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authorTanaka Akira2019-02-01 11:00:19 +0900
committerTanaka Akira2019-02-01 11:00:19 +0900
commit162101e6bc5b3bb33b741ff51e37805ffd624d0d (patch)
treeb991010d4c6e75e0a82579c57c7d22f7a5be0557 /pretyping/typeclasses_errors.mli
parentf6f9cf742ee5894be65d6e2de527e3ab5a643491 (diff)
The lowest universe level is 1.
Cic description doesn't describe the lowest universe level clearly. - "Type(i) for any integer i" seems Type(-1) is possible - "S = {Prop,Set,Type(i)| i ∈ ℕ }" depends on the definition of "ℕ" which is not described. It is well known that there are two definitions that ℕ includes 0 or not. In Coq, it is natural that ℕ includes 0 because the inductive type nat includes 0. - "Prop:Type(1), Set:Type(1)" suggests the lowest level is 1. - AX-Prop and AX-Set describes Prop:Type(1) and Set:Type(1). So, Prop and Set are not belongs to Type(0). Also, CPDT describes that "The type of Set is Type(0)". http://adam.chlipala.net/cpdt/html/Universes.html I think the lowest universe level is 1 because AX-Prop and AX-Set. I'm not certain to fix this problem but my idea to fix this problem is changing "Type(i) for any integer i" to "Type(i) for any integer i ≥ 1".
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