from itertools import product def h(w): """Gödelisierung""" sum = 0 for index, ch in enumerate(w): ko = 0 if ch == "a": ko = 1 if ch == "b": ko = 2 sum += ko * 3 ** (len(w) - index - 1) return sum def p_pred(goed): """Prädikat testet, ob eine natürliche Zahl Gödelnummer ist""" n = 0 sum = 0 while sum < goed: for combination in product([1, 2], repeat = n): sum = 0 #combination = list(combination)[::-1] #print("Combination", combination) for index, coeff in enumerate(combination): sum += coeff * 3 ** index #print(str(coeff) + " * 3 ** " + str(index)) #print("Sum", sum, "=", goed, "?") if sum == goed: return list(combination)[::-1] n += 1 return [] def p(r, y): if p_pred(y) and r <= y: return 1 return 0 def g(n): """Folge der Gödelnummern""" def f(p1, p2): m = 0 while True: minus = 1 - p(p1, m) if minus < 0: minus = 0 if minus == 0: #print("return f", m) return m m += 1 if n == 1: ret = f(0, n) #print("return n==1", ret) return ret else: res = f(g(n - 1) + 1, n) #print("return else", res) return res def k(n): """k(n) = h^-1(g(n))""" w = "" coeffs = p_pred(n) print(coeffs) for coeff in coeffs: ch = "" if coeff == 1: ch = "a" if coeff == 2: ch = "b" w += ch return w w = "a" goedel_number = h(w)
#h(w): Goedelnummer zu w #g(n): n-te Goedelnummer #k(n): w zur n-ten Goedelnummer w = "abb" print("w", w) goedel_number = h(w) print("goedel_number", goedel_number) print("g", g(goedel_number)) print(k(goedel_number))
ausführen
for i in range(1, 11): print(g(i))
