async-quicksort.js

function asyncQuicksort(xs = []) {
  // get the "head" and "tail" of the array
  let [h, ...t] = xs
  // create the initial Promise
  return new Promise((res, rej) => {
    // resolve immediately if "head" was undefined
    if (!h) return res([])
    // recurse for the "left" half of the partition
    asyncQuicksort(t.filter(a => a <= h)).then(a => {
      // recurse for the "right" half of the partition
      asyncQuicksort(t.filter(a => a > h)).then(b => {
        // join each half on the pivot and resolve the promise
        res(a.concat(h, b))
      }).catch(rej) // in case your array is too long catch the error
    }).catch(rej)
  })
}

asyncQuicksort('the quick brown fox jumps over the lazy dog'.split(''))
  .then(a => log(a.join('')))
  .catch(log)