I've never used F#, so I might get this completely wrong, but I think they are a practical form of dependently typed programming: a type provider builds new typ

I've never used F#, so I might get this completely wrong, but I think they are a practical form of dependently typed programming: a type provider builds new types that depend on values in your program. If you have some sort of schema for data, a type provider could parse it and build appropriate types to hold data that conforms to the schema. A type provider for a database, say, could take a string that specifies a database connection, connect to the database, and then query it to figure out what sorts of tables it holds and then construct F# types capable of holding a record from one of the tables.