recursivefun.js

const formula = 
  {'+': [
    2, 2, 3,
    {'-': [
      5,
      {'+': [
        2, {'var': 'base-val'}, {var: 'base'},
        {'+': [
          1,
          {'*': [
            1, 4]}]}]}]}]};

const plumbDepths = (depth) => (obj) => {
  const [operator, args] = Object.entries(obj)[0];
  return (operator === 'var')
    ? depth - 1
    : args.map(
      (item) => (is(Object, item)
        ? plumbDepths(depth + 1)(item)
        : depth));
};

const deepestLevel = compose(
  apply(Math.max),
  flatten,
  plumbDepths(0)
);

const obj2ListRec = (obj) => map(map((item) => (Array.isArray(item)
  ? map(
    (child) => (is(Object, child)
      ? obj2ListRec(child)
      : child
    ),
    item)
  : item
  )),
  Object.entries(obj)
);

[
  deepestLevel(formula),
  obj2ListRec(formula),
];