Related
Context: I'm using Maxima on a platform that also uses KaTeX. For various reasons related to content management, this means that we are regularly using Maxima functions to generate the necessary KaTeX commands.
I'm currently trying to develop a group of functions that will facilitate generating different sets of strings corresponding to KaTeX commands for various symbols related to vectors.
Problem
I have written the following function makeKatexVector(x), which takes a string, list or list-of-lists and returns the same type of object, with each string wrapped in \vec{} (i.e. makeKatexVector(string) returns \vec{string} and makeKatexVector(["a","b"]) returns ["\vec{a}", "\vec{b}"] etc).
/* Flexible Make KaTeX Vector Version of List Items */
makeKatexVector(x):= block([ placeHolderList : x ],
if stringp(x) /* Special Handling if x is Just a String */
then placeHolderList : concat("\vec{", x, "}")
else if listp(x[1]) /* check to see if it is a list of lists */
then for j:1 thru length(x)
do placeHolderList[j] : makelist(concat("\vec{", k ,"}"), k, x[j] )
else if listp(x) /* check to see if it is just a list */
then placeHolderList : makelist(concat("\vec{", k, "}"), k, x)
else placeHolderList : "makeKatexVector error: not a list-of-lists, a list or a string",
return(placeHolderList));
Although I have my doubts about the efficiency or elegance of the above code, it seems to return the desired expressions; however, I would like to modify this function so that it can distinguish between single- and multi-character strings.
In particular, I'd like multi-character strings like x_1 to be returned as \vec{x}_1 and not \vec{x_1}.
In fact, I'd simply like to modify the above code so that \vec{} is wrapped around the first character of the string, regardless of how many characters there may be.
My Attempt
I was ready to tackle this with brute force (e.g. transcribing each character of a string into a list and then reassembling); however, the real programmer on the project suggested I look into "Regular Expressions". After exploring that endless rabbit hole, I found the command regex_subst; however, I can't find any Maxima documentation for it, and am struggling to reproduce the examples in the related documentation here.
Once I can work out the appropriate regex to use, I intend to implement this in the above code using an if statement, such as:
if slength(x) >1
then {regex command}
else {regular treatment}
If anyone knows of helpful resources on any of these fronts, I'd greatly appreciate any pointers at all.
Looks like you got the regex approach working, that's great. My advice about handling subscripted expressions in TeX, however, is to avoid working with names which contain underscores in Maxima, and instead work with Maxima expressions with indices, e.g. foo[k] instead of foo_k. While writing foo_k is a minor convenience in Maxima, you'll run into problems pretty quickly, and in order to straighten it out you might end up piling one complication on another.
E.g. Maxima doesn't know there's any relation between foo, foo_1, and foo_k -- those have no more in common than foo, abc, and xyz. What if there are 2 indices? foo_j_k will become something like foo_{j_k} by the preceding approach -- what if you want foo_{j, k} instead? (Incidentally the two are foo[j[k]] and foo[j, k] when represented by subscripts.) Another problematic expression is something like foo_bar_baz. Does that mean foo_bar[baz], foo[bar_baz] or foo_bar_baz?
The code for tex(x_y) yielding x_y in TeX is pretty old, so it's unlikely to go away, but over the years I've come to increasing feel like it should be avoided. However, the last time it came up and I proposed disabling that, there were enough people who supported it that we ended up keeping it.
Something that might be helpful, there is a function texput which allows you to specify how a symbol should appear in TeX output. For example:
(%i1) texput (v, "\\vec{v}");
(%o1) "\vec{v}"
(%i2) tex ([v, v[1], v[k], v[j[k]], v[j, k]]);
$$\left[ \vec{v} , \vec{v}_{1} , \vec{v}_{k} , \vec{v}_{j_{k}} ,
\vec{v}_{j,k} \right] $$
(%o2) false
texput can modify various aspects of TeX output; you can take a look at the documentation (see ? texput).
While I didn't expect that I'd work this out on my own, after several hours, I made some progress, so figured I'd share here, in case anyone else may benefit from the time I put in.
to load the regex in wxMaxima, at least on the MacOS version, simply type load("sregex");. I didn't have this loaded, and was trying to work through our custom platform, which cost me several hours.
take note that many of the arguments in the linked documentation by Dorai Sitaram occur in the reverse, or a different order than they do in their corresponding Maxima versions.
not all the "pregexp" functions exist in Maxima;
In addition to this, escaping special characters varied in important ways between wxMaxima, the inline Maxima compiler (running within Ace editor) and the actual rendered version on our platform; in particular, the inline compiler often returned false for expressions that compiled properly in wxMaxima and on the platform. Because I didn't have sregex loaded on wxMaxima from the beginning, I lost a lot of time to this.
