Article

Automated Theory Exploration for Interactive Theorem Proving:: An Introduction to the Hipster System

Author:

Moa JohanssonAuthors Info & Claims

Interactive Theorem Proving: 8th International Conference, ITP 2017, Brasília, Brazil, September 26–29, 2017, Proceedings

Pages 1 - 11

https://doi.org/10.1007/978-3-319-66107-0_1

Published: 26 September 2017 Publication History

Abstract

Theory exploration is a technique for automatically discovering new interesting lemmas in a mathematical theory development using testing. In this paper I will present the theory exploration system Hipster, which automatically discovers and proves lemmas about a given set of datatypes and functions in Isabelle/HOL. The development of Hipster was originally motivated by attempts to provide a higher level of automation for proofs by induction. Automating inductive proofs is tricky, not least because they often need auxiliary lemmas which themselves need to be proved by induction. We found that many such basic lemmas can be discovered automatically by theory exploration, and importantly, quickly enough for use in conjunction with an interactive theorem prover without boring the user.

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Cited By

Autexier S(2024)On Using Large Language Models Pre-trained on Digital Twins as Oracles to Foster the Use of Formal Methods in PracticeLeveraging Applications of Formal Methods, Verification and Validation. Software Engineering Methodologies10.1007/978-3-031-75387-9_3(30-43)Online publication date: 27-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-75387-9_3
Nagashima YXu ZWang NGoc DBang J(2023)Template-Based Conjecturing for Automated Induction in Isabelle/HOLFundamentals of Software Engineering10.1007/978-3-031-42441-0_9(112-125)Online publication date: 4-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-42441-0_9
Einarsdóttir SSmallbone NJohansson M(2020)Template-based Theory Exploration: Discovering Properties of Functional Programs by TestingProceedings of the 32nd Symposium on Implementation and Application of Functional Languages10.1145/3462172.3462192(67-78)Online publication date: 2-Sep-2020
https://dl.acm.org/doi/10.1145/3462172.3462192

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Automated Theory Exploration for Interactive Theorem Proving:: An Introduction to the Hipster System

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Published In

cover image Guide Proceedings

Interactive Theorem Proving: 8th International Conference, ITP 2017, Brasília, Brazil, September 26–29, 2017, Proceedings

Sep 2017

549 pages

ISBN:978-3-319-66106-3

DOI:10.1007/978-3-319-66107-0

Editors:
Mauricio Ayala-Rincón
University of Brasília, Brasília D.F., Brazil
,
César A. Muñoz
NASA, Hampton, VA, USA

© Springer International Publishing AG 2017.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 26 September 2017

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Cited By

Autexier S(2024)On Using Large Language Models Pre-trained on Digital Twins as Oracles to Foster the Use of Formal Methods in PracticeLeveraging Applications of Formal Methods, Verification and Validation. Software Engineering Methodologies10.1007/978-3-031-75387-9_3(30-43)Online publication date: 27-Oct-2024
https://dl.acm.org/doi/10.1007/978-3-031-75387-9_3
Nagashima YXu ZWang NGoc DBang J(2023)Template-Based Conjecturing for Automated Induction in Isabelle/HOLFundamentals of Software Engineering10.1007/978-3-031-42441-0_9(112-125)Online publication date: 4-May-2023
https://dl.acm.org/doi/10.1007/978-3-031-42441-0_9
Einarsdóttir SSmallbone NJohansson M(2020)Template-based Theory Exploration: Discovering Properties of Functional Programs by TestingProceedings of the 32nd Symposium on Implementation and Application of Functional Languages10.1145/3462172.3462192(67-78)Online publication date: 2-Sep-2020
https://dl.acm.org/doi/10.1145/3462172.3462192

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