webinar 2 Javascript

webinar2.js

print("\n\n\n")

// волшебная троица
const cons = (x, y) => [x,y]
const car = (l) => l[0]
const cdr = (l) => l[1]


// scons(h, t) = cons(h, lz(() => t))

const lz = (x) => x

// хвост потока
const stail = (s) => {
  const t = cdr(s) 
  return (typeof t === "function") ? t() : t
  }


// часть потока в вектор
const stake = (n, s) => {
  r = []
  while (n>0) {
    r.push(car(s))
    s = stail(s)
    n = n-1
    }
  return r
  }



const ones = cons(1, lz(() => ones))
print(stake(10, ones))


const intfrom = (n) => cons(n, lz(() => intfrom(n+1)))
print(stake(10, intfrom(1)))


const ssum = (a, b) => cons(car(a)+car(b), lz(() => ssum(stail(a), stail(b))))


const fibs = cons(0, cons(1, lz(() => ssum(stail(fibs), fibs))))
print(stake(10, fibs))


const smap = (f, s) => cons(f(car(s)), lz(() => smap(f, stail(s))))
const sk = (k, s) => smap((x) => k*x, s)


const n = 50


print("\nчисла Хэмминга:")
const merge = (a, b) =>
  (car(a) < car(b)) ? cons(car(a), lz(() => merge(stail(a), b))) :
  (car(a) > car(b)) ? cons(car(b), lz(() => merge(a, stail(b)))) :
                      cons(car(a), lz(() => merge(stail(a), stail(b))))

const hamm = cons(1, lz(() => merge(sk(2,hamm), merge(sk(3,hamm), sk(5,hamm)))))
print(stake(n, hamm))

    
// потоковые аналоги списковых функций

const sfilter = (f, s) =>
  f(car(s)) ? cons(car(s), lz(() => sfilter(f, stail(s)))) : sfilter(f, stail(s))


// тестовые примеры

print("\nряд Фибоначчи (НЕ экспоненциальный расчет):")
const fibgen = (a,b) => cons(a, lz(() => fibgen(b, a+b)))
const fibs1 = fibgen(0,1)
print(stake(n, fibs1))

print("\nчетные числа:")
const evens = sfilter((x) => x%2 === 0, intfrom(0))
print(stake(n, evens))

print("\nпростые числа через решето Эратосфена:")
const sieve = (s) => {
    const r = sfilter((x) => x % car(s) != 0, stail(s))
    return cons(car(s), lz(() => sieve(r)))
    }
const primesErat = sieve(intfrom(2))
print(stake(n, primesErat))

print("\nпростые числа через гипотезу Бертрана:")
const primesBert = () => cons(2, lz(() => sfilter(isprime, intfrom(3))))
const isprime = (n) => {
    const iter = (ps) => 
      (car(ps)*car(ps) > n) ? true :
      (n % car(ps) === 0) ? false :
      iter(stail(ps))
    return iter(primesBert())
    }
print(stake(n, primesBert()))

print("\nчастичные суммы натурального ряда:")
const partialsums = (s) => {
  const go = (a, s) => cons(a+car(s), lz(() => go(a+car(s), stail(s))))
  return go(0, s)
  }
print(stake(n, partialsums(intfrom(1))))