Finally, the regex expression that achieved the desired substitution, in my case, was:
regex_subst("\vec{\\1}", "([[:alpha:]])", "v_1");
which returns vec{v}_1 in wxMaxima (N.B. none of my attempts to get wxMaxima to return \vec{v}_1 were successful; escaping the backslash just does not seem to work; fortunately, the usual escaped version \\vec{\\1} does return the desired form).
I have yet to adjust the code for the rest of the function, but I doubt that will be of use to anyone else, and wanted to be sure to post an update here, before anyone else took time to assist me.
Always interested in better methods / practices or any other pointers / feedback.
Seeing as the Maybe type is isomorphic to the set of null and singleton lists, why would anyone ever want to use the Maybe type when I could just use lists to accomodate absence?
Because if you match a list against the patterns [] and [x] that's not an exhaustive match and you'll get a warning about that, forcing you to either add another case that'll never get called or to ignore the warning.
Matching a Maybe against Nothing and Just x however is exhaustive. So you'll only get a warning if you fail to match one of those cases.
If you choose your types such that they can only represent values that you may actually produce, you can rely on non-exhaustiveness warnings to tell you about bugs in your code where you forget to check for a given a case. If you choose more "permissive" types, you'll always have to think about whether a warning represents an actual bug or just an impossible case.
You should strive to have accurate types. Maybe expresses that there is exactly one value or that there is none. Many imperative languages represent the "none" case by the value null.
If you chose a list instead of Maybe, all your functions would be faced with the possibility that they get a list with more than one member. Probably many of them would only be defined for one value, and would have to fail on a pattern match. By using Maybe, you avoid a class of runtime errors entirely.
Building on existing (and correct) answers, I'll mention a typeclass based answer.
Different types convey different intentions - returning a Maybe a represents a computation with the possiblity of failing while [a] could represent non-determinism (or, in simpler terms, multiple possible return values).
This plays into the fact that different types have different instances for typeclasses - and these instances cater to the underlying essence the type conveys. Take Alternative and its operator (<|>) which represents what it means to combine (or choose) between arguments given.
Maybe a Combining computations that can fail just means taking the first that is not Nothing
[a] Combining two computations that each had multiple return values just means concatenating together all possible values.
Then, depending on which types your functions use, (<|>) would behave differently. Of course, you could argue that you don't need (<|>) or anything like that, but then you are missing out on one of Haskell's main strengths: it's many high-level combinator libraries.
As a general rule, we like our types to be as snug fitting and intuitive as possible. That way, we are not fighting the standard libraries and our code is more readable.
Lisp, Scheme, Python, Ruby, JavaScript, etc., manage to get along with just one type each, which you could represent in Haskell with a big sum type. Every function handling a JavaScript (or whatever) value must be prepared to receive a number, a string, a function, a piece of the document object model, etc., and throw an exception if it gets something unexpected. People who program in typed languages like Haskell prefer to limit the number of unexpected things that can occur. They also like to express ideas using types, making types useful (and machine-checked) documentation. The closer the types come to representing the intended meaning, the more useful they are.
Because there are an infinite number of possible lists, and a finite number of possible values for the Maybe type. It perfectly represents one thing or the absence of something without any other possibility.
Several answers have mentioned exhaustiveness as a factor here. I think it is a factor, but not the biggest one, because there is a way to consistently treat lists as if they were Maybes, which the listToMaybe function illustrates:
listToMaybe :: [a] -> Maybe a
listToMaybe [] = Nothing
listToMaybe (a:_) = Just a
That's an exhaustive pattern match, which rules out any straightforward errors.
The factor I'd highlight as bigger is that by using the type that more precisely models the behavior of your code, you eliminate potential behaviors that would be possible if you used a more general alternative. Say for example you have some context in your code where you uses a type of the form a -> [b], though the only correct alternatives (given your program's specification) are empty or singleton lists. Try as hard as you may to enforce the convention that this context should obey that rule, it's still possible that you'll mess up and:
Somehow a function used in that context will produce a list of two or more items;
And somehow a function that uses the results produced in that context will observe whether the lists have two or more items, and behave incorrectly in that case.
Example: some code that expects there to be no more than one value will blindly print the contents of the list and thus print multiple items when only one was supposed to be.
But if you use Maybe, then there really must be either one value or none, and the compiler enforces this.
Even though isomorphic, e.g. QuickCheck will run slower because of the increase in search space.
I want to learn how to add spaces in variable names.
