TBH i only have statically typed languages in mind (like C++ and Free Pascal), so i'm not sure how it'd work in a dynamically typed language with type annotations, but to refactor i'd just... change the type and then work through the compiler errors to find the places that need their type updated. Some IDEs also provide you with tools to find all those uses and even can do the refactor themselves.
Your refactor will contain more lines of code since it'll need to also contain the updated use sites, but i do not see that as a problem at all - and even if it is one, it is only a short term small problem that is certainly not as important as having the code more obvious and readable in the long term (assuming of course you feel the same about readability as i do - after all as i wrote in my message above it is a subjective issue :-P).
> dynamically typed language with type annotations
I'm talking about statically typed languages also, just ones with inference. Haskell, Rust, Ocaml, F#, Go, etc, and increasingly languages like C# and Java are adding more and more inference.
Your response makes me think you don't really get what type inference is.
Your refactor will contain more lines of code since it'll need to also contain the updated use sites, but i do not see that as a problem at all - and even if it is one, it is only a short term small problem that is certainly not as important as having the code more obvious and readable in the long term (assuming of course you feel the same about readability as i do - after all as i wrote in my message above it is a subjective issue :-P).