Equality, Quasi-Implicit Products, and Large Eliminations

@inproceedings{Sjberg2011EqualityQP,
  title={Equality, Quasi-Implicit Products, and Large Eliminations},
  author={Vilhelm Sj{\"o}berg and Aaron Stump},
  booktitle={ITRS},
  year={2011}
}
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We develop the metatheory for an undecidable version of the system with unannotated terms. We then devise a decidable system with annotated terms, justified in terms of the unannotated system. Finally, we show how the approach can be extended to account for large… 
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