Generalized Algebraic Theory and Dependent Type Theory Semantics

Explore a 51-minute seminar presentation from Berkeley where Kevin Arlin delves into Generalized Algebraic Theories (GATs) and their relationship with dependent type theory semantics. Learn about Cartmell's pioneering work from the 1980s and its practical applications in AlgebraicJulia, where dependent types offer elegant implementation solutions. Discover how the categorical semantics of dependent type theory has evolved, particularly focusing on Martin-Löf type theory's influence. Gain insights into how GATs fit within modern theoretical frameworks, specifically examining their semantics through Dybjer's categories with families (cwfs) perspective.