CAS Mode in Nspire Lua? - lua

I have another question here: Inspired Lua Program is Different on Computer and Calculator which answers this question. My attempt to mark as duplicate aged away.
I am writing a program for the Nspire CX CAS. I have a d2Editor mathbox that I would like to evaluate an expression I am giving it without using decimals. I would like it to simplify square roots and/or reduce fractions. How can this be accomplished?
I've spent around an hour looking through the wiki.
Thanks for any help you can offer.

Actually, no. I don't know if this is new but math.eval(expr) will evaluate expr as if you were running it from the tab calculator (Although still, if you have CAS disabled on your calculator, it will not be able to do use it)
math.eval('123+321=444') -> 'True'

Unless TI added new features recently, the answer is unfortunately that you will need to write it from scratch.
In a Lua program you do not have access to the representation that are used internally (say in a Notes workshop) to represent mathematical expressions.
You are handed, sigh, a string.
That means you will need to write your own parser for mathematical expressions in order to get a reasonable representation. Then you will need to write your own functions for manipulating and reducing expressions.
... no I am not kidding ...

Related

Performance issues with z3py using modulo and optimization

I'm experimenting with Z3 (using the python api) where I'm building up a scheduling model for a class assignment, where I have to use modulo quite often (because its periodic). Modulo seems already to slow down z3 by a lot, but if I try do some optimization on top (minimize a cost function which is a sum), then it takes quite some time for fairly small problems.
Without optimization it works okayish (few seconds for a smaller problem). So that being said, I have now 2 questions:
1) Is there any trick with the modulo function of how to use it? I already assign the modulo value to a function. Or is there any other way to express periodic/ring behavior?
2) I am not interested in finding THE best solution. A good one, will be good enough. Is there a way to set some bounds for the cost function. Like, if know the upper and lower bound of it? Any other tricks, where I could use domain knowledge to find solutions fast.
Furthermore, I thought that if I ll use timeout option solver.set("timeout" 10000), then the solver would time out with the best solution so far. That doesnt seem to be the case. It just times out.
Impossible to comment on the mod function without seeing some code. But as a rule of thumb, division is difficult. Are you using Int values, or bit-vectors? If you are using unbounded integers, you might want to try bit-vectors which might benefit from better internal heuristics. Or try Real values, and then do a proper reduction.
Regarding how to get the "best so far" optimal value, see this answer: Finding suboptimal solution (best solution so far) with Z3 command line tool and timeout
Instead of using the built-in modulo and division, you could introduce uninterpreted functions mymod and mydiv, for which you only provide the necessary axioms of division and modulo that your problem requires. If I remember correctly, Microsoft's Ironclad and/or Ironfleet team did that when they had modulo/division-related performance problems (using the pipeline Dafny -> Boogie -> Z3).

