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- W3162133925 abstract "When we investigate a type system, it is helpful if we can establish the well-foundedness of types or terms with respect to a certain hierarchy, and the Extended Calculus of Constructions (called $ECC$, defined and studied comprehensively in [Luo,1994]) is no exception. However, under a very natural hierarchy relation (called the cumulativity relation in [Luo,1994]), the well-foundedness of the hierarchy does not hold generally. In this article,we show that the cumulativity relation is well-founded if it is restricted to one of the following two natural families of terms: begin{enumerate} item types in a valid context item terms having normal forms end{enumerate} Also, we give an independent proof of the existence of principal types in $ECC$ since it is used in the proof of well-foundedness of cumulativity relation in a valid context although it is often proved by utilizing the well-foundedness of the hierarchy, which would make our argument circular if adopted." @default.
- W3162133925 created "2021-05-24" @default.
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- W3162133925 date "2020-09-07" @default.
- W3162133925 modified "2023-09-25" @default.
- W3162133925 title "On principal types and well-foundedness of the cummulativity relation in ECC" @default.
- W3162133925 cites W1538467230 @default.
- W3162133925 doi "https://doi.org/10.48550/arxiv.2009.03486" @default.
- W3162133925 hasPublicationYear "2020" @default.
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