Faster Smarter Induction for Isabelle/HOL
- Venue: The 30th International Joint Conference on Artificial Intelligence (IJCAI 2021)
- Location: Montreal-Themed Virtual Reality
- Author: Yutaka Nagashima
- Paper: https://www.ijcai.org/proceedings/2021/273
- Video: https://youtu.be/4umf8Zhjy7c
Abstract
We present sem_ind, a recommendation tool for proof by induction in Isabelle/HOL. Given an inductive problem, sem_ind produces candidate arguments for proof by induction, and selects promising ones using heuristics. Our evaluation based on 1,095 inductive problems from 22 source files shows that sem_ind improves the accuracy of recommendation from 20.1% to 38.2% for the most promising candidates within 5.0 seconds of timeout compared to its predecessor while decreasing the median value of execution time from 2.79 seconds to 1.06 seconds.
Video
Project Dependency Graph
flowchart LR
VerifyC["VerifyC"]
Refinement["Refinement"]
VeriFile["VeriFile"]
TowardsEvo["TowardsEvo"]
GeneticSyn["GeneticSyn"]
PSL["PSL"]
GoalOriented["Goal-Oriented"]
TemplateBased["Template-Based"]
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 SmarterInduct 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