Good practice to parse data in a custom format

I'm writing a program that takes in input a straight play in a custom format and then performs some analysis on it (like number of lines and words for each character). It's just for fun, and a pretext for learning cool stuff.
The first step in that process is writing a parser for that format. It goes :
####Play
###Act I
##Scene 1
CHARACTER 1. Line 1, he's saying some stuff.
#Comment, stage direction
CHARACTER 2, doing some stuff. Line 2, she's saying some stuff too.
It's quite a simple format. I read extensively about basic parser stuff like CFG, so I am now ready to get some work done.
I have written my grammar in EBNF and started playing with flex/bison but it raises some questions :
Is flex/bison too much for such a simple parser ? Should I just write it myself as described here : Is there an alternative for flex/bison that is usable on 8-bit embedded systems? ?
What is good practice regarding the respective tasks of the tokenizer and the parser itself ? There is never a single solution, and for such a simple language they often overlap. This is especially true for flex/bison, where flex can perform some intense stuff with regex matching. For example, should "#" be a token ? Should "####" be a token too ? Should I create types that carry semantic information so I can directly identify for example a character ? Or should I just process it with flex the simplest way then let the grammar defined in bison decide what is what ?
With flex/bison, does it makes sense to perform the analysis while parsing or is it more elegant to parse first, then operate on the file again with some other tool ?
This got me really confused. I am looking for an elegant, perhaps simple solution. Any guideline ?
By the way, about the programing language, I don't care much. For now I am using C because of flex/bison but feel free to advise me on anything more practical as long as it is a widely used language.
It's very difficult to answer those questions without knowing what your parsing expectations are. That is, an example of a few lines of text does not provide a clear understanding of what the intended parse is; what the lexical and syntactic units are; what relationships you would like to extract; and so on.
However, a rough guess might be that you intend to produce a nested parse, where ##{i} indicates the nesting level (inversely), with i≥1, since a single # is not structural. That violates one principle of language design ("don't make the user count things which the computer could count more accurately"), which might suggest a structure more like:
#play {
#act {
#scene {
#location: Elsinore. A platform before the castle.
#direction: FRANCISCO at his post. Enter to him BERNARDO
BERNARDO: Who's there?
FRANCISCO: Nay, answer me: stand, and unfold yourself.
BERNARDO: Long live the king!
FRANCISCO: Bernardo?
or even something XML-like. But that would be a different language :)
The problem with parsing either of these with a classic scanner/parser combination is that the lexical structure is inconsistent; the first token on a line is special, but most of the file consists of unparsed text. That will almost inevitably lead to spreading syntactic information between the scanner and the parser, because the scanner needs to know the syntactic context in order to decide whether or not it is scanning raw text.
You might be able to avoid that issue. For example, you might require that a continuation line start with whitespace, so that every line not otherwise marked with #'s starts with the name of a character. That would be more reliable than recognizing a dialogue line just because it starts with the name of a character and a period, since it is quite possible for a character's name to be used in dialogue, even at the end of a sentence (which consequently might be the first word in a continuation line.)
If you do intend for dialogue lines to be distinguished by the fact that they start with a character name and some punctuation then you will definitely have to give the scanner access to the character list (as a sort of symbol table), which is a well-known but not particularly respected hack.
Consider the above a reflection about your second question ("What are the roles of the scanner and the parser?"), which does not qualify as an answer but hopefully is at least food for thought. As to your other questions, and recognizing that all of this is opinionated:
Is flex/bison too much for such a simple parser ? Should I just write it myself...
The fact that flex and bison are (potentially) more powerful than necessary to parse a particular language is a red herring. C is more powerful than necessary to write a factorial function -- you could easily do it in assembler -- but writing a factorial function is a good exercise in learning C. Similarly, if you want to learn how to write parsers, it's a good idea to start with a simple language; obviously, that's not going to exercise every option in the parser/scanner generators, but it will get you started. The question really is whether the language you're designing is appropriate for this style of parsing, not whether it is too simple.
With flex/bison, does it makes sense to perform the analysis while parsing or is it more elegant to parse first, then operate on the file again with some other tool?
Either can be elegant, or disastrous; elegance has more to do with how you structure your thinking about the problem at hand. Having said that, it is often better to build a semantic structure (commonly referred to as an AST -- abstract syntax tree) during the parse phase and then analyse that structure using other functions.
Rescanning the input file is very unlikely to be either elegant or effective.

