Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise and proofs, where some parts have been omitted. Current theories gradual types, though, lack central feature type theory: propositional equality. Lennon-Bertrand et al. show that, when reflexive proof refl is only closed value an equality type, extension Cal...

Recursive types extend the simply-typed lambda calculus (STLC) with additional expressive power to enable diverging computation and encode recursive data-types (e.g., lists). Two formulations of exist: iso-recursive equi-recursive. The relative advantages iso- equi-recursion are well- studied when it comes their impact on type-inference. However, semantic expressiveness two remains unclear so f...

We formally introduce arc-typed nets as a model for causality based speciica-tions. The new feature of arc-typed nets is the distinction of diierent arc-types; the diierent arc-types carry over to a process of the net. Therefore, there are diierent types of causalities in a run of an arc-typed net. Arc-typed nets have informally been used for modelling and verifying consistency protocols. It tu...