I was given the following task:
Write a recursive grammar for the language of strings of one or more letters. The first letter of each string must be uppercase, and all other letters in the string must be lowercase.
After reading the chapter on grammar, and exploring some examples, this is my attempt:
<goodString> =<UpCh>|<UpCh> <ch>
<UpCh> = A|B|C...|Z
<ch> = a|b|c...|z
or maybe
<goodString> =<UpCh>|<goodString> <ch>
<UpCh> = A|B|C...|Z
<ch> = a|b|c...|z
Is this right? If not, what did I do wrong?
Right now your grammar isn't recursive. A recursive grammar would/will include at least one production that invokes itself (directly or indirectly) on the right side.
In this case, the obvious place to use that would be "an indefinite number of lower case letters". For that I'd define a lower case string (or whatever) as either nil, or a lower case string followed by a lower case letter. Then your word will be an upper case letter followed by a lower case string.
Note that for a case like this, you can define the lower case string as a character followed by a string, or as a string followed by a character. These are known as right recursive and left recursive respectively. If there's any chance you'll ever implement the grammar, you probably want to know that you want the right recursive form for a recursive descent parser, but generally prefer the left recursive form for a bottom up parser (such as many generators such as yacc, Bison, byacc, etc., produce).
Related
Identifiers typically consist of underscores, digits; and uppercase and lowercase characters where the first character is not a digit. When writing lexers, it is common to have helper functions such as is_digit or is_alnum. If one were to implement such a function to scan a character used in an identifier, what would it be called? Clearly, is_identifier is wrong as that would be the entire token that the lexer scans and not the individual character. I suppose is_alnum_or_underscore would be accurate though quite verbose. For something as common as this, I feel like there should be a single word for it.
Unicode Annex 31 (Unicode Identifier and Pattern Syntax, UAX31) defines a framework for the definition of the lexical syntax of identifiers, which is probably as close as we're going to come to a standard terminology. UAX31 is used (by reference) by Python and Rust, and has been approved for C++23. So I guess it's pretty well mainstream.
UAX31 defines three sets of identifier characters, which it calls Start, Continue and Medial. All Start characters are also Continue characters; no Medial character is a Continue character.
That leads to the simple regular expression (UAX31-D1 Default Identifier Syntax):
<Identifier> := <Start> <Continue>* (<Medial> <Continue>+)*
A programming language which claims conformance with UAX31 does not need to accept the exact membership of each of these sets, but it must explicitly spell out the deviations in what's called a "profile". (There are seven other requirements, which are not relevant to this question. See the document if you want to fall down a very deep rabbit hole.)
That can be simplified even more, since neither UAX31 nor (as far as I know) the profile for any major language places any characters in Medial. So you can go with the flow and just define two categories: identifier-start and identifier-continue, where the first one is a subset of the second one.
You'll see that in a number of grammar documents:
Pythonidentifier ::= xid_start xid_continue*
RustIDENTIFIER_OR_KEYWORD : XID_Start XID_Continue*
| _ XID_Continue+
C++identifier:
identifier-start
identifier identifier-continue
So that's what I'd suggest. But there are many other possibilities:
SwiftCalls the sets identifier-head and identifier-characters
JavaCalls them JavaLetter and JavaLetterOrDigit
CDefines identifier-nondigit and identifier-digit; Continue would be the union of the two sets.
My input consists of a series of names, each on a new line. Each name consists of a firstname, optional middle initial, and lastname. The name fields are separated by tabs. Here is a sample input:
Sally M. Smith
Tom V. Jones
John Doe
Below are the rules for my Flex lexer. It works fine but I am concerned that my lexer is doing too much: it is determining that a token is a firstname or a middle initial or a lastname. Should that determination be done in the parser, not the lexer? Am I abusing the Flex state capability? What I am seeking is a critique of my lexer. I am just a beginner, how would a parsing expert create lexer rules for this input?
<INITIAL>{
[a-zA-Z]+ { yylval.strval = strdup(yytext); return(FIRSTNAME); }
\t { BEGIN MI_STATE; }
. { BEGIN JUNK_STATE; }
}
<MI_STATE>{
[A-Z]\. { yylval.strval = strdup(yytext); return(MI); }
\t { BEGIN LASTNAME_STATE; }
. { BEGIN JUNK_STATE; }
}
<LASTNAME_STATE>{
[a-zA-Z]+ { yylval.strval = strdup(yytext); return(LASTNAME); }
\n { BEGIN INITIAL; return EOL; }
. { BEGIN JUNK_STATE; }
}
<JUNK_STATE>. { printf("JUNK: %s\n", yytext); }
You can use lexer states as you do in this question. But it's better to use them as a means to conditionally activate rules. For examples, think of handling multi-line comments or here documents or (for us silverbacks) embedded SQL.
In your question, there's no lexical difference between a given name and a family name -- they both are matched by [a-zA-Z]+, as would be middle names, if you were to extend your lexer.
Short answer: yes, lex NAME tokens and let the parser determine whether you have three NAME tokens on a line.