Partial parsing with flex/antlr

I encountered a problem while doing my student research project. I'm an electrical engineering student, but my project has somewhat to do with theoretical computer science: I need to parse a lot of pascal sourcecode-files for typedefinitions and constants and visualize all occurrences. The typedefinitions are spread recursively over various files, i.e. there is type a = byte in file x, in file y, there is a record (struct) b, that contains type a and then there is even a type c in file z that is an array of type b.
My idea so far was to learn about compiler construction, since the compiler has to resolve all typedefinitions and break them down to the elemental types.
So, I've read about compiler construction in two books (one of which is even written by the pascal inventor), but I'm lacking so many basics of theoretical computer science that it took me one week alone to work my way halfway through. What I've learned so far is that for achieving my goal, lexer and parser should be sufficient. Since this software is only a really smart part of the whole project, I can't spend so much time with it, so I started experimenting with flex and later with antlr.
My hope was, that parsing for typedefinitions only was such an easy task, that I could manage to do it with only using a scanner and let it do some parser's work: The pascal-files consist of 5 main-parts, each one being optional: A header with comments, a const-section, a type-section, a var-section and (in least cases) a code-section. Each section has a start-identifier but no clear end-identifier. So I started searching for the start of the type- and const-section (TYPE, CONST), discarding everything else. In flex, this is fairly easy, because it allows "start conditions". They can be used as various states like "INITIAL", "TYPE-SECTION", "CONST-SECTION" and "COMMENT" with different rules for each state. I wanted to get back a string from the scanner with following syntax " = ". There was one thing that made this task difficult: Some type contain comments like in this example: AuEingangsBool_t {PCMON} = MAX_AuEingangsFeld;. The scanner can not extract such type-definition with a regular expression.
My next step was to do it properly with scanner AND parser, so I searched for a parsergenerator and found antlr. Since I write the tool in C# anyway, I decided to use its scannergenerator, too, so that I do not have to communicate between different programs. Now I encountered following Problem: AFAIK, antlr does not support "start conditions" as flex do. That means, I have to scan the whole file (okay, comments still get discarded) and get a lot of unneccessary (and wrong) tokens. Because I don't use rules for the whole pascal grammar, the scanner would identify most keywords of the pascal syntax as user-identifiers and the parser would nag about all those series of tokens, that do not fit to type- and constant-defintions
Now, finally my question(s): Can anyone of you tell me, which approach leads anywhere for my project? Is there a possibility to scan only parts of the source-files with antlr? Or do I have to connect flex with antlr for that purpose? Can I tell antlr's parser to ignore every token that is not in the const- or type-section? Are those tools too powerful for my task and should I write own routines instead?
You'd be better off to find a compiler for Pascal, and simply modify to report the information you want. Presumably there is such a compiler for your Pascal, and often the source code for such compilers is available.
Otherwise you essentially need to build a parser. Building lexer, and then hacking around with the resulting lexemes, is essentially building a bad parser by ad hoc methods. ANTLR is a good way to go; you can define the lexemes (including means to pick up and ignore comments) pretty easily, especially for older dialects of Pascal. You'll need good BNF rules for the type information that you want, and translate those rules to the parser generator. What you can do to minimize work, is to cheat on rules for the parts of the language you don't care about. For instance, you could write an accurate subgrammar for assignment statements. Since you don't care about them, you can write a sloppy subgrammar that treats assignment statements as anything that begins with an identifier, is followed by arbitrary other tokens, and ends with semicolon. This kind of a grammar is called an "island grammar"; it is only accurate where it needs to be accurate.
I don't know about the recursive bit. Is there a reason you can't just process each file separately? The answer may depend on what information you want to know about each type declaration, and if you go deep enough, you may need a symbol table as well as an island parser. Parser generators offer you no help for this.
First, there can be type and const blocks within other blocks (procedures, in later Delphi versions also classes).
Moreover, I'm not entirely sure that you can actually simply scan for a const token, and then start parsing. Const is also used for other purposes in most common (Borland) Pascal dialects. Some keywords can be reused in a different context, and if you don't parse the global blockstructure, and only look for const and type in specific places you will erroneously start parsing there.
A base problem of course is the comments. Scanners cut out comments as early as possible, and don't regard them further. You probably have to setup the scanner so that comments are attached to the adjacent tokens as field (associate with token before or save them up till a certain token follows).
As far antlr vs flex, no clue. The only parsergenerator I have some minor experience in parsing Pascal with is Coco/R (a parsergenerator popular by Wirthians), but in general I (and many pascalians) prefer handcoded.

What is parsing in terms that a new programmer would understand? [closed]

