It's true that this Church language seems to be little more than Scheme with a few clever tricks that allows it to walk through code paths and execute programs

It's true that this Church language seems to be little more than Scheme with a few clever tricks that allows it to walk through code paths and execute programs in clever probabilistic ways. I don't claim to understand it all, however, the clever tricks seem to be very clever and things are put together so well with emphasis on just the right concepts that, to me at least, it makes certain aspects of probabilistic models like the relationship between correlation, causation, induction and deduction much clearer than anything I have seen before. Years ago when I was a grad student, I tried to tackle some NLP problems using similar approaches (ie. unsupervised generative bayesian models organized in hierarchical ways that try to mimic our intuitive concept of causality) but mostly failed at making much headway. I couldn't figure out some of the math and my models usually failed to perform any better than other probabilistic algorithms. No one at my university did anything similar or knew much about bayesian probabilities back then which didn't help. I always believed in the approach however and until I stumbled on this book, never knew there was significant progress being made. I wish it was available to build upon when I was a student. In the "Learning as Conditional Inference" chapter the section "Inferring an Arithmetic Expression" show the first example I have seen of a legitimate and flexible approach that could some day allow a computer to program itself. I mean the algorithm is still far from doing general programming tasks but I could imagine extending the approach so that given a programming language grammar and a unit tests as inputs, a computer could write a well chosen and simplified program that pass the tests (simplified with the automatic Occam's razor inherent in the bayesian approaches) . That to me is mind-blowing. Now not all is perfect in the book, the "Inference about Inference" chapter seems oversimplified to me. The last few chapter seem to get a bit mathematically ad-hoc with an alpha parameter introduced to tie categories and sub-categories together in hierarchical models without much mathematical justification. On the other hand, there is strong evidence for this kind of transfer of information in hierarchies and it's not totally unreasonable to make up a parameter, assign it a bayesian uninformative prior that reflects ignorance of how this parameter should be set and try to induce a value for it from data. It's a perfect example of meta probabilities where probabilities are used to guess parameters that govern other probabilities. It's very bayesian. Anyways before reading this book I was convinced that general AI was not going to happen in my lifetime. Now I'm not so sure.