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2017 | Supplement | Chapter

Automated Theory Exploration for Interactive Theorem Proving:

An Introduction to the Hipster System

Author : Moa Johansson

Published in: Interactive Theorem Proving

Publisher: Springer International Publishing

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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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next chapter Automating Formalization by Statistical and Semantic Parsing of Mathematics

This example can be found online: https://github.com/moajohansson/IsaHipster/blob/master/Examples/ITP2017/Tree.thy.

The source code is at: https://github.com/moajohansson/IsaHipster/blob/master/Examples/ITP2017/Qrev.thy.

The proof command metis (followed by a list of required library facts) in the proof of lemma_aa is produced by Sledgehammer. Metis is Isabelle’s built in first order prover used to reconstruct proofs from external provers.

The interested reader may consult the file Tactic_Data.ML in the Hipster source code repository for details of several pre-defined combinations of easy/hard reasoning tactics, as well as how to define additional ones.

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Title: Automated Theory Exploration for Interactive Theorem Proving:
Author: Moa Johansson
Publisher: Springer International Publishing
Book: Interactive Theorem Proving
Print ISBN: 978-3-319-66106-3

Electronic ISBN: 978-3-319-66107-0

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-66107-0_1

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