case)?
Since I want to build more and more around this program maybe I should start now to fix bad design before it's too late. :)
About Design-Problem 1:
My go-to would be to register a lot of Handlers, which you can base on a common interface and then implement the specific behavior individually. This is good, because the central method handling your input is slim, and you only need to register a lot of singletons once, on initialization. Disadvantage: if you forget one, it will not work. So maybe, you can register them automatically (reflection or something thelike).
Aside from that, a map is better than a List in this case, because (I assume) you don't need a sorting. You need a mapping from key to behavior, so a map seems better (though even a very large set of keywords would probably not be very inefficient, if you stick to a list).
About Design Problem 2:
If I was you, I'd use actual Regular-Expression patterns. Take a look at the java.util.regex.Pattern-class. You can isolate groups and validate the values you receive. Though it does not spare you the exception/error-handling, it does help a lot in segmentation and interpretation efforts.
I just want to get some information before I go ask my teacher during his offices hours tomorrow.
We have have project to do thats something like an iclicker question answer collector. He told us to avoid using switch case statements. I was just wondering why and why don't people in the field like using them, what alternative is there to do? and I doubt he wants us to use if statements either.
I think we have to use polymorphism/interfaces but I just cant rap my head around that, switch cases seems so much straight forward.
Thank you.
Usually when an instructor asks "don't use feature X", it's because they want you to learn how to do something without using a feature that might be a shortcut. In your case, it sounds like your instructor wants you to wrap your head around polymorphism. If you don't, you won't learn that bit and will have much more trouble later in the class.
It depends upon the project. For example, in using a RESTful APi, you do have switch statements because there is a limit, known set. But, with your program there might be a lot of different options and that option can change, increase (or decrease), so while you started out with three cases, then something else is wanted, that's four, then five, and so on. You end up with 50 cases, and that's probably not good or easy to maintain.
With your OOP class, the instructor is probably going to show you that. Come back and show the whole problem and the final result, and maybe others can shed light.
There's an example that I've seen in my old Java book, and did a search and see it is still decent. Consider employees and salaries. You have three types of employees, then you have 50 types.
On a small scale, there appears to be not much difference. It requires enlarging the problem and considering consequences.
Ways to eliminate switch in code
That is a good example. Sure, there's only two cases in that example. But, again, what if it were 50? How easy will it be to maintain that? A lot of things in programming are about saving time and making things logical in the long run, as you will be coming back to your code or someone else's, and you have to maintain and support it.
I want to write a program to do this, based on Soot's build-in Reaching-Definition analysis. Now I'm wondering is this the correct approach? I searched and found nobody seems to ever be interested in this direction.
Any suggestions?
What you probably want to do is combine a set of ranges using an iterative data flow solver. You want to combine range-values from inputs into range-values for the set of definitions that cross basic blocks.
For this you generally need a control flow graph and the transfer functions across the basic blocks. I suppose you can treat the reaching-definitions graph in a similar way.
You'll then need interprocedural range propagation to push the ranges across the code.
This is a really generic problem you are stating. Reaching Definitions does not have much to do with this. Global Value Numbering is more what you apparently want but it's too hard to tell from your description. Try the Soot mailing list with a more detailed problem statement.
I now have an idea, that I use the function as a string, and I calculate the real integral by hand, and ask a question to the user what the definite integral is, but that isn't a real solution.
I was wondering if there was a way to input a function and output an integral/derivative (depending on user choice). My initial step was to put it into an array somehow, but given the many types of functions, this wasn't happening.
I researched everywhere, and I haven't found a method that actually does this with no additional code, nor any code that actually does this, period.
Also, I want to see if there was a way to make a GUI interface and plot inputted functions on to that, if that's possible too.
Thanks :)
What you're describing is known as symbolic integration. There's currently no fully general way to implement it, but there are some techniques available. One such is the Risch algorithm.
Alternatively, an easier problem than symbolic integration is [symbolic differentiation -- and, if the differential of the user's input is equivalent* to the expression which they were asked to integrate, then their integral is probably correct.
You may also want to consider using an existing CAS**, such as Mathematica, to implement this. They've already implemented most of the tools you're after.
*: Keep in mind, though, that two mathematical expressions may be equivalent without being identical, either in trivial ways (e.g, terms in a different order), more complex ones (e.g, large expressions factored differently), or fundamentally (e.g, trig functions replaced with complex exponentials or vice versa).
**: Computer algebra system
Javacalculus is what you are looking for.
Good luck!
Given the source code of a program, how do I analyze it and count the function points within it?
Thanks!
You might find this tutorial on FPA of interest. Personally, I don't put much stock in this estimation method. From my perspective it attempts to provide a precise estimate in for things that have been shown repeatedly to not be precisely measurable. I much prefer planning poker or something similar that tries to group things within a similar order of magnitude and provide an estimate based on your previous estimations for similarly sized stories.
If you're doing this for a class, simply follow the rules given in the text book and crank out the answer. If you're really intending to try this as a software development estimation method, my advice is to simplify the process rather than make it more complex. I would imagine that members of the International Function Point User Group (yes, there is one), will disagree.
With a code analysis tool. If you want to write one yourself, you might want to start with cglib or ASM.