What's the status of functional relational programming languages? The term could (according to me) be defined as languages which represent their data primarily as relations, acting on them with associated relational operators, but with the additional ability to express pure functional transformations (like Haskell). The term first appeared (I believe) in the well-known paper "Out of the Tar Pit" (the authors never chased it further). I think Datafun by @rntz hopes to be something like this, and there's also http://cell-lang.net/ .

Do Mosley and Marks argue we need a new language to achieve functional relational programming? It seemed to me that they were saying: “logic programming is the right medium for business logic; use user-defined functions to extend that where needed; write your user-defined functions and/or infrastructure in an imperative language if you absolutely have to for performance reasons”. The most exciting development I’ve seen in this area is what folks in academia are doing with Answer Set Programming, particularly in the Clingo toolchain (https://potassco.org), which provides a very powerful logic language with an extensible architecture that I think could get us a long way.

Well the authors of the paper were designing their own language, so I believe that was their perspective (they stopped working on it shortly after).