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

TL;DR

This paper introduces Memelang, a novel axial grammar-based language for LLM-generated vector-relational queries, enabling deterministic, compact, and structured IRs for database querying.

Contribution

It presents axial grammar as a new linear token sequence method for recovering multi-dimensional structure, and instantiates it in Memelang, a compact, LLM-emittable query language with advanced referencing and grouping features.

Findings

Supports deterministic parsing without parentheses

Enables direct mapping to SQL with PostgreSQL compatibility

Reduces repetition in LLM-generated 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).