I know that a lot languages prevent me from doing this, but I believe that there is a trick to do this because I saw someone did it in MQL5
A MetaTrader Terminal allows to show a UI-Dialogue Panel for MMI-assisted setting values for input and extern variables declared in { Expert Advisor | Technical Indicator | Script } code, during a code-execution launch.
( Ref. a picture below ): .
If you really want to be evil you can sometimes use the left-to-right mark, U+200E which looks like a regular space but is generally not considered whitespace. Different languages and/or specific platforms may behave differently.
This trick seems to work in C# and apparently you can do similar things in ruby.
I tried this using g++ and luckily for everyone's sanity it is not allowed:
foo.cc:5:10: error: non-ASCII characters are not allowed outside of literals and identifiers
int a<U+200E> b = 3;
Please don't do this outside of pranks and April fool's day jokes.
In C++ you can't put spaces in variable names but you can get what you want using a std::map.
For example:
#include <map>
#include <string>
int main()
{
std::map<std::string, std::string> vars;
vars["Time Frame"] = "15 minutes";
vars["Indicator Period"] = "16";
// ... etc
}
The std::map is an associative container that maps one std::string onto another.
Depending on how you intend to use the map you may also want to consider using an std::unordered_map which should have higher performance but will not keep the keys sorted and may have a higher memory usage.
As much as I know, there isn't any option to add spaces to variables name.
The trouble with using spaces in names (whether filenames, variable names or something else) is that you need to have some other mechanism for determining what is part of this name and what is part of the next section of code. Your sample looks like a form, so that has it's own formatting and structure.
SQL does allow you to "quote" variable names with either [name with space] or with backticks `name with space`.
Most other languages do not allow spaces in variable names, because any whitedspace is considered a separator for different lexical unit [different name/word/variable]. There is no way you can change this, as it would alter the meaning of "normal code". Most languages do allow/use _ as a "space in names" character.
Of course, if you have "variables" that are your own construct, read from for example a database or file, you can use your own syntax, and use for example std::map<std::string, sometype> or std::unordered_map<std::string, sometype> to connect the string from your data to the corresponding value.
Spaces (white space) are used in C++ to isolate keywords and variable names, thus they cannot exist in a variable name or the compiler will treat the text as multiple identifiers.
Example - valid: static const unsigned int my_variable = 6U;
If there is a space between my and variable how does the compiler know which is the variable name? If there are two variables here, it doesn't make sense.
Also, as you can see, there may be more than one keyword in a statement.
I find a solution .In Mql5 , when you add a comment next to the variable name , it will appear instead of the variable name .
See this image : http://prntscr.com/79vaae
I need to write a parser to parse commands. 5 such commands are:
"a=10"
"b=foo"
"c=10,10"
"clear d"
"c push_back 2"
In the case of the first example, set is the command, a is the object and 10 is the value.
What do you think the parser should return for each line above?
Here is my idea:
"a=10" -> SET (COMMAND_ENUM), INT (VALUE_TYPE), "a", ("10")
"b=foo" -> SET (COMMAND_ENUM), STRING (VALUE_TYPE), "b", ("foo")
Is this a good approach? What is the standard approach for this problem? Should I dispatch instead?
I have a function which checks the type associated with an object. For example, a above is of type INT and must be assigned an INT value, otherwise the parser should return or throw an error of some sort. I also have a convert function for converting values from strings to the desired type. These throw if the conversion is not possible. If the parser tries to convert the values from strings to the required type, then it is probably a good idea to return them via a boost::variant.
You need to come up with at least a semi-formal grammar for the command language you want to recognize, since you've left a whole lot of things really vaguely specified (e.g. in b=foo you want b to be a variable name but foo to be a string literal. How do you distinguish them?. Does a sequence of characters represent an identifier if it's on the right side of an assignment, but a literal if it's on the left side? Or does a single character represent an identifier, but multiple characters represent a literal?) In c=10,10 does 10,10 represent a list or a vector? Writing a grammar will at least force you to think about such things, and it will also serve at least as a guide to how to write your parser (at most it will be something that can be automatically translated into your parser).
You're on the right track by thinking of how statements should be represented as Abstract Syntax Trees (ASTs), but you need to take a step backwards and look at what you want in terms of concrete syntax.
I was working with a new C++ developer a while back when he asked the question: "Why can't variable names start with numbers?"
I couldn't come up with an answer except that some numbers can have text in them (123456L, 123456U) and that wouldn't be possible if the compilers were thinking everything with some amount of alpha characters was a variable name.
