I'm trying to study C grammar with flex/bison.
I found bison cannot parse this bison grammar: https://www.lysator.liu.se/c/ANSI-C-grammar-y.html, because LALR algorithm cannot process recursively multiple expressions.
Is GLR algorithm a must for C grammar?
There is nothing wrong with that grammar except:
IDENTIFIER and TYPE_NAMEAlso, it has one shift/reduce conflict as a result of the "dangling else" ambiguity. However, that conflict can be ignored because bison's conflict resolution algorithm produces the correct result in this case. (You can suppress the warning either with an %expect directive or by including a precedence declaration which favours shifting else over reducing if. Or you can eliminate the ambiguity in the grammar using the technique described in the Wikipedia page linked above. (Note: I'm not talking about copy-and-pasting code from the Wikipedia page. In the case of C, you need to consider all cases of compound statements which terminate with an if statement.)
Moreover, an LR parser is not recursive, and it has no problems which could be described as a failure to "process recursively multiple expressions". (You might have that problem with a recursive descent parser, although it's pretty easy to work around the issue.)
So any problems you might have experienced (if your question refers to a concrete issue) have nothing to do with what's described in your question.
Of the problems I listed above, the most troubling is the syntactic ambiguity of the cast operator. The cast operator is not actually ambiguous; clearly, C compilers manage to correct compile such expressions. But distinguishing between the two possible parses of, for example, (x)-y*z requires knowing whether x names a type or a variable.
In C, all names are lexically scoped, so it is certainly possible to resolve x at compile time. But the resolution is not context-free. Since GLR is also a technique for parsing context-free grammars, using a GLR parser won't directly help you. It might be useful in the sense that GLR parsers can theoretically produce "parse forests" rather than parse trees; that is, the output of a GLR parser might effectively contain all possible correct parses, leaving the possibility to resolve the ambiguity by building symbol tables for each scope and then choosing between alternative parses by examining the name binding in effect at each site. (This works because type alias declarations -- "typedefs" -- are not ambiguous, so all the potential parses will have the same alias declarations.)
The usual solution, though, is to parse the program text using a deterministic parser, maintaining a symbol table during the parse, and giving the lexical analyser access to this symbol table so that it can distinguish between IDENTIFIER and TYPE_NAME, as expected by the grammar you link. This technique is politely called "lexical feedback", although it's also often called "the lexer hack".