Observational equality: now for good
نویسندگان
چکیده
Building on the recent extension of dependent type theory with a universe definitionally proof-irrelevant types, we introduce TTobs, new based setoidal interpretation theory. TTobs equips every an identity relation that satisfies function extensionality, propositional and definitional uniqueness proofs (UIP). Compared to other existing proposals enrich these principles, our features notion reduction is normalizing provides algorithmic canonicity result, which formally prove in Agda using logical framework Abel et al. Our paper thoroughly develops meta-theoretical properties such as decidability conversion checking, well consistency. We also explain how extend quotient version Swan's Id types turn it into proper MLTT inductive equality.
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ژورنال
عنوان ژورنال: Proceedings of the ACM on programming languages
سال: 2022
ISSN: ['2475-1421']
DOI: https://doi.org/10.1145/3498693