Yes; your lexer is parsing. The main evidence is that it's implementing identical rules in different start states. Two rules have exactly the same pattern.
The purpose of start states in the context of lexing is to modify the lexical grammar in order to shield the parser from certain differences. It works with the parser. For instance, say you had some document language in which $ shifts into math expression mode, which has different tokenizing rules. The lexer still just returns tokens in math mode; it doesn't try to parse the math expressions. It is the parser which will determine that, if the brackets are balanced, then another $ can shift out of math mode.
In your code the rules for returning a last name and first name are identical; you have used to start state to handle phrase structure syntax: the fact that the last name comes later than the first name.
Another bit of telltale evidence that the lexer is parsing is that the lexer itself is handling all of the start condition changes. In our $...$ math mode example, we might have the lexer shift into a start state when it sees the $ symbol. However, if the lexer also recognizes the end of math mode, then that is evidence it is parsing the math mode expression. The end can only be recognized by following the nested phrase structure grammar of math mode expressions. The way you would handle that would be for the lexer to expose a function lex_end_math_mode(). When the parser processes and reduces the entire math mode expression, it calls this function to tell the lexer to switch back to the lexical syntax outside of math mode. The math-mode-terminating dollar sign would likely also appear as a token visible to the parser, though the leading one might not. So that is to say, the parser parses math_mode_expr : expr '$': a math mode expression followed by a required dollar sign to end math mode. The action for that rule would include the call to lex_end_math_mode, so the lexer returns to the tokenization rules outside of math mode for scanning the next token after the closing $.
There is no right or wrong answer because it's all parsing. Every grammar that is divided into tokens and phrase structure rules could be expressed by a unified grammar which includes the rules for the token structure.
Why we often use a design which separates lexical scanning and parsing is that:
Unifying the lexical and phrase structure grammar into one will turn LL(1) into LL(k). A recursive-descent parser then needs to look k symbols ahead to make parsing decisions. For instance if you're parsing C with this holistic approach, you need to treat int as a reserved keyword. That requires four symbols of lookahead: you have to recognize i, n, t, and then if the next symbol indicates that the token has ended, you treat that as the keyword, otherwise an identifier.
Performance: lexical scanning uses efficient techniques tailored to that task, which take advantage of the restriction that the lexical grammar is regular.
Correspondence to spec: if you have a language whose specification is described in terms of a lexical grammar separate from a phrase structure grammar, then if you implement it that way, features of your code are more readily traceable to features of requirement spec. You may be able to write unit tests which separately show that the lexing and parsing obeys the spec.
Schooling: people who went through a CS program that included a course on compiler construction had separate lexing and parsing drilled into their heads, and whenever it comes up in their subsequent career, they just lean on that wisdom. They are never confronted with situations in which they recognize it as not being a good approach, and don't question it.
Whatever works in your individual situations with whatever you're parsing overrules the theory. If it's convenient for you to recognize some phrase-like fragments in the lexer, and you're able to convince yourself that it's a clean approach, then by all means do it that way.
I am working on a parser for a language that has
identifiers (say, a letter followed by a number of alphanumeric characters or an underscore),
integers (any number of digits and possibly carets ^),
some operators,
filename (a number of alphanumeric characters and possibly slashes, and dots)
Apparently filename overlaps integers and identifiers, so in general I cannot decide if I have a filename or, say, an identifier unless the filename contains a slash or a dot.
But filename can only follow a specific operator.
My question is how this situation is usually handled during tokenization? I have a table driven tokenizer (lexer), but I am not sure how to tell a filename from either an integer or an identifier. How is this done?
If filename was a superset of integers and identifiers then I probably could have grammar productions that could handle that, but the tokens overlap...
Flex and other lexers have the concept of start conditions. Essentially the lexer is a state machine and its exact behaviour will depend on its current state.
In your example, when your lexer encounters the operator preceding a filename it should switch to a FilenameMode state (or whatever) and then switch back once it has produced the filename token it was expecting.
EDIT:
Just to give some concrete code this side of the hyperlink:
You would trigger your FILENAME_MODE when you encounter the operator...
{FILENAME_PREFIX} { BEGIN(FILENAME_MODE); }
You would define your rule to parse a filename:
<FILENAME_MODE>{FILENAME_CHARS}+ { BEGIN(INITIAL); }
...switching back to the INITIAL state in the action.
Say I have a string "abacabacabadcdcdcd" and I want to apply a simple set of rules:
abaca->a
dcd->d
From left to right s.t. the string ends up being "abad". This output will be used to make a decision. After the rules are applied, if the output string does not match preset strings such as "abad", the original string would be discarded. ex. Every string should distill down to "abad", kick if it doesn't.
I have this hard-coded right now as regex, but there are many instances of these small rule sets. I am looking for something that will take a set of simple rules and compile (or just a function?) into something I can feed the string to and retrieve a result. The rule sets are independent of each other.
The input is tightly controlled, and the rules in use will be simple. Speed is the most important aspect.
