Lecture
This lecture covers the concept of algorithmic subtyping and focuses on proving transitivity in the context of subtype relationships. The instructor explains how to derive subtype relationships between different types using induction on the derivation of subtyping judgments. Through a step-by-step analysis of the transitivity rule, the lecture demonstrates how to apply induction hypotheses to prove transitivity in various scenarios. The lecture also discusses the challenges of implementing transitivity in an algorithmic subtyping system and provides insights into the process of deriving subtype relationships between function types. Additionally, the lecture explores the importance of understanding the shapes of types and how it influences the derivation of subtype relationships.