Halting in non-Turing-complete languages

Question

The halting problem cannot be solved for Turing complete languages and it can be solved trivially for some non-TC languages like regexes where it always halts.

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Answer 1

The short answer is yes, and such languages can even be extremely useful.

There was a discussion about it a few months ago on LtU: http://lambda-the-ultimate.org/node/2846