Memelang: An Axial Grammar for LLM-Generated Vector-Relational Queries

Structured generation for LLM tool use highlights the value of compact DSL intermediate representations (IRs) that can be emitted directly and parsed deterministically. This paper introduces axial grammar: linear token sequences that recover multi-dimensional structure from the placement of rank-specific separator tokens. A single left-to-right pass assigns each token a coordinate in an n-dimensional grid, enabling deterministic parsing without parentheses or clause-heavy surface syntax. This grammar is instantiated in Memelang, a compact query language intended as an LLM-emittable IR whose fixed coordinate roles map directly to table/column/value slots. Memelang supports coordinate-stable relative references, parse-time variable binding, and implicit context carry-forward to reduce repetition in LLM-produced queries. It also encodes grouping, aggregation, and ordering via inline tags on value terms, allowing grouped execution plans to be derived in one streaming pass over the coordinate-indexed representation. Provided are a reference lexer/parser and a compiler that emits parameterized PostgreSQL SQL (optionally using pgvector operators).