newParser.js

function parse(fullString) {
  let strArray = fullString.split(" ");
  let pos = 0;

  function checkPos() {
    return strArray[pos];
  }

  function isNumber(e) {
    return e !== undefined && e.match(/^-?([1-9][0-9]*|([0]))$/) !== null;
  }

  function jumpNext() {
    pos++;
  }

  function parseNumber() {
    let k = checkPos();
    if (isNumber(k)) {
      jumpNext();
      return { type: "number", value: k };
    } else {
      throw SyntaxError("Invalid Format");
    }
  }

  function parseExp() {
    let expr = parseNumber();
    let k = checkPos();
    while (k === "^") {
      jumpNext();
      let lhs = parseExp();
      expr = { type: k, left: lhs, right: expr };
      k = checkPos();
    }
    return expr;
  }

  function parseMulDiv() {
    let expr = parseExp();
    let k = checkPos();
    while (k === "*" || k === "/") {
      jumpNext();
      let rhs = parseExp();
      expr = { type: k, left: expr, right: rhs };
      k = checkPos();
    }
    return expr;
  }

  function parseAddSub() {
    let expr = parseMulDiv();
    let k = checkPos();
    while (k === "-" || k === "+") {
      jumpNext();
      let rhs = parseMulDiv();
      expr = { type: k, left: expr, right: rhs };
      k = checkPos();
    }
    return expr;
  }

  let output = parseAddSub();
  return output;
}