const N = 10

// sum natural numbers from 1 to n
const sumNat = n => n * (n + 1) / 2
console.log(`sumNat(${N}) = ${sumNat(N)}`)

// implement iteratively
const sumNat1 = n => {
  let count = 0
  for (let i = 1; i <= n; i++) count += i
  return count
}
console.log(`sumNat1(${N}) = ${sumNat1(N)}`)

// implement exact algorithm recursively
const sumNat2 = (n, i = 1, count = 0) =>
  i <= n ? sumNat2(n, i + 1, count + i) : count
console.log(`sumNat2(${N}) = ${sumNat2(N)}`)

// recurse from n to 1 instead of 1 to n
const sumNat3 = (n, count = 0) =>
  n ? sumNat3(n - 1, count + n) : count
console.log(`sumNat3(${N}) = ${sumNat3(N)}`)

// recurse then add instead of add then recurse
const sumNat4 = n => n ? sumNat4(n - 1) + n : 0
console.log(`sumNat4(${N}) = ${sumNat4(N)}`)

// generate array from 1 to n with ugly hack
const range = n => [...Array(n).keys()].map(i => i + 1)

// add all the things
const sum1 = ns => ns.reduce((count, n) => count + n)
console.log(`sum1(range(${N})) = ${sum1(range(N))}`)

// create reusable function
const add_ = (x, y) => x + y
const sum2 = ns => ns.reduce(add_)
console.log(`sum2(range(${N})) = ${sum2(range(N))}`)

// curry all the things
const reduce = combine => init => xs => {
  const uncurry = f => (x, y) => f(x)(y)
  return xs.reduce(uncurry(combine), init)
}
const add = x => (y => x + y)
// sum = ns => helper(ns) is just sum = helper
const sum3 = /* ns => */ reduce(add)(0)/* (ns) */
console.log(`sum3(range(${N})) = ${sum3(range(N))}`)

// multiply all the things
const mult = x => y => x * y
const prod1 = reduce(mult)(1)
// calculate the factorial
console.log(`prod1(range(${N})) = ${prod1(range(N))}`)

// generalize the pattern
const combineAll = ({combine, makeInit}) => {
  const init = makeInit()
  return reduce(combine)(init)
}

// implement addition
const addMonoid = { combine: add, makeInit: () => 0 }
const sum4 = combineAll(addMonoid)
console.log(`sum4(range(${N})) = ${sum4(range(N))}`)

// implement multiplication
const multMonoid = { combine: mult, makeInit: () => 1 }
const prod2 = combineAll(multMonoid)
console.log(`prod2(range(${N})) = ${prod2(range(N))}`)

// implement concatenation
const concat = xs => ys => [...xs, ...ys]
const concatMonoid = { combine: concat, makeInit: () => [] }
const flatten = combineAll(concatMonoid)
const nestedArrays = [range(3), range(2), range(1)]
console.log(`flatten(${
  JSON.stringify(nestedArrays)}) = ${
  JSON.stringify(flatten(nestedArrays))}`)

/*
 * Tex recommends:
 * - drboolean.gitbooks.io/mostly-adequate-guide-old
 * - sanctuary.js.org
 * - gcanti.github.io/fp-ts
 * - reasonml.github.io
 */