6÷2(1＋2)＝9 using Racc (failed)

calc2.rb

#!/usr/bin/env ruby

# $ ruby calc2.rb
# 1＋2×3＝7
# 3×(8＋5×(6－2))÷2＝42
# 2(1＋2)－2＝4
# 2(1＋2)÷2＝3
# 6÷2(1＋2)＝1
# 6÷2×(1＋2)＝9

# Racc required (gem install racc)

system("rm calc.y") if test(?f, "calc.y")
system("rm calc.rb") if test(?f, "calc.rb")

open("calc.y", "w") do |f_out|
  f_out.print DATA.read
end

command = "racc -o calc.rb calc.y"
result = `#{command} 2>&1`
if $DEBUG
  puts "$ " + command
  print result
end

require "./calc.rb"

calc = Calc.new()

["1＋2×3", "3×(8＋5×(6－2))÷2",
  "2(1＋2)－2", "2(1＋2)÷2",
  "6÷2(1＋2)", "6÷2×(1＋2)"].each do |expr|
  puts expr + "＝" + calc.parse(expr).to_s
end

# http://mollifier.hatenablog.com/entry/20090823/p1
__END__
class Calc
  token NUM
prechigh
  left '×' '÷' CONCAT
  left '＋' '－'
preclow
rule
  expr : expr '＋' expr { result = val[0] + val[2] }
       | expr '－' expr { result = val[0] - val[2] }
       | expr '×' expr { result = val[0] * val[2] }
       | expr expr =CONCAT { result = val[0] * val[1] }
       | expr '÷' expr { result = val[0] / val[2] }
       | prim          { result = val[0] }

  prim : NUM          { result = val[0] }
       | '(' expr ')' { result = val[1] }
end

---- inner
  def parse(str)
    @tokens = str.split(/([\(\)＋－×÷])/).select{|c| !c.nil? && c != ""}
    do_parse()
  end

  def next_token()
    token = @tokens.shift()
    case token
    when /^\d+\z/
      return [:NUM, token.to_i]
    when nil
      return nil
    else
      return [token, nil]
  end
end