MathDSL: A Domain-Specific Language for Concise Mathematical Solutions Via Program Synthesis
This work addresses the challenge of generating concise and accurate mathematical solutions, potentially benefiting mathematical education, but it is incremental as it builds on existing program synthesis methods.
The paper tackles the problem of mathematical equation solving by introducing MathDSL, a domain-specific language for program synthesis, which outperforms state-of-the-art reinforcement-learning-based methods in accuracy and conciseness for linear equations.
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.