First off, consider what would happen if we had a halting detector. We know from the diagonal argument that there exists at least one program that would cause a halting detector to either never halt or give a wrong answer. But that's a bizarre and unlikely program.

There is another argument though that a halting detector is impossible, and that is the more intuitive argument that a halting detector would be magical. Suppose you want to know if Fermat's Last Theorem is true or false. You just write a program that halts if it is true and runs forever if it is false, and then run the halting detector on it. You don't run the program, you just run the halting detector on the program. A halting detector would enable us to immediately solve a huge number of open problems in number theory just by writing programs.

So, can you write a programming language that is guaranteed to produce programs whose halting can be always determined? Sure. It just can't have loops, conditions or be able to use arbitrarily much storage. If you're willing to live with no loops, or no "if" statements, or a strictly restricted amount of storage, then sure, you can write a language whose halting is always determinable.

First off, consider what would happen if we had a halting detector. We know from the diagonal argument that there exists at least one program that would cause a halting detector to either never halt or give a wrong answer. But that's a bizarre and unlikely program.

There is another argument though that a halting detector is impossible, and that is the more intuitive argument that a halting detector would be magical. Suppose you want to know if Fermat's Last Theorem is true or false. You just write a program that halts if it is true and runs forever if it is false, and then run the halting detector on it. You don't run the program, you just run the halting detector on the program. A halting detector would enable us to immediately solve a huge number of open problems in number theory just by writing programs.

So, can you write a programming language that is guaranteed to produce programs whose halting can be always determined? Sure. It just cannot have loops, conditions and use arbitrarily much storage. If you're willing to live with no loops, or no "if" statements, or a strictly restricted amount of storage, then sure, you can write a language whose halting is always determinable.