# PPDL: LLM-Based Flows as Probabilistic Programs

arXiv: https://arxiv.org/abs/2608.05234 · HTML: https://mlsanity.com/paper/2608.05234/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 52 references that are in the map.
- First posted on arXiv 5 Aug 2026.

## Builds on (most cited first, 30 of 34)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [SWE-bench: Can Language Models Resolve Real-World GitHub Issues?](https://mlsanity.com/paper/2310.06770/) (2023)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [FEVER: a large-scale dataset for Fact Extraction and VERification](https://mlsanity.com/paper/1803.05355/) (2018)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [DSPy: Compiling Declarative Language Model Calls into Self-Improving Pipelines](https://mlsanity.com/paper/2310.03714/) (2023)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Prompting Is Programming: A Query Language for Large Language Models](https://mlsanity.com/paper/2212.06094/) (2022)
- [An In-Context Learning Agent for Formal Theorem-Proving](https://mlsanity.com/paper/2310.04353/) (2023)
- [Sequential Monte Carlo Steering of Large Language Models using Probabilistic Programs](https://mlsanity.com/paper/2306.03081/) (2023)
- [Trace is the Next AutoDiff: Generative Optimization with Rich Feedback, Execution Traces, and LLMs](https://mlsanity.com/paper/2406.16218/) (2024)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)
- [It's MBR All the Way Down: Modern Generation Techniques Through the Lens of Minimum Bayes Risk](https://mlsanity.com/paper/2310.01387/) (2023)
- [Magnushammer: A Transformer-Based Approach to Premise Selection](https://mlsanity.com/paper/2303.04488/) (2023)
- [Syntactic and Semantic Control of Large Language Models via Sequential Monte Carlo](https://mlsanity.com/paper/2504.13139/) (2025)
- [AutoPDL: Automatic Prompt Optimization for LLM Agents](https://mlsanity.com/paper/2504.04365/) (2025)
- [PDL: A Declarative Prompt Programming Language](https://mlsanity.com/paper/2410.19135/) (2024)

## Abstract (arXiv)

Building reliable applications that leverage large language models (LLMs) remains a significant challenge. While LLMs offer impressive capabilities across diverse tasks, their outputs often lack accuracy and provide no clear measure of confidence. This uncertainty compounds in flows of multiple calls to LLMs and other tools, making it difficult for developers and end-users to trust the results. This paper introduces a probabilistic language for programming LLM-based flows. It enables developers to quantify and propagate uncertainty throughout the application's flow, and experiment with different inference scaling techniques without adding a single line of code beyond the flow's logic. We present an experimental study to demonstrate this capability, and a case study building a theorem proving agent for the Rocq theorem prover.