Inductive Logic Programming is really interesting. I'd really like to explore similarities between ILP and the synthesis used in Barliman--I suspect Barliman's example-based synthesis could get a real boost from ILP.

One book I highly recommend, and which I've found very accessible, is Ivan Bratko's 'Prolog Programming for Artificial Intelligence'. The 4th edition has a section on ILP.

If you are interested in ILP and also in Barliman, maybe this is a topic we could explore together.

A good resource for relational learning in general including ILP is this:

http://www.springer.com/gp/book/9783540200406

And this is a good introduction to the statistical side of things, a.k.a. statistical relational learning:

http://www.cs.umd.edu/srl-book/

Also, if you're considering adding stochastic search this might be a good pointer:

https://dtai.cs.kuleuven.be/problog/

Problog is a probabilistic Prolog. Above is the implementation in Python but there's a few Prolog versions floating around, unfortunately the ones I tried did not seem to work out of the box.

Thanks for the great links!

I really enjoyed the Statistical Relational Learning book.

Rob Zinkov and I have worked on two prototypes of probKanren (https://github.com/webyrd/probKanren), a probabilistic version of miniKanren inspired partly by the Hakaru language (http://indiana.edu/~ppaml/HakaruTutorial.html, https://github.com/hakaru-dev/hakaru). We learned a lot from our two prototypes of probKanren, but neither version is ready for real use (and neither version is documented!).

Rob and I have taken a step back, and are now working with Evan Donahue on just adding stochastic search to miniKanren. If you are interested in joining us, please let me know! :)