[magusdei]

Context-free grammars were originally invented by linguists for analyzing natural language. You can see examples of phrase structure and dependency diagrams e.g. here: https://en.wikipedia.org/wiki/Dependency_grammar

For what it's worth, I agree with OP, and have a very "language-oriented" thinking style. I certainly don't visualize anything while programming or doing math (except for geometry and the like). My thinking feels like it's more based on constraint solving and seeing analogies between domains.