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I am a college student getting my Computer Science degree. A lot of my fellow students really haven't done a lot of programming. They've done their class assignments, but let's be honest here those questions don't really teach you how to program.
I have had several other students ask me questions about how to parse things, and I'm never quite sure how to explain it to them. Is it best to start just going line by line looking for substrings, or just give them the more complicated lecture about using proper lexical analysis, etc. to create tokens, use BNF, and all of that other stuff? They never quite understand it when I try to explain it.
What's the best approach to explain this without confusing them or discouraging them from actually trying.
I'd explain parsing as the process of turning some kind of data into another kind of data.
In practice, for me this is almost always turning a string, or binary data, into a data structure inside my Program.
For example, turning
":Nick!User#Host PRIVMSG #channel :Hello!"
into (C)
struct irc_line {
char *nick;
char *user;
char *host;
char *command;
char **arguments;
char *message;
} sample = { "Nick", "User", "Host", "PRIVMSG", { "#channel" }, "Hello!" }
Parsing is the process of analyzing text made of a sequence of tokens to determine its grammatical structure with respect to a given (more or less) formal grammar.
The parser then builds a data structure based on the tokens. This data structure can then be used by a compiler, interpreter or translator to create an executable program or library.
(source: wikimedia.org)
If I gave you an english sentence, and asked you to break down the sentence into its parts of speech (nouns, verbs, etc.), you would be parsing the sentence.
That's the simplest explanation of parsing I can think of.
That said, parsing is a non-trivial computational problem. You have to start with simple examples, and work your way up to the more complex.
What is parsing?
In computer science, parsing is the process of analysing text to determine if it belongs to a specific language or not (i.e. is syntactically valid for that language's grammar). It is an informal name for the syntactic analysis process.
For example, suppose the language a^n b^n (which means same number of characters A followed by the same number of characters B). A parser for that language would accept AABB input and reject the AAAB input. That is what a parser does.
In addition, during this process a data structure could be created for further processing. In my previous example, it could, for instance, to store the AA and BB in two separate stacks.
Anything that happens after it, like giving meaning to AA or BB, or transform it in something else, is not parsing. Giving meaning to parts of an input sequence of tokens is called semantic analysis.
What isn't parsing?
Parsing is not transform one thing into another. Transforming A into B, is, in essence, what a compiler does. Compiling takes several steps, parsing is only one of them.
Parsing is not extracting meaning from a text. That is semantic analysis, a step of the compiling process.
What is the simplest way to understand it?
I think the best way for understanding the parsing concept is to begin with the simpler concepts. The simplest one in language processing subject is the finite automaton. It is a formalism to parsing regular languages, such as regular expressions.
It is very simple, you have an input, a set of states and a set of transitions. Consider the following language built over the alphabet { A, B }, L = { w | w starts with 'AA' or 'BB' as substring }. The automaton below represents a possible parser for that language whose all valid words starts with 'AA' or 'BB'.
A-->(q1)--A-->(qf)
/
(q0)
\
B-->(q2)--B-->(qf)
It is a very simple parser for that language. You start at (q0), the initial state, then you read a symbol from the input, if it is A then you move to (q1) state, otherwise (it is a B, remember the remember the alphabet is only A and B) you move to (q2) state and so on. If you reach (qf) state, then the input was accepted.
As it is visual, you only need a pencil and a piece of paper to explain what a parser is to anyone, including a child. I think the simplicity is what makes the automata the most suitable way to teaching language processing concepts, such as parsing.
Finally, being a Computer Science student, you will study such concepts in-deep at theoretical computer science classes such as Formal Languages and Theory of Computation.
