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Goal-Oriented Conjecturing for Isabelle/HOL

Abstract

We present PGT, a Proof Goal Transformer for Isabelle/HOL. Given a proof goal and its background context, PGT attempts to generate conjectures from the original goal by transforming the original proof goal. These conjectures should be weak enough to be provable by automation but sufficiently strong to identify and prove the original goal. By incorporating PGT into the pre-existing PSL framework, we exploit Isabelle’s strong automation to identify and prove such conjectures.

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 GoalOriented 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 GoalOriented at CICM2018