// a recognizer that also interprets

ometa Calc {
  digit    = ^digit:d                 -> d.digitValue(),
  number   = number:n digit:d         -> (n * 10 + d)
           | digit,
  addExpr  = addExpr:x '+' mulExpr:y  -> (x + y)
           | addExpr:x '-' mulExpr:y  -> (x - y)
           | mulExpr,
  mulExpr  = mulExpr:x '*' primary -> (x * y)
           | mulExpr:x '/' primary -> (x / y)
           | primary,
  primary = '(' expr:x ')'           -> x
           | number,
  expr     = addExpr
}

Calc.matchAll('3+4*(5+1)', 'expr')


ometa Calc2 {
  digit    = ^digit:d                 -> d.digitValue(),
  number   = number:n digit:d         -> (n * 10 + d)
           | digit,
  Expr  = Expr:x '+'Term:y  -> (x + y)
           | Expr:x '-' Term:y  -> (x - y)
           | Term,
  Term  = Term:x '*' Factor:y -> (x * y)
           | Term:x '/' Factor:y -> (x / y)
           | Factor,
  Factor = Factor:x '^' Primary:y -> Math.pow(x,y),
  Factor2 = '(' Expr:x ')' -> x
           | number,
  Start     = Expr
}

Calc2.matchAll('3+4*5', 'Start')