# MathDSL: A Domain-Specific Language for Concise Mathematical Solutions Via Program Synthesis

arXiv: https://arxiv.org/abs/2409.17490 · HTML: https://mlsanity.com/paper/2409.17490/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Deep RL algorithms and representations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 26 Sep 2024.

## Placed in

- Deep reinforcement learning methods / [Deep RL algorithms and representations](https://mlsanity.com/deeprl/deep-rl-algorithms-and-representations/)

## Builds on (most cited first, 9 of 9)

- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Learning to Execute](https://mlsanity.com/paper/1410.4615/) (2014)
- [Top-Down Synthesis for Library Learning](https://mlsanity.com/paper/2211.16605/) (2022)
- [LILO: Learning Interpretable Libraries by Compressing and Documenting Code](https://mlsanity.com/paper/2310.19791/) (2023)
- [Leveraging Language to Learn Program Abstractions and Search Heuristics](https://mlsanity.com/paper/2106.11053/) (2021)
- [Contrastive Reinforcement Learning of Symbolic Reasoning Domains](https://mlsanity.com/paper/2106.09146/) (2021)
- [Peano: Learning Formal Mathematical Reasoning](https://mlsanity.com/paper/2211.15864/) (2022)
- [LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions](https://mlsanity.com/paper/2211.08671/) (2022)

## Abstract (arXiv)

We present MathDSL, a Domain-Specific Language (DSL) for mathematical equation solving, which, when deployed in program synthesis models, outperforms state-of-the-art reinforcement-learning-based methods. We also introduce a quantitative metric for measuring the conciseness of a mathematical solution and demonstrate the improvement in the quality of generated solutions compared to other methods. Our system demonstrates that a program synthesis system (DreamCoder) using MathDSL can generate programs that solve linear equations with greater accuracy and conciseness than using reinforcement learning systems. Additionally, we demonstrate that if we use the action spaces of previous reinforcement learning systems as DSLs, MathDSL outperforms the action-space-DSLs. We use DreamCoder to store equation-solving strategies as learned abstractions in its program library and demonstrate that by using MathDSL, these can be converted into human-interpretable solution strategies that could have applications in mathematical education.