System \(F_\omega\) is a system of higher-kinded types and type-constructors. It is relevant to compiling SML in the way that it relates to the module system. If we extend the kind system of "true" \(F_\omega\) with product kinds, we might represent the module signature
sig type t type 'a u end
as the kind \(* \times (* \rightarrow *)\), and so on. This even extends to functors that act on modules via type-level lambdas.