My 10-minute talk on a full-featured functional programming language with a purely subtyping-based type system is viewable online under the catchy title of Type Checking Without Types. The system is designed with the aim of functionally modelling relational data in both the object and type spaces in mind.

After the talk, a commenter referred to Hutchins' work on pure subtype systems, which explores a related idea in a rather different manner and with a different focus. If the topic seems interesting to you, you might want to take a look.