Improver from Y-NOT RIP Jim

jim-weirich-rip-y-not.ex

fx = 
(fn improver -> improver.(improver) end)
.( fn improver -> fn n -> if n == 0,  do: 1, else: n * improver.(improver).(n-1) end end )

iex(15)> fx = fn  gen ->
...(15)> gen.(gen)
...(15)> end.(
...(15)> fn gen ->
...(15)>   fn n ->
...(15)>     fn partial ->
...(15)>       fn n -> if n == 0, do: 1, else: n * partial.(n-1) end
...(15)>     end.( gen.(gen)).(n)
...(15)> end
...(15)> end)

iex(19)> fact_improver = fn partial -> fn n -> if n < 2, do: n, else: n*partial.(n-1) end end

#Function<44.65746770/1 in :erl_eval.expr/5>
iex(20)> y = fn improver -> fn gen -> gen.(gen) end.(
...(20)>   fn gen -> fn n -> improver.(gen.(gen)).(n) end end
...(20)> ) end
#Function<44.65746770/1 in :erl_eval.expr/5>
iex(21)> fact = y.(fact_improver)
#Function<44.65746770/1 in :erl_eval.expr/5>
iex(22)> fact.(5)
120

# The final, textbook form:
iex(24)> y = fn f ->
...(24)>       fn g -> fn n -> f.(g.(g)).(n) end end.(
...(24)>       fn g -> fn n -> f.(g.(g)).(n) end end )
...(24)> end
#Function<44.65746770/1 in :erl_eval.expr/5>
iex(25)> fibo_improver = fn partial ->
...(25)> fn n -> if n < 2, do: n, else: partial.(n-1) + partial.(n-2) end
...(25)> end
#Function<44.65746770/1 in :erl_eval.expr/5>
iex(26)> fibo = y.(fibo_improver)
#Function<44.65746770/1 in :erl_eval.expr/5>
iex(27)> fibo.(2)
1
iex(28)> fibo.(3)
2
iex(29)> fibo.(4)
3
iex(30)> fibo.(6)
8
iex(31)> fibo.(8)
21