PaMpeR: Proof Method Recommendation System for Isabelle/HOL (1806.07239v1)

Abstract: Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof methods to discharge the proof goal and provides qualitative explanations as to why it suggests these methods. PaMpeR generates these recommendations based on existing hand-written proof corpora, thus transferring experienced users' expertise to new users. Our evaluation shows that PaMpeR correctly predicts experienced users' proof methods invocation especially when it comes to special purpose proof methods.

• The paper introduces PaMpeR, a machine learning system using regression trees trained on proof corpora to recommend proof methods in Isabelle/HOL.
• PaMpeR achieves strong evaluation results, showing a 50% coincidence rate for 72 methods and over 90% for 34 specialized methods within the top 15 recommendations.
• The system helps new users and enhances productivity by accurately suggesting methods and parameters, facilitating expert knowledge transfer in interactive theorem proving.

An Expert Overview of "PaMpeR: Proof Method Recommendation System for Isabelle/HOL"

The paper "PaMpeR: Proof Method Recommendation System for Isabelle/HOL" presents a machine learning-based approach to recommending proof methods for Isabelle's Higher-Order Logic (Isabelle/HOL). The system, named PaMpeR (proof method recommendation), aims to assist users in selecting appropriate proof methods during interactive theorem proving (ITP), particularly within the Isabelle/HOL framework.

Objectives and Contributions

PaMpeR addresses challenges inherent in theorem proving, where expertise is often required to decide which sub-tool or method to apply to a given proof state. By leveraging existing proof corpora, PaMpeR facilitates the transfer of knowledge from experienced users to novices, reducing the entry barrier and expediting the proof development process. This recommendation system provides a sophisticated solution to a common problem faced by engineers and mathematicians working with ITPs.

The paper outlines PaMpeR's two-phased approach: preparation and recommendation. During the preparation phase, the system extracts features from existing large proof corpora, such as the Isabelle standard library and the Archive of Formal Proofs (AFP), converting them into databases used for training machine learning models. PaMpeR then constructs regression trees to predict proof method utility based on these features. The recommendation phase utilizes these models to suggest proof methods for new proof goals, complemented by qualitative explanations to enhance user understanding.

Strong Numerical Results

PaMpeR was evaluated using a cross-validation approach on a database extracted from substantial proof corpora comprising over 425,000 unique data points. The evaluation highlights PaMpeR's effectiveness, particularly for specialized proof methods. For 72 methods within the top 15 recommendations, PaMpeR achieved a 50% coincidence rate, indicating alignment between its suggestions and human choices 50% of the time. Furthermore, its coincidence rate surpassed 90% for 34 methods, including less commonly used specialized methods, demonstrating effectiveness in recognizing optimal methods for specific proof goals.

Implications and Future Directions

The practical implications of PaMpeR are notable. It not only assists new users in traversing the extensive suite of methods within Isabelle/HOL but also enhances productivity through accurate suggestion of proof methods and parameters. The theoretical implications extend into understanding how meta-information about proof states can assist in fine-tuning proof method selection.

Potential enhancements to PaMpeR include addressing the sequence of proof method applications and integrating with complementary systems like the Proof Strategy Language (PSL), enabling history-sensitive recommendations and strategic proof step navigation. An exploration of alternative machine learning algorithms and richer feature sets could also augment its predictive capabilities.

Conclusion

"PaMpeR: Proof Method Recommendation System for Isabelle/HOL" reveals an insightful synergy between machine learning and interactive theorem proving. It addresses a critical need in the ITP community by empirically supporting the transition of expert knowledge to broader user bases. The authors' decision to employ regression trees affords an interpretable model, aligning human reasoning with machine predictions effectively.

PaMpeR sets a benchmark in tool-assisted proof developments, advocating for further research into customizable, high-utility recommendation systems within theorem proving frameworks. As such, it is a valuable addition, particularly for large-scale theorem verification projects and those utilizing Isabelle/HOL.