Lecture 1: Review of Type Safety Proofs

In this lecture, Neelakantan Krishnaswami introduces type systems, highlighting their dual role in programming languages and logic/proof theory. Type systems are essential for error detection, program structuring, and efficient code compilation. The lecture recaps basic type systems with booleans and integers, introducing typing judgments and rules. It extends the discussion to include variables and let bindings, emphasizing the need for context in typing judgments. The lecture also covers substitution, weakening, and exchange properties, along with operational semantics, progress, and type preservation to ensure program safety, aiming to prove that well-typed programs do not lead to undefined behaviors.