> What practical advantages are there?
The major advantage of a language that isn't Turing complete is not having the major risk inherent to Turing complete languages: asking if any non-trivial program will produce any given result or behavior is undecidable[1].
> write a program that runs until the heat death of the universe even in a Turing-incomplete language.
The Halting Problem is just a simple example of program behavior. The undecidability extends to any other behavior. Asking if a given program will behave maliciously is still undecidable even if we only consider the set of programs that do halt in a reasonable amount of time.
When you are using a regular language or deterministic pushdown automata, questions about the behavior or even asking if two implementations are equivalent is decidable. It is at lest possible8 to create software/tools to help answer the question "is this input safe." When you use a non-deterministic pushdown automata or stronger, you problem becomes provably undecidable*,
I highly recommend the talk "The Science of Insecurity"[2].
[1] https://en.wikipedia.org/wiki/Rice%27s_theorem
[2] video: https://archive.org/details/The_Science_of_Insecurity_ slides: [pdf] https://langsec.org/insecurity-theory-28c3.pdf
The major advantage of a language that isn't Turing complete is not having the major risk inherent to Turing complete languages: asking if any non-trivial program will produce any given result or behavior is undecidable[1].
> write a program that runs until the heat death of the universe even in a Turing-incomplete language.
The Halting Problem is just a simple example of program behavior. The undecidability extends to any other behavior. Asking if a given program will behave maliciously is still undecidable even if we only consider the set of programs that do halt in a reasonable amount of time.
When you are using a regular language or deterministic pushdown automata, questions about the behavior or even asking if two implementations are equivalent is decidable. It is at lest possible8 to create software/tools to help answer the question "is this input safe." When you use a non-deterministic pushdown automata or stronger, you problem becomes provably undecidable*,
I highly recommend the talk "The Science of Insecurity"[2].
[1] https://en.wikipedia.org/wiki/Rice%27s_theorem
[2] video: https://archive.org/details/The_Science_of_Insecurity_ slides: [pdf] https://langsec.org/insecurity-theory-28c3.pdf