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Questions tagged [universe-polymorphism]

Universe polymorphism is the ability for definitions to be implicitly duplicated at different universe levels, with the types they contain. (from nLab).

13 votes
1 answer
429 views

Why did Agda give up cumulative universes?

In Ulf Norell's PhD thesis, which is considered the standard reference of the Agda 2 language, the universes are cumulative, say, Set i is not just an instance of <...
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16 votes
1 answer
400 views

What happened to Conor McBride's universe polymorphism proposal?

Conor proposed a seemingly promising way towards universe polymorphism: https://mazzo.li/epilogue/index.html%3Fp=857&cpage=1.html IMHO, the idea behind this proposal is: You build things starting ...
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8 votes
4 answers
246 views

What's the difference between a universe level and a natural number?

It seems that universe levels are just a type generated by a zero constant and a successor constructor (like in Agda), so why don't we adapt natural numbers as universe levels? In Lean, it is also ...
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