Has anyone had experience with Datalog or Datafun? What was the programming experience like? What did you build with it? Did you find that you were more productive or less? What sorts of problems was it a good fit for, and what sorts of things was it a bad fit for?
The reason for the restriction is completeness and efficiency. Definite datalog programs are guaranteed to terminate (given a finite predicate and constant signature), so the search for a hypothesis (the learned program) cannot "go infinite" even when the target theory (what you are trying to learn) is recursive, even when it has mutually recursive clauses. As a result our algorithms can learn recursive programs (which, is rather important). The space of hypotheses doubles in size when negation as failure is allowed, which improves the efficiency of the search for hypotheses.
The problem of course is that some programs cannot be expressed in definite datalog than can be expressed in Prolog with negation as failure and arbitrary functions as arguments. So that's a bit of a limitation. For instance, one has to jump through hoops to learn programs with "exceptions" (A if B except if C), say like a program calculating leap years (which have exceptions for years divisible by 100 and 400) or fizzbuzz.
This is not directly programming with datalog- it's machine learning of datalog programs from data. But I think it's similar to the experience you're asking for.
My group's algorithms:
Metagol (a meta-interpretive learner for definite datalog programs):
https://github.com/metagol/metagol
Louise (a polynomial-time version of Metagol):