class Parser
{
    List<Token()> TokenStorage;
    Stack<Token>() RPNStack;
    IExpression# RootNode;
    TokenLinkedList() TokensInRPN;

    internal IExpression# Parse!(){
        SortTokensInRPN();
        BuildTreeFromRPN();
        return RootNode;
    }

    // Implementation of https://en.wikipedia.org/wiki/Shunting_yard_algorithm
    void SortTokensInRPN!(){
        for(int i = 0; i < TokenStorage.Count; i++){
            Token tok = TokenStorage[i];
            int type = tok.GetType();
            switch(type){
                case Token.Type_Number:
                    TokensInRPN.AddToEnd(tok);
                    break;
                case Token.Type_OperatorPow:
                case Token.Type_OperatorMul:
                case Token.Type_OperatorDiv:
                case Token.Type_OperatorMod:
                case Token.Type_OperatorAdd:
                case Token.Type_OperatorSub:
                    while(RPNStack.Count != 0 && RPNStack.Peek().GetType() >= type){
                        Token op2 = RPNStack.Pop();
                        TokensInRPN.AddToEnd(op2);
                    }
                    RPNStack.Push(tok);
                    break;
                case Token.Type_BracketOpen:
                    RPNStack.Push(tok);
                    break;
                case Token.Type_BracketClose:
                    while(RPNStack.Count != 0){
                        Token op2 = RPNStack.Pop();
                        TokensInRPN.AddToEnd(op2);
                    }
                    break;
                case Token.Type_Literal:
                    // not implemented
                    assert false;
                default:
                    // unexpected token type
                    assert false;
            }
        }
        
        // add remaining operators
        while(RPNStack.Count != 0){
            Token op2 = RPNStack.Pop();
            TokensInRPN.AddToEnd(op2);
        }
    }
    
    void BuildTreeFromRPN!(){
        RootNode = new NumericExpression { N = 0 };
        string() graphviz = TokensInRPN.ToGraphVizCode();
        Console.WriteLine(graphviz);
    }
}