def P1():
sumU = 0;
for(#U=1; #U<3^^^3; #U++):
if(#U encodes a well-defined boundedly-recursive parameterless function,
that calls an undefined single-parameter function "A" with #U as a parameter):
sumU += eval(#U + #A)
return sumU
def P2():
sumU = 0;
for(#U=1; #U<3^^^3; #U++):
if(#U encodes a well-defined boundedly-recursive parameterless function that calls
an undefined single-parameter function "A" with #U as a parameter):
code = A(#P2)
sumU += eval(#U + code)
return sumU
def A(#U):
Enumerate proofs by length L = 1 ... INF
if found any proof of the form "A()==a implies eval(#U + #A)==u, and A()!=a implies eval(#U + #A)<=u"
break;
Enumerate proofs by length up to L+1 (or more)
if found a proof that A()!=x
return x
return a
Although A(#P2) won’t return #A, I think eval(A(#P2)(#P2)) will return A(#P2), which will therefore be the answer to the reflection problem.
Thoughts on problem 3:
Although A(#P2) won’t return #A, I think eval(A(#P2)(#P2)) will return A(#P2), which will therefore be the answer to the reflection problem.