type preservation

I discuss the perhaps surprising fact that union and intersection types are quite actively used and promoted for languages like TypeScript, also OO languages like Scala.  I also try to explain briefly a counterexample to type preservation with union types, which you can find at the start of Section 2 of Barbanera and Dezani-Ciancaglini's paper "Intersection and Union Types: Syntax and Semantics", where it is attributed to Benjamin Pierce.

Type safety proofs are big confirmations requiring consideration of all your operational and typing rules.  So they rarely contain much deep insight, but are needed to confirm your language's type system is correct.  Looking ahead, this episode also talks about the different between normalization and termination when your language is nondeterministic, and the property of confluence. 

We review the metatheoretic property of type safety, decomposed into two properties called type preservation and progress.  Discussion of progress in the context of type theory, where adding axioms can lead to a failure of progress.