# Play by the Type Rules: Inferring Constraints for LLM Functions in Declarative Programs

arXiv: https://arxiv.org/abs/2509.20208 · HTML: https://mlsanity.com/paper/2509.20208/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Knowledge- and tool-augmented reasoning, one of 17 directions in LLM reasoning.
- Builds on 26 of its 36 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Placed in

- LLM reasoning / [Knowledge- and tool-augmented reasoning](https://mlsanity.com/lr/knowledge-and-tool-augmented-reasoning/)

## Builds on (most cited first, 26 of 26)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
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- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [MPNet: Masked and Permuted Pre-training for Language Understanding](https://mlsanity.com/paper/2004.09297/) (2020)
- [Can LLM Already Serve as A Database Interface? A BIg Bench for Large-Scale Database Grounded Text-to-SQLs](https://mlsanity.com/paper/2305.03111/) (2023)
- [HybridQA: A Dataset of Multi-Hop Question Answering over Tabular and Textual Data](https://mlsanity.com/paper/2004.07347/) (2020)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Binding Language Models in Symbolic Languages](https://mlsanity.com/paper/2210.02875/) (2022)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [Grammar-Constrained Decoding for Structured NLP Tasks without Finetuning](https://mlsanity.com/paper/2305.13971/) (2023)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Break It Down: A Question Understanding Benchmark](https://mlsanity.com/paper/2001.11770/) (2020)
- [XGrammar: Flexible and Efficient Structured Generation Engine for Large Language Models](https://mlsanity.com/paper/2411.15100/) (2024)
- [EHRXQA: A Multi-Modal Question Answering Dataset for Electronic Health Records with Chest X-ray Images](https://mlsanity.com/paper/2310.18652/) (2023)
- [Flexible and Efficient Grammar-Constrained Decoding](https://mlsanity.com/paper/2502.05111/) (2025)
- [Type-Constrained Code Generation with Language Models](https://mlsanity.com/paper/2504.09246/) (2025)
- [Semantic Operators: A Declarative Model for Rich, AI-based Data Processing](https://mlsanity.com/paper/2407.11418/) (2024)
- [Text2SQL is Not Enough: Unifying AI and Databases with TAG](https://mlsanity.com/paper/2408.14717/) (2024)
- [BlendSQL: A Scalable Dialect for Unifying Hybrid Question Answering in Relational Algebra](https://mlsanity.com/paper/2402.17882/) (2024)
- [Divide-or-Conquer? Which Part Should You Distill Your LLM?](https://mlsanity.com/paper/2402.15000/) (2024)
- [Beyond Quacking: Deep Integration of Language Models and RAG into DuckDB](https://mlsanity.com/paper/2504.01157/) (2025)
- [SUQL: Conversational Search over Structured and Unstructured Data with Large Language Models](https://mlsanity.com/paper/2311.09818/) (2023)
- [Exploring Hybrid Question Answering via Program-based Prompting](https://mlsanity.com/paper/2402.10812/) (2024)
- [Saving GPU Hours in LLM Inference System Development and Online Workloads with Simulation and DBMS-Inspired Cache Replacement Policies](https://mlsanity.com/paper/2411.07447/) (2024)

## Abstract (arXiv)

Integrating LLM powered operators in declarative query languages allows for the combination of cheap and interpretable functions with powerful, generalizable language model reasoning. However, in order to benefit from the optimized execution of a database query language like SQL, generated outputs must align with the rules enforced by both type checkers and database contents. Current approaches address this challenge with orchestrations consisting of many LLM-based post-processing calls to ensure alignment between generated outputs and database values, introducing performance bottlenecks. We perform a study on the ability of various sized open-source language models to both parse and execute functions within a query language based on SQL, showing that small language models can excel as function executors over hybrid data sources. Then, we propose an efficient solution to enforce the well-typedness of LLM functions, demonstrating 7% accuracy improvement on a multi-hop question answering dataset with 53% improvement in latency over comparable solutions. We make our implementation available at https://github.com/parkervg/blendsql