[Agda] How does level polymorphism fit into a valid type theory?
(from "More universe polymorphism")
Darryl McAdams
psygnisfive at yahoo.com
Sun Jun 30 16:59:23 CEST 2013
Using type judgments like this suggests that there should be ways to have universe polymorphism but also allow "obnoxiously large" types like
((i : Level) -> Set i) -> (i : Level) -> Set i
but wouldn't allow something like this:
id : {i : Level} {A : Set i} -> A -> A
id x = x
-- this should fail
id id : {i : Level} {A : Set i} -> A -> A
because you can't get the judgment that the type of id is a Set i for some i, all you can get is that it's a type. is it then impossible to give id a type so that self application is possible, without yielding some form of inconsistency?
- darryl
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