Was that the right answer? Are there any more reasons?
string 2BeOrNot2Be = "that is the question"; // Why won't this compile?
Because then a string of digits would be a valid identifier as well as a valid number.
int 17 = 497;
int 42 = 6 * 9;
String 1111 = "Totally text";
Well think about this:
int 2d = 42;
double a = 2d;
What is a? 2.0? or 42?
Hint, if you don't get it, d after a number means the number before it is a double literal
It's a convention now, but it started out as a technical requirement.
In the old days, parsers of languages such as FORTRAN or BASIC did not require the uses of spaces. So, basically, the following are identical:
10 V1=100
20 PRINT V1
and
10V1=100
20PRINTV1
Now suppose that numeral prefixes were allowed. How would you interpret this?
101V=100
as
10 1V = 100
or as
101 V = 100
or as
1 01V = 100
So, this was made illegal.
Because backtracking is avoided in lexical analysis while compiling. A variable like:
Apple;
the compiler will know it's a identifier right away when it meets letter 'A'.
However a variable like:
123apple;
compiler won't be able to decide if it's a number or identifier until it hits 'a', and it needs backtracking as a result.
Compilers/parsers/lexical analyzers was a long, long time ago for me, but I think I remember there being difficulty in unambiguosly determining whether a numeric character in the compilation unit represented a literal or an identifier.
Languages where space is insignificant (like ALGOL and the original FORTRAN if I remember correctly) could not accept numbers to begin identifiers for that reason.
This goes way back - before special notations to denote storage or numeric base.
I agree it would be handy to allow identifiers to begin with a digit. One or two people have mentioned that you can get around this restriction by prepending an underscore to your identifier, but that's really ugly.
I think part of the problem comes from number literals such as 0xdeadbeef, which make it hard to come up with easy to remember rules for identifiers that can start with a digit. One way to do it might be to allow anything matching [A-Za-z_]+ that is NOT a keyword or number literal. The problem is that it would lead to weird things like 0xdeadpork being allowed, but not 0xdeadbeef. Ultimately, I think we should be fair to all meats :P.
When I was first learning C, I remember feeling the rules for variable names were arbitrary and restrictive. Worst of all, they were hard to remember, so I gave up trying to learn them. I just did what felt right, and it worked pretty well. Now that I've learned alot more, it doesn't seem so bad, and I finally got around to learning it right.
It's likely a decision that came for a few reasons, when you're parsing the token you only have to look at the first character to determine if it's an identifier or literal and then send it to the correct function for processing. So that's a performance optimization.
The other option would be to check if it's not a literal and leave the domain of identifiers to be the universe minus the literals. But to do this you would have to examine every character of every token to know how to classify it.
There is also the stylistic implications identifiers are supposed to be mnemonics so words are much easier to remember than numbers. When a lot of the original languages were being written setting the styles for the next few decades they weren't thinking about substituting "2" for "to".
Variable names cannot start with a digit, because it can cause some problems like below:
int a = 2;
int 2 = 5;
int c = 2 * a;
what is the value of c? is 4, or is 10!
another example:
float 5 = 25;
float b = 5.5;
is first 5 a number, or is an object (. operator)
There is a similar problem with second 5.
Maybe, there are some other reasons. So, we shouldn't use any digit in the beginnig of a variable name.
The restriction is arbitrary. Various Lisps permit symbol names to begin with numerals.
COBOL allows variables to begin with a digit.
Use of a digit to begin a variable name makes error checking during compilation or interpertation a lot more complicated.
Allowing use of variable names that began like a number would probably cause huge problems for the language designers. During source code parsing, whenever a compiler/interpreter encountered a token beginning with a digit where a variable name was expected, it would have to search through a huge, complicated set of rules to determine whether the token was really a variable, or an error. The added complexity added to the language parser may not justify this feature.
As far back as I can remember (about 40 years), I don't think that I have ever used a language that allowed use of a digit to begin variable names. I'm sure that this was done at least once. Maybe, someone here has actually seen this somewhere.
As several people have noticed, there is a lot of historical baggage about valid formats for variable names. And language designers are always influenced by what they know when they create new languages.
That said, pretty much all of the time a language doesn't allow variable names to begin with numbers is because those are the rules of the language design. Often it is because such a simple rule makes the parsing and lexing of the language vastly easier. Not all language designers know this is the real reason, though. Modern lexing tools help, because if you tried to define it as permissible, they will give you parsing conflicts.
OTOH, if your language has a uniquely identifiable character to herald variable names, it is possible to set it up for them to begin with a number. Similar rule variations can also be used to allow spaces in variable names. But the resulting language is likely to not to resemble any popular conventional language very much, if at all.
