.ts

    class Balance {
        
        static Left = new Balance(0, 1)
        static Right = new Balance(1, 0)
        static Empty = new Balance(0, 0)

        L: number
        R: number
        constructor(l: number, r: number) {
            this.L = l;
            this.R = r;
        }

    }

    class MonoidWeight implements monoid<Balance> {
        empty: Balance = Balance.Empty;
        concat(x: Balance, y: Balance): Balance {
            if (x.R < y.L)
                return new Balance(x.L + y.L - x.R, y.R);
            else
                return new Balance(x.L, y.R + x.R - y.L);
        }

    }

    var parse: (c: string) => Balance = (c: string) => {
          switch (c) {
            case "(": return Balance.Left
            case ")": return Balance.Right
            default:  return Balance.Empty
        }
    }

    var weight = new MonoidWeight();
    
    var parsed = Array.from("((()))()").map(parse).reduce(weight.concat, weight.empty); //{L:0,R:0}
    var parsed = Array.from("((()))(").map(parse).reduce(weight.concat, weight.empty); //{L:0,R:1}  
    var parsed = Array.from(")((()))(").map(parse).reduce(weight.concat, weight.empty); //{L:1,R:1}