To follow the rule of rigor is to see how conducting a proof with rigor is like a machine executing a program. This is not a mere analogy but an isomorphism. Once we omit the content of an argument by symbolizing its logical structure, drawing inferences becomes isomorphic with running software. That is, every proof is a kind of computation, and vice versa . Logical expressions composed of symbols correspond to bytes of bits.
Premises correspond to input.
Rules of inference correspond to the functions in a program. Conclusions correspond to output. Proof corresponds to computation. Hence, limits on provability correspond to limits on computability. This brings clarity to both logic and computation.