[paperwork]

I've wondered this as well. However, I couple of notes. CTM is indeed an awesome book, but the idea of language kernel is older. I believe academic papers often start with a minimal language, like the lambda calculus, then show how it can be extended with one feature or another. If I recall correctly, I don't think CTM spends any time showing you how to implement these features using a parser/interpreter/compiler/etc.

If you are looking for a theoretical model of relational databases, you may look up relational algebra. I'm sure others will chime in about how sql is not a very good representation of relational algebra; however, if you are not aware of it, RA is certainly something to study.

I suspect that you may be referring to a kernel database, the way there are simple implementations of operating systems--written expressly to study how OSes work. I wish something like that existed for databases, but I'm not aware of it.

Finally, there are several text books on relational database management systems. I haven't used one in a while so can't recommend a specific one. However, these books often show you how to implement various parts of a database, such as b-treee for storage, indexes, how to design a pipeline to implement selection/projection/group by, etc. Make sure that the book is showing you how to implement a DBMS, not how to design a datamodel.