I've looked at Bison and ANTLR, but I don't think I need anything nearly that powerful...
What am I looking for?
Edit: Should mention that the strings are made up of a couple letters. Usually 5, i.e. "abcde". There are no spaces, etc. Just letters.
If it is going to go fast, you can start out with a map, that contains your rules as key value pairs of strings. You can then compile this map to a sort of state machine, a tree with char keys, where the associated value is either a replacement string, or another tree.
You then go char by char through your string. Look up the current char in the tree. If you find another tree, look up the next character in that tree, etc.
At some point, either:
the lookup will fail, and then you know that the string you've seen so far is not the prefix of any rule. You can skip the current character and continue with the next.
or you get a replacement string. In that case, you can replace the characters between the current char and the last one you looked up inclusive by the replacement string.
The only difficulty is if the replacement can itself be part of a pattern to replace. Example:
ab -> e
cd -> b
The input:
acd -> ab (by rule 2)
ab -> e (by rule 1) ????
Now the question is if you want to reconsider ab to give e?
If this is so, you must start over from the beginning after each replacement. In addition, it will be hard to tell whether the replacement ever ends, except if all the rules you have are such that the right hand side is shorter than the left hand side. For, in that case, a finite string will get reduced in a finite amount of time.
But if we don't need to reconsider, the algorithm above will go straight through the string.
I am writing my first parser and have a few questions conerning the tokenizer.
Basically, my tokenizer exposes a nextToken() function that is supposed to return the next token. These tokens are distinguished by a token-type. I think it would make sense to have the following token-types:
SYMBOL (such as <, :=, ( and the like
WHITESPACE (tab, newlines, spaces...)
REMARK (a comment between /* ... */ or after // through the new line)
NUMBER
IDENT (such as the name of a function or a variable)
STRING (Something enclosed between "....")
Now, do you think this makes sense?
Also, I am struggling with the NUMBER token-type. Do you think it makes more sense to further split it up into a NUMBER and a FLOAT token-type? Without a FLOAT token-type, I'd receive NUMBER (eg 402), a SYMBOL (.) followed by another NUMBER (eg 203) if I were about to parse a float.
Finally, what do you think makes more sense for the tokenizer to return when it encounters a -909? Should it return the SYMBOL - first, followed by the NUMBER 909 or should it return a NUMBER -909 right away?
It depends upon your target language.
The point behind a lexer is to return tokens that make it easy to write a parser for your language. Suppose your lexer returns NUMBER when it sees a symbol that matches "[0-9]+". If it sees a non-integer number, such as "3.1415926" it will return NUMBER . NUMBER. While you could handle that in your parser, if your lexer is doing an appropriate job of skipping whitespace and comments (since they aren't relevant to your parser) then you could end up incorrectly parsing things like "123 /* comment / . \n / other comment */ 456" as floating point numbers.
As for lexing "-[0-9]+" as a NUMBER vs MINUS NUMBER again, that depends upon your target language, but I would usually go with MINUS NUMBER, otherwise you would end up lexing "A = 1-2-3-4" as SYMBOL = NUMBER NUMBER NUMBER NUMBER instead of SYMBOL = NUMBER MINUS NUMBER MINUS NUMBER MINUS NUMBER.
While we're on the topic, I'd strongly recommend the book Language Implementation Patterns, by Terrance Parr, the author of ANTLR.
You are best served by making your token types closely match your grammar's terminal symbols.
Without knowing the language/grammar, I expect you would be better served by having token types for "LESS_THAN", "LESS_THAN_OR_EQUAL" and also "FLOAT", "DOUBLE", "INTEGER", etc.
From my experience with actual lexers:
Make sure to check if you actually need comment / whitespace tokens. Compilers typically don't need them, while IDEs often do (to color comments green, for example).
Usually there's no single "operator" token; instead, there's a token for each distinct operator. So there's a PLUS token and AMPERSAND token and LESSER_THAN token etc.. This means that you only care about the lexeme (the actual text matched) when the token is an identifier or some sort of literal.
Avoid splitting literals. If "hello world" is a string literal, parse it as a single token. If -3.058e18 is a float literal, parse it as a single token as well. Lexers usually rely on regular expressions, which are expressive enough for all these things, and more. Of course, if the literals are complex enough you have to split them (e.g. the block literal in Smalltalk).
I think that the answer to your question is strictly tied to the semantic of NUMBER.
What a NUMBER should be? An always positive integer, a float...
I'd like to suggest you to lookup to the flex and yacc (aka lex & bison) tools of the U**x operating systems: these are powerful parsers and scanners generators that take a grammar and output a compilable and readily usable program.
It depends on how you are taking in tokens, if you are doing it character by character, then it might be a bit tricky, but if you are doing it word by word i.e.
int a = a + 2.0
then the tokens would be (discarding whitespace)
int
a
=
a
+
2.0
So you wouldn't run into the situation where you interpret the . as at token but rather take the whole string in - which is where you can determine if it's a FLOAT or NUMBER or whatever you want.