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

TL;DR

MathDSL is a specialized language for mathematical problem solving that enhances program synthesis models by producing more accurate, concise, and interpretable solutions compared to reinforcement learning approaches.

Contribution

Introduction of MathDSL, a domain-specific language that improves the quality and conciseness of mathematical solutions in program synthesis systems, with applications in education.

Findings

MathDSL outperforms reinforcement learning methods in accuracy and conciseness.

Using MathDSL improves the interpretability of solutions.

MathDSL enables conversion of learned strategies into human-understandable forms.

Abstract

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.