What are Types? Kinds? Constraints? Propositions? Are these always values?
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I'm not sure I agree so universally. Values are granted a lot of power, and consequently need to be evaluated (implying some sort of runtime). Having more constraints on what these things can do can remove the need for evaluation (and its fragility, partiality and performance).
c.f. reflection macros, where types are values. But having said that, one person's compiletime is the next person's runtime!
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I think it's nicer when types and kinds can be manipulated with the same operational semantics (and even syntax!) we use for normal values. Haskell at least now has DataKinds. Scala had path-dependent types since very early, but it's really bulky to use.
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Yes, but the more freedom you have to manipulate them arbitrarily, the less freedom you have to reason about them quickly... it's definitely a trade-off! :)
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Is it really types as values? I though it was much more AST as value.
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You get types as values, too.
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That's only a issue for scala afaik.
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