Equality, Quasi-Implicit Products, and Large Eliminations

Details Equality, Quasi-Implicit Products, and Large Eliminations Equality, Quasi-Implicit Products, and Large Eliminations

2011-01-24

arxiv.org/abs/1101.4430v1

EPTCS 45, 2011, pp. 90-100

Computer Science

Programming Languages

In Proceedings ITRS 2010, arXiv:1101.4104

Scientific paper

10.4204/EPTCS.45.7

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 eliminations, using what we call quasi-implicit products.

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