ANTLR4 simple expression grammar. Note that left recursion is now allowed and operator precedence is just order of definition.

Expr.g4

grammar Expr;

// Need to call recursive rule expr from non-recursive rule
r     : expr+ ;

// ANTLR4 : Left recursion!
// Operator precedence matches order of definition
expr  : '-' expr                // Unary minus
      | expr ('*' | '/' ) expr
      | expr ('+' | '-' ) expr
      | '(' expr ')'
      | INT
      | ID
      ;

INT   : [0-9]+ ;
ID    : [a-z]+ ;
WS    : [ \t\r\n]+ -> skip;

Testing:

>> grun Expr r -tree
1 - -2
^D
(r (expr (expr 1) - (expr - (expr 2))))

Thank you a lot, I couldn't deal with right order of operations for a long time, and now after I run into your example, it finally works as I expected!