Wow, those are some interesting links.

As somebody who's learned a foreign language to near-fluency as an adult, I've spent a lot of time trying to figure out how my brain infers a grammar from large quantities of input. Subjectively, it feels like my brain learns fixed phrases, and then notices that certain chunks can be replaced by subtrees of the appropriate type.

There are complications: inflections, gender, agreement, probability, and so on. But still, grammar compression looks like a fascinating formulation of the problem.