• Corpus ID: 244773615

Finitary type theories with and without contexts

@article{Haselwarter2021FinitaryTT,
  title={Finitary type theories with and without contexts},
  author={Philipp G. Haselwarter and A. Bauer},
  journal={ArXiv},
  year={2021},
  volume={abs/2112.00539}
}
We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin-L\"of type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We prove several general meta-theorems about finitary type theories: weakening, admissibility of substitution and instantiation of metavariables, derivability of presuppositions, uniqueness of typing, and inversion principles. We then give a second formulation of… 
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An extensible equality checking algorithm for dependent type theories
TLDR
A general and user-extensible equality checking algorithm that is applicable to a large class of type theories, which has a type-directed phase for applying extensionality rules and a normalization phase based on computation rules.