String Deduplication on the Type Level

The string deduplication problem is a canonical one within computer science, serving a similar purpose as fizz-buzz in terms of being an example of a simple problem that a reasonably knowledgable practitioner should be able to solve with minimal effort. The problem appears in a few variants, but briefly one such variant is to remove duplicate letters in a given string, such that the string then has only one instance of any given letter.