Verifying a Semantic βη-Conversion Test for Martin-Löf Type Theory

@inproceedings{Abel2008VerifyingAS,
  title={Verifying a Semantic βη-Conversion Test for Martin-L{\"o}f Type Theory},
  author={Andreas Abel and Thierry Coquand and Peter Dybjer},
  year={2008}
}

• Andreas Abel, Thierry Coquand, Peter Dybjer
• Published 2008

Type-checking algorithms for dependent type theories often rely on the interpretation of terms in some semantic domain of values when checking equalities. Here we analyze a version of Coquand’s algorithm for checking the βη-equality of such semantic values in a theory with a predicative universe hierarchy and large elimination rules. Although this algorithm does not rely on normalization by evaluation explicitly, we show that similar ideas can be employed for its verification. In particular… CONTINUE READING

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