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Is it that different than a fiat currency with an equally opaque issuance method? At least crypto has whitepapers and the promise of transparency.

I have the same question... if a type is used by the type-checker to verify the consistency of the data it’s annotating, then I don’t see how a recursive definition could provide anything new, other than potentially making type checking run forever...

Although maybe there’s something conceptually satisfying about defining bottom as the only type that refers to itself?

I don’t think the point is being able to use a specific language or to know a specific algorithm, unless the role requires it. If the goal is to test a person’s knowledge and understanding, then the actual implementation is probably less important than their ability to explain and reason about the problem. OTOH, if the goal is to find out whether the person is highly skilled in a specific language and has a lot of experience with an algorithmic domain, then what you’re asking isn’t unreasonable.

I think the point is that no one is being asked to derive a novel algorithm. It’s taken for granted that a person with enough experience will have an understanding of broad categories of algorithms and should be able to reason about the small changes to those algorithms that would be necessary for practical application.