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

Abstract

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).