Have them try to write a program that can evaluate arbitrary simple arithmetic expressions. This is a simple problem to understand but as you start getting deeper into it a lot of basic parsing starts to make sense.
Parsing is about READING data in one format, so that you can use it to your needs.
I think you need to teach them to think like this. So, this is the simplest way I can think of to explain parsing for someone new to this concept.
Generally, we try to parse data one line at a time because generally it is easier for humans to think this way, dividing and conquering, and also easier to code.
We call field to every minimum undivisible data. Name is field, Age is another field, and Surname is another field. For example.
In a line, we can have various fields. In order to distinguish them, we can delimit fields by separators or by the maximum length assign to each field.
For example:
By separating fields by comma
Paul,20,Jones
Or by space (Name can have 20 letters max, age up to 3 digits, Jones up to 20 letters)
Paul 020Jones
Any of the before set of fields is called a record.
To separate between a delimited field record we need to delimit record. A dot will be enough (though you know you can apply CR/LF).
A list could be:
Michael,39,Jordan.Shaquille,40,O'neal.Lebron,24,James.
or with CR/LF
Michael,39,Jordan
Shaquille,40,O'neal
Lebron,24,James
You can say them to list 10 nba (or nlf) players they like. Then, they should type them according to a format. Then make a program to parse it and display each record. One group, can make list in a comma-separated format and a program to parse a list in a fixed size format, and viceversa.
Parsing to me is breaking down something into meaningful parts... using a definable or predefined known, common set of part "definitions".
For programming languages there would be keyword parts, usable punctuation sequences...
For pumpkin pie it might be something like the crust, filling and toppings.
For written languages there might be what a word is, a sentence, what a verb is...
For spoken languages it might be tone, volume, mood, implication, emotion, context
Syntax analysis (as well as common sense after all) would tell if what your are parsing is a pumpkinpie or a programming language. Does it have crust? well maybe it's pumpkin pudding or perhaps a spoken language !
One thing to note about parsing stuff is there are usually many ways to break things into parts.
For example you could break up a pumpkin pie by cutting it from the center to the edge or from the bottom to the top or with a scoop to get the filling out or by using a sledge hammer or eating it.
And how you parse things would determine if doing something with those parts will be easy or hard.
In the "computer languages" world, there are common ways to parse text source code. These common methods (algorithims) have titles or names. Search the Internet for common methods/names for ways to parse languages. Wikipedia can help in this regard.
In linguistics, to divide language into small components that can be analyzed. For example, parsing this sentence would involve dividing it into words and phrases and identifying the type of each component (e.g.,verb, adjective, or noun).
Parsing is a very important part of many computer science disciplines. For example, compilers must parse source code to be able to translate it into object code. Likewise, any application that processes complex commands must be able to parse the commands. This includes virtually all end-user applications.
Parsing is often divided into lexical analysis and semantic parsing. Lexical analysis concentrates on dividing strings into components, called tokens, based on punctuationand other keys. Semantic parsing then attempts to determine the meaning of the string.
http://www.webopedia.com/TERM/P/parse.html
Simple explanation: Parsing is breaking a block of data into smaller pieces (tokens) by following a set of rules (using delimiters for example),
so that this data could be processes piece by piece (managed, analysed, interpreted, transmitted, ets).
Examples: Many applications (like Spreadsheet programs) use CSV (Comma Separated Values) file format to import and export data. CSV format makes it possible for the applications to process this data with a help of a special parser.
Web browsers have special parsers for HTML and CSS files. JSON parsers exist. All special file formats must have some parsers designed specifically for them.

