The Calc parser from http://www.vpri.org/pdf/tr2008003_experimenting.pdf in Scala

gistfile1.scala

class Calc extends PackratParsers {
  type Elem = Char

  val vars = mutable.Map[Char,Int]()

  def parse(input:CharSequence) = doIt(new PackratReader(new CharSequenceReader(input)))

  val spaces:  Parser[Seq[Char]] = elem("Whitespace", _.isWhitespace)*
  val digit:   Parser[Char]      = elem("Digit",      _.isDigit)
  val letter:  Parser[Char]      = elem("Letter",     _.isLetter)

  val aVar:    Parser[Char]      = letter
  val num:     Parser[Int]       = ((digit)+) ^^ { _.mkString.toInt }
  
  val priExpr: Parser[Int] = 
    ( spaces ~> aVar ^^ { vars(_) }
    | spaces ~> num
    | '('~>expr<~')'  )
  
  lazy val mulExpr: PackratParser[Int] =
    ( mulExpr~'*'~priExpr ^^ { case x~_~y => x*y } 
    | mulExpr~'/'~priExpr ^^ { case x~_~y => x/y }
    | priExpr )
  
  lazy val addExpr: PackratParser[Int] =
    ( addExpr~'+'~mulExpr ^^ { case x~_~y => x+y }
    | addExpr~'-'~mulExpr ^^ { case x~_~y => x-y }
    | mulExpr )

  lazy val expr: Parser[Int] = 
    ( aVar~'='~expr ^^ { case v~_~e => vars(v) = e; e }
    | addExpr )

  lazy val doIt: Parser[Int] = rep1sep(expr,';'~spaces)<~spaces ^^ ( _.last )
}

object CalcSpec extends Properties("Calc") {
  val N = Gen.choose(0,100)
  val Np = Gen.choose(1,100)
  val C = Gen.choose('A','Z')

  property("Literals") = forAll(N)     {   i => parse(i.toString) == i }

  property("Sum")      = forAll(N,N)   {  (x,y) => parse(x+"+"+y)    == x+y }
  property("Subt")     = forAll(N,N)   {  (x,y) => parse(x+"-"+y)    == x-y }
  property("Mult")     = forAll(N,N)   {  (x,y) => parse(x+"*"+y)    == x*y }
  property("Div")      = forAll(N,Np)  {  (x,y) => parse(x+"/"+y)    == x/y }
 
  property("Presedence") = 
     ( forAll(N,N,N) { (x,y,z) => parse(    x+"+"+y+ "*"+z) == x+(y*z) }
    && forAll(N,N,N) { (x,y,z) => parse("("+x+"+"+y+")*"+z) == (x+y)*z } )

   property("Store") = forAll(C,N) { (c,n) => parse(c+"="+n) == n }
   property("Load" ) = forAll(C,N) { (c,n) => parse(c+"="+n+";"+c+"+"+c) == n+n }
   property("Mutation" ) = forAll(C,N,N) { (c,x,y) => parse(c+"="+x+";"+c+"="+y+";"+c) == y }

  private def parse(in:String) = (new Calc).parse(in).get
}