Does FRP augment or replace FP? Can FRP be implemented as a library in an FP language?
Functional relational programming seems to be, just as the name suggests, a blend of both functional programming and the relational model. I think this sentence pretty much sums it up (p. 42):
In FRP all essential state takes the form of relations, and the essential logic is expressed using relational algebra extended with (pure) user defined functions.
Functional programming removes state from the equation and deals only with pure functions (no side effects). This is supposed to make things easier on everyone by preventing data manipulation from being hidden therefore making it easier to reason about the program. FP is a beautiful ideal but in real life applications state is necessary and often useful. It is of course possible to have state in FP it's just a little more involved.
Based on a quick glance at the paper it seems they're trying to simplify FP by allowing state in a tightly controlled manner. Relational data is well structured and easy to reason about and functional programs are easy to reason about (maybe not in the human sense mind you) so let's augment FP with R and make everyone's state-loving live easier.