Parsing Source Code - Unique Identifiers for Different Languages? [closed]

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I'm building an application that receives source code as input and analyzes several aspects of the code. It can accept code from many common languages, e.g. C/C++, C#, Java, Python, PHP, Pascal, SQL, and more (however many languages are unsupported, e.g. Ada, Cobol, Fortran). Once the language is known, my application knows what to do (I have different handlers for different languages).
Currently I'm asking the user to input the programming language the code is written in, and this is error-prone: although users know the programming languages, a small percentage of them (on rare occasions) click the wrong option just due to recklessness, and that breaks the system (i.e. my analysis fails).
It seems to me like there should be a way to figure out (in most cases) what the language is, from the input text itself. Several notes:
I'm receiving pure text and not file names, so I can't use the extension as a hint.
The user is not required to input complete source codes, and can also input code snippets (i.e. the include/import part may not be included).
it's clear to me that any algorithm I choose will not be 100% proof, certainly for very short input codes (e.g. that could be accepted by both Python and Ruby), in which cases I will still need the user's assistance, however I would like to minimize user involvement in the process to minimize mistakes.
Examples:
If the text contains "x->y()", I may know for sure it's C++ (?)
If the text contains "public static void main", I may know for sure it's Java (?)
If the text contains "for x := y to z do begin", I may know for sure it's Pascal (?)
My question:
Are you familiar with any standard library/method for figuring out automatically what the language of an input source code is?
What are the unique code "tokens" with which I could certainly differentiate one language from another?
I'm writing my code in Python but I believe the question to be language agnostic.
Thanks
Vim has a autodetect filetype feature. If you download vim sourcecode you will find a /vim/runtime/filetype.vim file.
For each language it checks the extension of the file and also, for some of them (most common), it has a function that can get the filetype from the source code. You can check that out. The code is pretty easy to understand and there are some very useful comments there.
build a generic tokenizer and then use a Bayesian filter on them. Use the existing "user checks a box" system to train it.
Here is a simple way to do it. Just run the parser on every language. Whatever language gets the farthest without encountering any errors (or has the fewest errors) wins.
This technique has the following advantages:
You already have most of the code necessary to do this.
The analysis can be done in parallel on multi-core machines.
Most languages can be eliminated very quickly.
This technique is very robust. Languages that might appear very similar when using a fuzzy analysis (baysian for example), would likely have many errors when the actual parser is run.
If a program is parsed correctly in two different languages, then there was never any hope of distinguishing them in the first place.
I think the problem is impossible. The best you can do is to come up with some probability that a program is in a particular language, and even then I would guess producing a solid probability is very hard. Problems that come to mind at once:
use of features like the C pre-processor can effectively mask the underlyuing language altogether
looking for keywords is not sufficient as the keywords can be used in other languages as identifiers
looking for actual language constructs requires you to parse the code, but to do that you need to know the language
what do you do about malformed code?
Those seem enough problems to solve to be going on with.
One program I know which even can distinguish several different languages within the same file is ohcount. You might get some ideas there, although I don't really know how they do it.
In general you can look for distinctive patterns:
Operators might be an indicator, such as := for Pascal/Modula/Oberon, => or the whole of LINQ in C#
Keywords would be another one as probably no two languages have the same set of keywords
Casing rules for identifiers, assuming the piece of code was writting conforming to best practices. Probably a very weak rule
Standard library functions or types. Especially for languages that usually rely heavily on them, such as PHP you might just use a long list of standard library functions.
You may create a set of rules, each of which indicates a possible set of languages if it matches. Intersecting the resulting lists will hopefully get you only one language.
The problem with this approach however, is that you need to do tokenizing and compare tokens (otherwise you can't really know what operators are or whether something you found was inside a comment or string). Tokenizing rules are different for each language as well, though; just splitting everything at whitespace and punctuation will probably not yield a very useful sequence of tokens. You can try several different tokenizing rules (each of which would indicate a certain set of languages as well) and have your rules match to a specified tokenization. For example, trying to find a single-quoted string (for trying out Pascal) in a VB snippet with one comment will probably fail, but another tokenizer might have more luck.
But since you want to perform analysis anyway you probably have parsers for the languages you support, so you can just try running the snippet through each parser and take that as indicator which language it would be (as suggested by OregonGhost as well).
Some thoughts:
$x->y() would be valid in PHP, so ensure that there's no $ symbol if you think C++ (though I think you can store function pointers in a C struct, so this could also be C).
public static void main is Java if it is cased properly - write Main and it's C#. This gets complicated if you take case-insensitive languages like many scripting languages or Pascal into account. The [] attribute syntax in C# on the other hand seems to be rather unique.
You can also try to use the keywords of a language - for example, Option Strict or End Sub are typical for VB and the like, while yield is likely C# and initialization/implementation are Object Pascal / Delphi.
If your application is analyzing the source code anyway, you code try to throw your analysis code at it for every language and if it fails really bad, it was the wrong language :)
My approach would be:
Create a list of strings or regexes (with and without case sensitivity), where each element has assigned a list of languages that the element is an indicator for:
class => C++, C#, Java
interface => C#, Java
implements => Java
[attribute] => C#
procedure => Pascal, Modula
create table / insert / ... => SQL
