Each 'leaf' statement of language should have a definite and finite list of exceptions that it can throw.
Each non-leaf statement is a composition of leaf statements. Therefore every exception can be determined, and that's our checked exceptions would work; work at the exceptions and check they match the list.
Therefore even without checked exceptions the compiler could provide the exceptions you want and you can check them or not if you please, so get the best of both worlds. All without forcing people to give an explicit list of exceptions everywhere. Forcing checked exceptions is not going to be popular, and much of the time is counter-productive.
Also someone broke your Liskof Substitution Principle which may be your bigger problem.
Each non-leaf statement is a composition of leaf statements. Therefore every exception can be determined, and that's our checked exceptions would work; work at the exceptions and check they match the list.
Therefore even without checked exceptions the compiler could provide the exceptions you want and you can check them or not if you please, so get the best of both worlds. All without forcing people to give an explicit list of exceptions everywhere. Forcing checked exceptions is not going to be popular, and much of the time is counter-productive.
Also someone broke your Liskof Substitution Principle which may be your bigger problem.