Equality Is Typable in Semi-full Pure Type Systems

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Equality Is Typable in Semi-full Pure Type Systems
—There are two usual ways to describe equality in a dependent typing system, one that uses an external notion of computation like beta-reduction, and one that introduces a typed judgement of beta-equality directly in the typing system. After being an open problem for some time, the general equivalence between both approaches has been solved by Adams for a class of pure type systems (PTSs) called functional. In this paper, we relax the functionality constraint and prove the equivalence for all semi-full PTSs by combining the ideas of Adams with a study of the general shape of types in PTSs. As one application, an extension of this result to systems with sub-typing would be a first step toward bringing closer the theory behind a proof assistant such as Coq to its implementation.
Vincent Siles, Hugo Herbelin
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where LICS
Authors Vincent Siles, Hugo Herbelin
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