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Interesting use cases for universal quantifiers in rank 2?Trevor Jim’s System P_{2} types the same terms as the secondrank System F_{2}, but function arguments can only be typed as (finite) intersections of simple types. This restriction is reasonable and also seems to correspond neatly to the inner workings of a compiler which specializes polymorphic functions for every usage (such as Rust’s, IIRC). What do we lose, relative to F_{2}? Here are the things that I can think of (in fact, they also apply to unrestricted System P, which prohibits universal quantifiers in negative positions):
Anything else? Side note: What is then the class of all datatypes whose induction principles fit into P_{2}? Is it interesting or any bigger than that for HM? I don’t understand what intersections could mean as eliminator arguments. By Alex Shpilkin at 20161023 00:23  LtU Forum  previous forum topic  next forum topic  other blogs  2738 reads

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