SML has arguably the most complicated/powerful module system of any existing programming language.  It is a luxury RV to Haskell's camper van.  I take a high-level look, following a very nice paper by Xavier Leroy, titled "A modular module system".

I briefly survey the main features of Haskell's module system, and reflect a bit on its design.

I start Chapter 13 (in Season 2) of the podcast, on module systems.  Almost all programming languages I know include some kind of scheme for modules, packages, namespaces, or something like this.  I discuss the high-level ideas of namespace management and type abstraction, two main use cases for module systems.  Subsequent episodes will discuss module systems (from papers or documentation) of various languages.

I was reading Benjamin Pierce's dissertation, and learning some intriguing things about intersection types in the context of Church-style typing.  I summarize the parts of this I comprehended so far.

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.

I sketch the argument that pure lambda terms in normal form are typable using intersection types.  This completes the argument started in the previous episode, that intersection types are complete for normalizing terms: normal forms are typable, and typing is preserved by beta-expansion.  Hence any normalizing term is typable (since it reduces to a normal form by definition, and from this normal form we can walk typing back to the term).

Type systems usually have the type preservation property: if a typable term beta-reduces, then the resulting term is still typable.  So typing is closed under beta-reduction.  With intersection typing, typing is also closed under beta-expansion, which is a critical step in showing that intersection typing is complete for normalizing terms: any normalizing term can be typed with intersection types (and simple function types).  

In a type system with intersection types, a term t that has type A and also has type B can be assigned the type 'A intersect B'.   This episode begins Chapter 12 of the podcast on intersection types.

Responding to an email question from a listener, I explain how to derive a form of inconsistency from the assumption that True is related to False at type Bool.

I muse about the hopeless prospect of a single intrinsic conceptual decomposition of a problem domain in software engineering, and relate this to the idea of intrinsic identity we discussed recently for Relational Type Theory.