Towards Evolutionary Theorem Proving for Isabelle/HOL

Abstract

Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers’ expertise and remains labor intensive. Recently, researchers have extracted heuristics of interactive proof development from existing large proof corpora using supervised learning. However, such existing proof corpora present only one way of proving conjectures, while there are often multiple equivalently effective ways to prove one conjecture. In this abstract, we identify challenges in discovering heuristics for automatic proof search and propose our novel approach to improve heuristics of automatic proof search in Isabelle/HOL using evolutionary computation.

Project Dependency Graph

flowchart LR VerifyC["VerifyC"] Refinement["Refinement"] VeriFile["VeriFile"] TowardsEvo["TowardsEvo"] GeneticSyn["GeneticSyn"] PSL["PSL"] GoalOriented["GoalOriented"] TemplateBased["TemplateBased"] LiFtEr["LiFtEr"] SeLFiE["SeLFiE"] SmartInduct["SmartInduct"] SmarterInduct["SmarterInduct"] PaMpeR["PaMpeR"] SimpleDataset["SimpleData"] Abduction["Abduction"] %% Style definitions classDef default fill:#f9f9f9,stroke:#333,stroke-width:2px; classDef futureWork fill:#fff,stroke:#333,stroke-width:2px,stroke-dasharray: 5 5; classDef highlighted fill:#ffff00,stroke:#333,stroke-width:2px; class Abduction futureWork; class TowardsEvo highlighted; %% Clickable Nodes click Abduction "https://yutakang.github.io/projects/proof-by-abduction-in-isabellehol" "Proof By Abduction in Isabelle/HOL" click TemplateBased "https://yutakang.github.io/projects/template-based-conjecturing-for-automated-induction-in-isabellehol" "Template-Based Conjecturing for Automated Induction in Isabelle/HOL" click GeneticSyn "https://yutakang.github.io/projects/genetic-algorithm-for-program-synthesis" "Genetic Algorithm for Program Synthesis" click SeLFiE "https://yutakang.github.io/projects/definitional-quantifiers-realise-semantic-reasoning-for-proof-by-induction" "Definitional Quantifiers Realise Semantic Reasoning for Proof by Induction" click SmarterInduct "https://yutakang.github.io/projects/faster-smarter-induction-for-isabellehol" "Faster Smarter Induction for Isabelle/HOL" click SmartInduct "https://yutakang.github.io/projects/smart-induction-for-isabellehol-tool-paper" "Smart Induction for Isabelle/HOL (Tool Paper)" click SimpleDataset "https://yutakang.github.io/projects/simple-dataset-for-proof-method-recommendation-in-isabellehol" "Simple Dataset for Proof Method Recommendation in Isabelle/HOL" click LiFtEr "https://yutakang.github.io/projects/lifter-language-to-encode-induction-heuristics-for-isabellehol" "LiFtEr: Language to Encode Induction Heuristics for Isabelle/HOL" click TowardsEvo "https://yutakang.github.io/projects/towards-evolutionary-theorem-proving-for-isabellehol-poster-only-paper" "Towards Evolutionary Theorem Proving for Isabelle/HOL" click PaMpeR "https://yutakang.github.io/projects/pamper-proof-method-recommendation-system-for-isabellehol" "PaMpeR: Proof Method Recommendation System for Isabelle/HOL" click GoalOriented "https://yutakang.github.io/projects/goal-oriented-conjecturing-for-isabellehol" "Goal-Oriented Conjecturing for Isabelle/HOL" click PSL "https://yutakang.github.io/projects/a-proof-strategy-language-and-proof-script-generation-for-isabellehol" "A Proof Strategy Language and Proof Script Generation for Isabelle/HOL" click VerifyC "https://yutakang.github.io/projects/a-framework-for-the-automatic-formal-verification-of-refinement-from-cogent-to-c" "A framework for the automatic formal verification of refinement from Cogent to C" click Refinement "https://yutakang.github.io/projects/refinement-through-restraint-bringing-down-the-cost-of-verification" "Refinement through Restraint: Bringing Down the Cost of Verification" click VeriFile "https://yutakang.github.io/projects/cogent-verifying-high-assurance-file-system-implementations" "Cogent: Verifying High-Assurance File System Implementations" %% Define Edges VerifyC -->|is part of| Refinement Refinement --> |is used in| VeriFile TowardsEvo -->|is realised in| GeneticSyn TowardsEvo -.-> |should be used in| Abduction PSL -->|is used in| Abduction PSL -->|is used in| GoalOriented PSL -->|is used in| TemplateBased TemplateBased -->|is used in| Abduction LiFtEr -->|is used in| SmartInduct LiFtEr -->|evolves to| SeLFiE SeLFiE -->|is used in| SmarterInduct SmartInduct -->|evolves to| SmarterInduct SmarterInduct -->|is used in| TemplateBased SimpleDataset -->|is used in| PaMpeR PaMpeR -.-> |should be used in| Abduction GoalOriented -->|is used in| Abduction SmarterInduct -->|is used in| Abduction SeLFiE -->|is used in| Abduction PSL -->|integrates| SmarterInduct

Mindmap

Mindmap for TemplateBased at FSEN2023