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In the $F\star$ tutorial it says

Dv, the effect of a computation that may diverge;

what does diverge mean here? It's not explained and it confuses me.

I guess it means the type consists but the value varies, but if so why there isn't a non-diverge non-terminate effect?

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In the theory of computation "diverge" means "does not terminate" or "runs forever". This is a computational effect (of a peculiar kind).

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