> It’s the only kind of program that can be actually reasoned about.
No. That is one restriction that allows you to theoretically escape the halting problem, but not the only one. Total functional programming languages for example do it by restricting recursion to a weaker form.
Also, more generally, we can reason about plenty of programs written in entirely Turing complete languages/styles. People keep mistaking the halting problem as saying that we can never successfully do termination analysis on any program. We can, on many practical programs, including ones that do dynamic allocations.
Conversely, there are programs that use only a statically bounded amount of memory for which this analysis is entirely out of reach. For example, you can write one that checks the Collatz conjecture for the first 2^1000 integers that only needs about a page of memory.
No. That is one restriction that allows you to theoretically escape the halting problem, but not the only one. Total functional programming languages for example do it by restricting recursion to a weaker form.
Also, more generally, we can reason about plenty of programs written in entirely Turing complete languages/styles. People keep mistaking the halting problem as saying that we can never successfully do termination analysis on any program. We can, on many practical programs, including ones that do dynamic allocations.
Conversely, there are programs that use only a statically bounded amount of memory for which this analysis is entirely out of reach. For example, you can write one that checks the Collatz conjecture for the first 2^1000 integers that only needs about a page of memory.