Operator precedence

Operator precedence is realized by means of grammar definition. In other words you put higher prioritized elements into sub-categories. Using this approach you force the parser to branch into those first which leads to earlier evaluation in the end.

Please have a look at this example:

%start Precedence
%title "Operator precedence"
%comment "Shows the handling of operator precedence in `parol`"

%%

// ---------------------------------------------------------
// VARIABLE
Variable: /(?i)[A-Z][0-9A-Z]*/
        ;
Literal : /[0-9]+/
        ;

// ---------------------------------------------------------
// OPERATOR SYMBOLS
Plus    : '+'
        ;
Minus   : '-'
        ;
MulOp   : "\*|/"
        ;

// ---------------------------------------------------------
// PARENTHESIS
LParen  : '('
        ;
RParen  : ')'
        ;

// ---------------------------------------------------------
// EXPRESSIONS in order of increasing precedence
Precedence
        : Summation
        ;
Summation
        : Multiplication { (Plus | Minus) Multiplication }
        ;
Multiplication
        : Factor { MulOp Factor }
        ;
Factor  : Literal
        | Variable
        | Minus Factor
        | LParen Precedence RParen
        ;

Parsing the string -1 + x * 5 with the generated parser will create the following parse tree:

Hint: If the picture is too small please open it in a separate tab via context menu.

Here you can see that the "inner most" operator is evaluated first by the parser, here the negation in production Factor.

The Multiplication is the second highest priority in our example. It is a sub-category of the Summation.

You can try this grammar by calling

parol new --bin --path .\precedence --tree

Open the generated crate and substitute the generated dummy grammar by the one above. Also change the test.txt to the content

-1 + x * 5

Now you can parse this text by calling

cargo run ./test.txt

from the generated crate's root folder.

Since we added the --tree flag at the parol new command parol generates parse trees for us. Search for a test.svg file beside the text.txt file.

I advice to use the parse tree generation feature when developing your grammar and to remove it again when putting your parser into production mode.