I think the best patch to fix this issue is to take a Turing-complete language such as the lambda calculus, and augment it by adding an operator that tests limiting expressions for convergence. A convergence tester is sufficient to build a halting oracle, and I believe but have not verified that a halting oracle is sufficient to build a convergence tester. Limits, however, are easier to translate into other languages that a prior might be defined over.
I think the best patch to fix this issue is to take a Turing-complete language such as the lambda calculus, and augment it by adding an operator that tests limiting expressions for convergence. A convergence tester is sufficient to build a halting oracle, and I believe but have not verified that a halting oracle is sufficient to build a convergence tester. Limits, however, are easier to translate into other languages that a prior might be defined over.