For an example of a fairly simple HTML templating language that does permit variables to begin with numbers and have embedded spaces, look at Qompose.
Because if you allowed keyword and identifier to begin with numberic characters, the lexer (part of the compiler) couldn't readily differentiate between the start of a numeric literal and a keyword without getting a whole lot more complicated (and slower).
C++ can't have it because the language designers made it a rule. If you were to create your own language, you could certainly allow it, but you would probably run into the same problems they did and decide not to allow it. Examples of variable names that would cause problems:
0x, 2d, 5555
One of the key problems about relaxing syntactic conventions is that it introduces cognitive dissonance into the coding process. How you think about your code could be deeply influenced by the lack of clarity this would introduce.
Wasn't it Dykstra who said that the "most important aspect of any tool is its effect on its user"?
The compiler has 7 phase as follows:
Lexical analysis
Syntax Analysis
Semantic Analysis
Intermediate Code Generation
Code Optimization
Code Generation
Symbol Table
Backtracking is avoided in the lexical analysis phase while compiling the piece of code. The variable like Apple, the compiler will know its an identifier right away when it meets letter ‘A’ character in the lexical Analysis phase. However, a variable like 123apple, the compiler won’t be able to decide if its a number or identifier until it hits ‘a’ and it needs backtracking to go in the lexical analysis phase to identify that it is a variable. But it is not supported in the compiler.
When you’re parsing the token you only have to look at the first character to determine if it’s an identifier or literal and then send it to the correct function for processing. So that’s a performance optimization.
Probably because it makes it easier for the human to tell whether it's a number or an identifier, and because of tradition. Having identifiers that could begin with a digit wouldn't complicate the lexical scans all that much.
Not all languages have forbidden identifiers beginning with a digit. In Forth, they could be numbers, and small integers were normally defined as Forth words (essentially identifiers), since it was faster to read "2" as a routine to push a 2 onto the stack than to recognize "2" as a number whose value was 2. (In processing input from the programmer or the disk block, the Forth system would split up the input according to spaces. It would try to look the token up in the dictionary to see if it was a defined word, and if not would attempt to translate it into a number, and if not would flag an error.)
Suppose you did allow symbol names to begin with numbers. Now suppose you want to name a variable 12345foobar. How would you differentiate this from 12345? It's actually not terribly difficult to do with a regular expression. The problem is actually one of performance. I can't really explain why this is in great detail, but it essentially boils down to the fact that differentiating 12345foobar from 12345 requires backtracking. This makes the regular expression non-deterministic.
There's a much better explanation of this here.
it is easy for a compiler to identify a variable using ASCII on memory location rather than number .
I think the simple answer is that it can, the restriction is language based. In C++ and many others it can't because the language doesn't support it. It's not built into the rules to allow that.
The question is akin to asking why can't the King move four spaces at a time in Chess? It's because in Chess that is an illegal move. Can it in another game sure. It just depends on the rules being played by.
Originally it was simply because it is easier to remember (you can give it more meaning) variable names as strings rather than numbers although numbers can be included within the string to enhance the meaning of the string or allow the use of the same variable name but have it designated as having a separate, but close meaning or context. For example loop1, loop2 etc would always let you know that you were in a loop and/or loop 2 was a loop within loop1.
Which would you prefer (has more meaning) as a variable: address or 1121298? Which is easier to remember?
However, if the language uses something to denote that it not just text or numbers (such as the $ in $address) it really shouldn't make a difference as that would tell the compiler that what follows is to be treated as a variable (in this case).
In any case it comes down to what the language designers want to use as the rules for their language.
The variable may be considered as a value also during compile time by the compiler
so the value may call the value again and again recursively
Backtracking is avoided in lexical analysis phase while compiling the piece of code. The variable like Apple; , the compiler will know its a identifier right away when it meets letter ‘A’ character in the lexical Analysis phase. However, a variable like 123apple; , compiler won’t be able to decide if its a number or identifier until it hits ‘a’ and it needs backtracking to go in the lexical analysis phase to identify that it is a variable. But it is not supported in compiler.
Reference
There could be nothing wrong with it when comes into declaring variable.but there is some ambiguity when it tries to use that variable somewhere else like this :
let 1 = "Hello world!"
print(1)
print(1)
print is a generic method that accepts all types of variable. so in that situation compiler does not know which (1) the programmer refers to : the 1 of integer value or the 1 that store a string value.
maybe better for compiler in this situation to allows to define something like that but when trying to use this ambiguous stuff, bring an error with correction capability to how gonna fix that error and clear this ambiguity.