fizzbuzz.cs

// FizzBuzz in pure lambda notation
// transcribed from http://codon.com/programming-with-nothing
// props to http://community.bartdesmet.net/blogs/bart/archive/2009/08/17/mis-using-c-4-0-dynamic-type-free-lambda-calculus-church-numerals-and-more.aspx
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApplication1
{
    using Fn = Func<dynamic, dynamic>;
    class Program
    {
        static int to_int(Fn fn)
        {
            return fn(new Fn(x => x + 1))(0);
        }
        static bool to_bool(dynamic fn)
        {
            return fn(true)(false);
        }
        static List<object> to_list(Fn fn)
        {
            var list = new List<object>();
            var LEFT = new Fn(p => p(new Fn(x => new Fn(y => x))));
            var RIGHT = new Fn(p => p(new Fn(x => new Fn(y => y))));
            var FIRST = new Fn(l => LEFT(RIGHT(l)));
            var REST = new Fn(l => RIGHT(RIGHT(l)));
            while (!to_bool(LEFT(fn)))
            {
                list.Add(FIRST(fn));
                fn = REST(fn);
            }
            return list;
        }
        static string to_string(Fn fn)
        {
            var str = "";
            var alpha = "0123456789BFiuz";
            foreach (var c in to_list(fn))
            {
                str += alpha[to_int((Fn)c)];
            }
            return str;
        }
        static void Main(string[] args)
        {
            var ZERO = new Fn(f => new Fn(x => x));
            var ONE = new Fn(f => new Fn(x => f(x)));
            var TWO = new Fn(f => new Fn(x => f(f(x))));
            var THREE = new Fn(f => new Fn(x => f(f(f(x)))));
            var FOUR = new Fn(f => new Fn(x => f(f(f(f(x))))));
            var FIVE = new Fn(f => new Fn(x => f(f(f(f(f(x)))))));

            var INC = new Fn(n => new Fn(p => new Fn(x => p(n(p)(x)))));
            var DEC = new Fn(n => new Fn(f => new Fn(x => n(new Fn(g => new Fn(h => h(g(f)))))(new Fn(u => x))(new Fn(u => u)))));
            var PLUS = new Fn(m => new Fn(n => new Fn(f => new Fn(x => m(f)(n(f)(x))))));
            var MINUS = new Fn(m => new Fn(n => n(DEC)(m)));
            var MUL = new Fn(m => new Fn(n => new Fn(f => n(m(f)))));
            var POW = new Fn(m => new Fn(n => n(m)));

            var FIFTEEN = MUL(FIVE)(THREE);
            var HUNDRED = MUL(MUL(FIVE)(FIVE))(FOUR);

            var FALSE = new Fn(a => new Fn(b => b));
            var TRUE = new Fn(a => new Fn(b => a));
            var IF = new Fn(b => new Fn(x => new Fn(y => b(x)(y))));
            var IS_ZERO = new Fn(n => n(new Fn(x => FALSE))(TRUE));
            var LEQ = new Fn(m => new Fn(n => IS_ZERO(MINUS(m)(n))));
            var Z = new Fn(f => new Fn(x => f(new Fn(y => x(x)(y))))
                               (new Fn(x => f(new Fn(y => x(x)(y))))));

            var MOD = Z(new Fn(f => new Fn(m => new Fn(n =>
                            IF(LEQ(n)(m))
                              (new Fn(x => f(MINUS(m)(n))(n)(x)))
                              (m)))));

            var PAIR = new Fn(x => new Fn(y => new Fn(f => f(x)(y))));
            var LEFT = new Fn(p => p(new Fn(x => new Fn(y => x))));
            var RIGHT = new Fn(p => p(new Fn(x => new Fn(y => y))));
            var EMPTY = PAIR(TRUE)(TRUE);
            var UNSHIFT = new Fn(l => new Fn(x => PAIR(FALSE)(PAIR(x)(l))));
            var IS_EMPTY = LEFT;
            var FIRST = new Fn(l => LEFT(RIGHT(l)));
            var REST = new Fn(l => RIGHT(RIGHT(l)));

            var RANGE =
                  Z(new Fn(f => new Fn(m => new Fn(n =>
                      IF(LEQ(m)(n))
                       (new Fn(x => UNSHIFT(f(INC(m))(n))(m)(x)))
                       (EMPTY)
                  ))));

            var FOLD =
              Z(new Fn(f => new Fn(l => new Fn(x => new Fn(g =>
                  IF(IS_EMPTY(l))
                    (x)
                    (new Fn(y =>
                      g(f(REST(l))(x)(g))(FIRST(l))(y))))))));

            var MAP =
               new Fn(k => new Fn(f =>
                FOLD(k)(EMPTY)
                   (new Fn(l => new Fn(x => UNSHIFT(l)(f(x)))))));

            var TEN = MUL(TWO)(FIVE);
            var B   = TEN;
            var F   = INC(B);
            var I   = INC(F);
            var U   = INC(I);
            var ZED = INC(U);
            var FIZZ = UNSHIFT(UNSHIFT(UNSHIFT(UNSHIFT(EMPTY)(ZED))(ZED))(I))(F);
            var BUZZ = UNSHIFT(UNSHIFT(UNSHIFT(UNSHIFT(EMPTY)(ZED))(ZED))(U))(B);
            var FIZZBUZZ = UNSHIFT(UNSHIFT(UNSHIFT(UNSHIFT(BUZZ)(ZED))(ZED))(I))(F);

            var DIV = Z(new Fn(f => new Fn(m => new Fn(n =>
                IF(LEQ(n)(m))
                   (new Fn(x => INC(f(MINUS(m)(n))(n))(x)))
                   (ZERO)))));

            var PUSH =
               new Fn(l => new Fn(x =>
                  FOLD(l)(UNSHIFT(EMPTY)(x))(UNSHIFT)));

            var TO_DIGITS =
              Z(new Fn(f => new Fn(n =>
                PUSH(
                  IF(LEQ(n)(DEC(TEN)))
                    (EMPTY)
                    (new Fn(x => f(DIV(n)(TEN))(x)))
                )(MOD(n)(TEN)))));

            var result = MAP(RANGE(ONE)(HUNDRED))(new Fn(n =>
              IF(IS_ZERO(MOD(n)(FIFTEEN)))
                (FIZZBUZZ)
                (IF(IS_ZERO(MOD(n)(THREE)))
                  (FIZZ)
                  (IF(IS_ZERO(MOD(n)(FIVE)))
                    (BUZZ)
                    (TO_DIGITS(n))))
            ));

            foreach (var row in to_list(result))
            {
                Console.WriteLine(to_string((Fn)row));
            }

        }
    }
}