/**
 * Created by pva701 on 4/13/15.
 */

object Parser {
    trait Expr {

    }
    case class +(l:Expr, r:Expr) extends Expr {}
    case class *(l:Expr, r:Expr) extends Expr {}
    case class W() extends Expr {}
    case class Number(s:String) extends Expr {}
    case class Power(l:Expr, r:Expr) extends Expr {}

    type State = (String, String)
    type Res = (Expr, State)
    def parse(s:String):Expr = expr(nextState(("", s)))._1
    def defaultExpr(state:State, nextOp:State=>Res, constr:(Expr, Expr)=>Expr, charOp:String):Res = {
        val exp = nextOp(state)
        if (exp._2._1 == charOp) {
            val nxSt = defaultExpr(exp._2, nextOp, constr, charOp)
            (constr(exp._1, nxSt._1), nxSt._2)
        } else exp
    }
    def expr(s:State):Res = defaultExpr(s, item, (x, y)=>new +(x, y), "+")
    def item(s:State):Res = power(defaultExpr(s, mul, (x, y)=>new *(x, y), "*"))
    def power(s:Res):Res = s._2._1 match {
        case "^" =>
            val st = expr(nextState(s._2))
            (new Power(s._1, st._1), st._2)
        case _ => s
    }
    def mul(s:State):Res = s._1 match {
        case "(" =>
            val st = expr(nextState(s))
            //if (st._2._1 != ")") throw RuntimeException
            (st._1, nextState(st._2))
        case "w" => (new W(), nextState(s))
        case _ => (new Number(s._1), nextState(s))
    }
    def nextState(s:State):State = {
        s
        /*val sym = s._2.charAt(0)
        sym match {
            //case if s._2
        }*/
    }
}