const concat = (x, y) => x.concat(y)
const mconcat = (xs, empty) => xs.length ? xs.reduce(concat) : empty()
const concatMap = (f, xs) => xs.reduce(
  (acc, x) => {
    const r = f(x)
    return (acc || r.empty()).concat(r)
  },
  null
)

const Sum = value => ({
  value,
  result: () => value,
  concat: y => Sum(value + y.value),
  empty: () => Sum.empty()
})
Sum.of = Sum
Sum.empty = () => Sum(0)

const Count = value => ({
  value,
  result: () => value,
  concat: y => Count(value + y.value),
  empty: () => Count.empty()
})
Count.of = () => Count(1)
Count.empty = () => Count(0)

const Mean = (sum, count) => ({
  sum,
  count,
  result: () => sum.value / count.value,
  concat: y => Mean(sum.concat(y.sum), count.concat(y.count)),
  empty: () => Mean.empty()
})
Mean.of = value => Mean(Sum(value), Count(1))
Mean.empty = () => Mean(Sum.empty(), Count.empty())

const Square = value => ({
  value,
  result: () => value,
  concat: y => Square(value + y.value),
  empty: () => Square.empty()
})
Square.of = x => Square(x * x)
Square.empty = () => Square(0)

const StdDev = (mean, square) => ({
  mean,
  square,
  result: () => Math.sqrt(mean.count.value * square.value - mean.sum.value * mean.sum.value) / mean.count.value,
  concat: y => StdDev(mean.concat(y.mean), square.concat(y.square)),
  empty: () => StdDev.empty()
})
StdDev.of = x => StdDev(Mean.of(x), Square.of(x))
StdDev.empty = () => StdDev(Mean.empty(), Square.empty())

mconcat([
  StdDev.of(600),
  StdDev.of(470),
  StdDev.of(170),
  StdDev.of(430),
  StdDev.of(300)
], StdDev.empty).result()
// 147.xyz

concatMap(StdDev.of, [600, 470, 170, 430, 300]).result()
// Same