Re: First/Follow sets in Recursive Descent Parsers

It seems like the best way to know if it is the integration variable
is not to use the prefix 'd' to discriminate, but to use the closing
"}". This seems to imply that you need two tokens of lookahead (or
lookbehind) between the lexer and the parser. If the lexer sees the
"}" it should fix the preceding token before the parser sees it.
Alternatively, you can use a parser with two tokens of lookahead. If
you decide to fix it in the lexer rather than the parser then an added
complication is nested "}" for integration. You'll probably need a
special flex START state to handle this properly.


Tom Moog
Polhode, Inc.


Dan Haxell <Dan.Haxell@btinternet.com> wrote:
>I am currently writing a utility to translate LaTeX math expressions
>into Maple syntax. So far I have been using Flex to generate the
>lexical analyser and then hand-coding a recursive descent parser (in
>C++).
>
>It is based on the following grammar expressed in EBNF:
>
>expression = ['+' | '-'] term { ('+' | '-') term }.
>term = factor ( { ('*' | '/') factor } | { factor } ).
>factor = entity [ '^' '{' expression '}' ].
>entity = NUMBER | VARIABLE [ '(' expression ')' ] | '(' expression ')' |
>integral.
>integral = '\int' [subscript superscript] '{' expression 'd' VARIABLE '}'.
>subscript = '_' ( '{' expression '}' | (VARIABLE | NUMBER) ).
>superscript = '^' ( '{' expression '}' | (VARIABLE | NUMBER) ).
>
>Using this, strings of letters such as 'abc' are translated as products:
>'a*b*c'.
>
>Each non-terminal is implemented as a void function that returns a
>string containing the Maple translation, e.g. string factor(void).
>
>The problem I have is when parsing an integral: during the parse, I
>want the letter 'd' to have a new meaning, namely to designate the end
>of the expression and indicate the variable to integrate. This should
>only be the case when parsing an integral and normally it should be
>treated as a simple variable.
>
>However, when parsing the expression 2x dx, the 'dx' is not recognised
>as being special since the program is still in the Expression()
>function and thus parses as 2*x*d*x.
>
>Would passing First/Follow sets (stop sets??) to each function allow
>for situations such as this? Many of the examples of RDPs use void
>functions as well.

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