How do I write a rule that represents left/right-associative infix operators¶ ↑

One of the good example is an arithmetic expression for *, /, + and -. If you use Racc (Yacc-style parser for Ruby), you would write the following rule:

prechigh
  left '*','/'
  left '+','-'
preclow
...
expr : expr '*' expr { result = val[0] * val[2]}
     | expr '/' expr { result = val[0] / val[2]}
     | expr '+' expr { result = val[0] + val[2]}
     | expr '-' expr { result = val[0] - val[2]}
     | NUMBER        { result = val[0].to_i() }

In TDParser, you can write the above rule as follows:

TDParser.define{|g|
  g.expr = chainl(NUMBER >> Proc.new{|x| x[0].to_i},
                  token("*")|token("/"),
                  token("+")|token("-")){|x|
    case x[1]
    when "*"
      x[0] * x[2]
    when "/"
      x[0] / x[2]
    when "+"
      x[0] + x[2]
    when "-"
      x[0] - x[2]
    end
  }
  # ...
}