Operator precedence

There are several methods for dealing with operator precedence in pest:

  1. directly in the PEG grammar;
  2. using a PrecClimber (deprecated);
  3. using a PrattParser.

Given PrattParser is the most general available method that supports unary prefix and suffix operators, we provide more details on its usage.

Pratt Parser

The following pest grammar defines a calculator which can be used for Pratt parsing.

WHITESPACE   =  _{ " " | "\t" | NEWLINE }
  
program      =   { SOI ~ expr ~ EOI }
  expr       =   { prefix* ~ primary ~ postfix* ~ (infix ~ prefix* ~ primary ~ postfix* )* }
    infix    =  _{ add | sub | mul | div | pow }
      add    =   { "+" } // Addition
      sub    =   { "-" } // Subtraction
      mul    =   { "*" } // Multiplication
      div    =   { "/" } // Division
      pow    =   { "^" } // Exponentiation
    prefix   =  _{ neg }
      neg    =   { "-" } // Negation
    postfix  =  _{ fac }
      fac    =   { "!" } // Factorial
    primary  =  _{ int | "(" ~ expr ~ ")" }
      int    =  @{ (ASCII_NONZERO_DIGIT ~ ASCII_DIGIT+ | ASCII_DIGIT) }

Below is a PrattParser that is able to parse an expr in the above grammar. The order of precedence corresponds to the order in which op is called. Thus, mul will have higher precedence than add. Operators can also be chained with | to give them equal precedence.

let pratt =
    PrattParser::new()
        .op(Op::infix(Rule::add, Assoc::Left) | Op::infix(Rule::sub, Assoc::Left))
        .op(Op::infix(Rule::mul, Assoc::Left) | Op::infix(Rule::div, Assoc::Left))
        .op(Op::infix(Rule::pow, Assoc::Right))
        .op(Op::postfix(Rule::fac))
        .op(Op::prefix(Rule::neg));

To parse an expression, call the map_primary, map_prefix, map_postfix, map_infix and parse methods as follows:

fn parse_expr(pairs: Pairs<Rule>, pratt: &PrattParser<Rule>) -> i32 {
    pratt
        .map_primary(|primary| match primary.as_rule() {
            Rule::int  => primary.as_str().parse().unwrap(),
            Rule::expr => parse_expr(primary.into_inner(), pratt), // from "(" ~ expr ~ ")"
            _          => unreachable!(),
        })
        .map_prefix(|op, rhs| match op.as_rule() {
            Rule::neg  => -rhs,
            _          => unreachable!(),
        })
        .map_postfix(|lhs, op| match op.as_rule() {
            Rule::fac  => (1..lhs+1).product(),
            _          => unreachable!(),
        })
        .map_infix(|lhs, op, rhs| match op.as_rule() {
            Rule::add  => lhs + rhs,
            Rule::sub  => lhs - rhs,
            Rule::mul  => lhs * rhs,
            Rule::div  => lhs / rhs,
            Rule::pow  => (1..rhs+1).map(|_| lhs).product(),
            _          => unreachable!(),
        })
        .parse(pairs)
}

Note that map_prefix, map_postfix and map_infix only need to be specified if the grammar contains the corresponding operators.