Maybe something like this:

def Q():
return Proof1("IsValidProof(X, Q()) => X") +
Proof2("IsValidProof(X, Q())") +
X

where IsValidProof(Statement, Proof) is Goedel's Bew function, Proof1 is a formalization of the argument that "if Q() returns a valid proof of X, then A() will return 1, and X will be true", and Proof2 is a formalization of the argument that "a valid proof of A=>B, followed by a valid proof of A, followed by B, is a valid proof".