etc. Then parse the file line-by-line, match each element of the list, and count the hits.
The language with the most hits wins ;)
How about word frequency analysis (with a twist)? Parse the source code and categorise it much like a spam filter does. This way when a code snippet is entered into your app which cannot be 100% identified you can have it show the closest matches which the user can pick from - this can then be fed into your database.
Here's an idea for you. For each of your N languages, find some files in the language, something like 10-20 per language would be enough, each one not too short. Concatenate all files in one language together. Call this lang1.txt. GZip it to lang1.txt.gz. You will have a set of N langX.txt and langX.txt.gz files.
Now, take the file in question and append to each of he langX.txt files, producing langXapp.txt, and corresponding gzipped langXapp.txt.gz. For each X, find the difference between the size of langXapp.gz and langX.gz. The smallest difference will correspond to the language of your file.
Disclaimer: this will work reasonably well only for longer files. Also, it's not very efficient. But on the plus side you don't need to know anything about the language, it's completely automatic. And it can detect natural languages and tell between French or Chinese as well. Just in case you need it :) But the main reason, I just think it's interesting thing to try :)
The most bulletproof but also most work intensive way is to write a parser for each language and just run them in sequence to see which one would accept the code. This won't work well if code has syntax errors though and you most probably would have to deal with code like that, people do make mistakes. One of the fast ways to implement this is to get common compilers for every language you support and just run them and check how many errors they produce.
Heuristics works up to a certain point and the more languages you will support the less help you would get from them. But for first few versions it's a good start, mostly because it's fast to implement and works good enough in most cases. You could check for specific keywords, function/class names in API that is used often, some language constructions etc. Best way is to check how many of these specific stuff a file have for each possible language, this will help with some syntax errors, user defined functions with names like this() in languages that doesn't have such keywords, stuff written in comments and string literals.
Anyhow you most likely would fail sometimes so some mechanism for user to override language choice is still necessary.
I think you never should rely on one single feature, since the absence in a fragment (e.g. somebody systematically using WHILE instead of for) might confuse you.
Also try to stay away from global identifiers like "IMPORT" or "MODULE" or "UNIT" or INITIALIZATION/FINALIZATION, since they might not always exist, be optional in complete sources, and totally absent in fragments.
Dialects and similar languages (e.g. Modula2 and Pascal) are dangerous too.
I would create simple lexers for a bunch of languages that keep track of key tokens, and then simply calculate a key tokens to "other" identifiers ratio. Give each token a weight, since some might be a key indicator to disambiguate between dialects or versions.
Note that this is also a convenient way to allow users to plugin "known" keywords to increase the detection ratio, by e.g. providing identifiers of runtime library routines or types.
Very interesting question, I don't know if it is possible to be able to distinguish languages by code snippets, but here are some ideas:
One simple way is to watch out for single-quotes: In some languages, it is used as character wrapper, whereas in the others it can contain a whole string
A unary asterisk or a unary ampersand operator is a certain indication that it's either of C/C++/C#.
Pascal is the only language (of the ones given) to use two characters for assignments :=. Pascal has many unique keywords, too (begin, sub, end, ...)
The class initialization with a function could be a nice hint for Java.
Functions that do not belong to a class eliminates java (there is no max(), for example)
Naming of basic types (bool vs boolean)
Which reminds me: C++ can look very differently across projects (#define boolean int) So you can never guarantee, that you found the correct language.
If you run the source code through a hashing algorithm and it looks the same, you're most likely analyzing Perl
Indentation is a good hint for Python
You could use functions provided by the languages themselves - like token_get_all() for PHP - or third-party tools - like pychecker for python - to check the syntax
Summing it up: This project would make an interesting research paper (IMHO) and if you want it to work well, be prepared to put a lot of effort into it.
There is no way of making this foolproof, but I would personally start with operators, since they are in most cases "set in stone" (I can't say this holds true to every language since I know only a limited set). This would narrow it down quite considerably, but not nearly enough. For instance "->" is used in many languages (at least C, C++ and Perl).
I would go for something like this:
Create a list of features for each language, these could be operators, commenting style (since most use some sort of easily detectable character or character combination).
For instance:
Some languages have lines that start with the character "#", these include C, C++ and Perl. Do others than the first two use #include and #define in their vocabulary? If you detect this character at the beginning of line, the language is probably one of those. If the character is in the middle of the line, the language is most likely Perl.
Also, if you find the pattern := this would narrow it down to some likely languages.
Etc.
I would have a two-dimensional table with languages and patterns found and after analysis I would simply count which language had most "hits". If I wanted it to be really clever I would give each feature a weight which would signify how likely or unlikely it is that this feature is included in a snippet of this language. For instance if you can find a snippet that starts with /* and ends with */ it is more than likely that this is either C or C++.
The problem with keywords is someone might use it as a normal variable or even inside comments. They can be used as a decider (e.g. the word "class" is much more likely in C++ than C if everything else is equal), but you can't rely on them.
After the analysis I would offer the most likely language as the choice for the user with the rest ordered which would also be selectable. So the user would accept your guess by simply clicking a button, or he can switch it easily.
In answer to 2: if there's a "#!" and the name of an interpreter at the very beginning, then you definitely know which language it is. (Can't believe this wasn't mentioned by anyone else.)

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