https://arxiv.org/abs/1905.02617 :
*A Type Theory for Defining Logics and Proofs* Brigitte Pientka, David Thibodeau, Andreas Abel, Francisco Ferreira, Rebecca Zucchini (Submitted on 7 May 2019) We describe a Martin-Löf-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that describes (recursive) computations. We mediate between HOAS representations and computations using contextual modal types. Our type theory also supports an infinite hierarchy of universes and hence supports type-level computation thereby providing metaprogramming and (small-scale) reflection. Our main contribution is the development of a Kripke-style model for Cocon that allows us to prove normalization. From the normalization proof, we derive subject reduction and consistency. Our work lays the foundation to incorporate the methodology of logical frameworks into systems such as Agda and bridges the longstanding gap between these two worlds. @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/698c5049-073f-42ff-9098-83eab4c53a17%40googlegroups.com.
