On many occasions, programming language researchers formulate claims about programming languages as relations between functions. Since the collection of terms in a language is usually defined in an inductive (self-referential) manner, they design recursive functions to process terms. To prove claims about functions (and relations), they then use structural induction. If you don’t, find reading material to supplement the lectures. This last introductory lecture summarizes what you are expected to know about structural induction and strengthening claims from your undergraduate curriculum.