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Well, some people disagree, as usual; not really an issue; if you need a theory and formal semantics, consult the standard work: https://www.amazon.com/Theory-Objects-Monographs-Computer-Sc....

That's just one person's model. It may be an interesting model, but it's not necessarily "true" in the sense of acceptance. Type theory is also a model, not a definition. It's useful in the practical sense, but that doesn't necessarily mean it defines "types". Competing models may be developed.

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