Combining Dependency, Grades, and Adjoint Logic in Type Systems

Explore a 19-minute conference talk from TyDe 2023 that introduces two innovative dependent type systems. Delve into the first system, which combines a graded dependent type system with a linear type system using modal operators in the style of Linear/Non-linear logic. Discover how the second system generalizes this concept by incorporating multiple graded systems connected through modal operators, utilizing modes from Adjoint Logic. Learn about the meta-theoretic properties proven for these systems, including graded substitution. Gain insights into advanced topics such as linear logic, graded types, adjoint logic, dependent types, semantics, and resource tracking. Presented by Peter Hanukaev and Harley Eades III from Augusta University, this talk offers a deep dive into cutting-edge research in type theory and programming language design.