Hydra is a programming language that uses mathematical abstraction to model graphs within the language itself. It’s an open-source project spearheaded by Josh Shinavier, co-creator of Apache TinkerPop. In Josh’s own words: “In Hydra, programs are graphs, and graphs are programs.”
An open source project to search SQL code 'semantically': up to the meaning of parse trees. For example, searching for 'select from A,B' matches 'select from B,A'.
The code in database vs database in code duality has a long history, and one way to formalize it mathematically uses category theory: the notion of LINQ (language integrated query, such as collection comprehensions) is formally related to the notion of "query-integrated languages" (where data integrity constraints are Turing-complete domain specific languages extending the database vocabulary). https://arxiv.org/pdf/1511.06459
There is a partial solution to this problem: use formal methods such as symbolic logic and theorem proving to check the LLM output for correctness. We are launching a semantic validator for LLM-generated SQL code at sql.ai even now. (It checks for things like missing joins.) And others are using logic and math to create LLMs that don't hallucinate or have safety nets for hallucination, such as Symbolica. It is only when the LLM output doesn't have a correct answer that the technical issues become complicated.