[gue5t]

These types don't seem to escape the scope of what can be described with algebraic types, but the relationships between them seem like you're looking for a notion of type-level functions: subset ≡ X => 2^X, partial ≡ A×B => (A+1)×partial(B)

[qazxcvbnm]

Consider the case of Partials - we might like to restrict the Partials to different subsets of the fields for different purposes; consider the modelling of an inverted index.

Certainly it is possible to represent each specific case as some algebraic type; but beyond trivial cases, I find that when I need such of these types, quickly I discover that there are myriad ways to express them, none of them uniquely natural, unlike the way a sum of products type (and its terms) can be pretty much unambiguously drawn from a specification.

This matters especially when e.g. I need to evolve my types in a data migration.