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There has never been a requirement for a "true" programming language to be Turing complete.

Also, basically every such language has escape hatches similar to unsafe in Rust to allow expressions that are not provably terminating.

They can then just be accepted as an axiom.

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I feel like Turing completeness has always been set as the boundary of programming language if there's any boundary at all. That's what people has been using to not include HTML as programming language for example. Or to include MTG as one.
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