Difficulties with functors and abstract types

Just remove the FunctorType type annotation on MyMod

module MyMod = {
  type a = string // this is where I want to set the type
  let injectedRun = (x: a) => Console.log(x)
}

Modules are structurally typed. Using a module type annotation can therefore only remove information. You do not need to (and cannot) specify that MyMod implements or conforms with FunctorType.