// Make a parser that eaves symbols unchanged
ometa CalcParser2 <: Parser {
  fromTo :x :y = seq(x) (~seq(y) char)* seq(y), 
  space        = super(#space) | fromTo('//', '\n') | fromTo('/*', '*/'),
  nameFirst    = letter | '$' | '_',
  nameRest     = nameFirst | digit,
  symbol       = firstAndRest(`nameFirst, `nameRest):r                         -> r.join(''),
 
  digit    = super(#digit):d          -> d.digitValue(),
  number   = number:n digit:d         -> (n * 10 + d)
           | digit,
  addExpr  = addExpr:x '+' mulExpr:y  -> [`Plus, x, y]
           | addExpr:x '-' mulExpr:y  -> [`Plus, x, [`Times, -1, y]]
           | mulExpr,
  mulExpr  = mulExpr:x '*' primExpr:y -> [`Times, x, y]
           | mulExpr:x '/' primExpr:y -> [`Times, x, [`Power, y, -1]]
           | primExpr,
  primExpr = '(' expr:x ')'           -> x
           | symbol:s                 -> s
           | number:n                 -> [`Number, n],
  expr     = addExpr
}

// Works as expected
CalcParser2.matchAll('xy2', 'primExpr')
CalcParser2.matchAll('2', 'primExpr')

CalcParser2.matchAll('6*(4+3)', 'expr')
CalcParser2.matchAll('6*(4-3)', 'expr')
CalcParser2.matchAll('6*(x+y)', 'expr')
CalcParser2.matchAll('x+0', 'expr')

// Try to normalize, using rules like x+0 = 0
ometa CalcNormalizer {
  anumber = [`Number anything:x],
  normalize = [`Plus anything:x [`Number 0]]        -> x
            | [`Plus anything:x anything:x]         -> [`Times, 2, x],
  normalizedistributive = [`Plus [`Times anumber:a anything:x]  [`Times anumber:b anything:x]] -> [`Times, [`Plus, a, b], x]
            | anything:x -> x
}

tree = CalcParser2.matchAll('x+0', 'expr')
CalcNormalizer.match(tree, 'normalize')

tree = CalcParser2.matchAll('x+x', 'expr')
CalcNormalizer.match(tree, 'normalize')


tree = CalcParser2.matchAll('2*x+3*x', 'expr')
CalcNormalizer.match(tree, 'normalizedistributive')

tree = CalcParser2.matchAll('2*x+a*x', 'expr')
CalcNormalizer.match(tree, 'normalizedistributive')

// Hmmm...
tree = CalcParser2.matchAll('2*(x+y)+3*(x+y+z)', 'expr')
CalcNormalizer.match(tree, 'normalizedistributive')