• Corpus ID: 221312116

# Isabelle/HOL: A Proof Assistant for Higher-Order Logic

@inproceedings{Nipkow2002IsabelleHOLAP,
title={Isabelle/HOL: A Proof Assistant for Higher-Order Logic},
author={Tobias Nipkow and Markus Wenzel and Lawrence Charles Paulson},
year={2002}
}
• Published 2002
• Computer Science
Elementary Techniques.- 1. The Basics.- 2. Functional Programming in HOL.- 3. More Functional Programming.- 4. Presenting Theories.- Logic and Sets.- 5. The Rules of the Game.- 6. Sets, Functions, and Relations.- 7. Inductively Defined Sets.- Advanced Material.- 8. More about Types.- 9. Advanced Simplification, Recursion, and Induction.- 10. Case Study: Verifying a Security Protocol.
2,611 Citations
Theorema-HOL, an add-on package for the Theorema 2.0 proof assistant which enables users to formalize their mathematical theories in classical higher-order logic, comes with an intuitive and easy-to-use theoryand proof language, inspired by Isabelle/Isar, for proving theorems interactively.
Using Isabelle/HOL, the syntax and semantics of MLSS are formalised as well as a sound and complete tableau calculus for it and an abstract specification of a decision procedure that applies the rules of the calculus exhaustively and proves its termination.
Nitpick is the development of Nitpick, a counterexample generator that builds on a first-order relational model finder that heuristically selects facts relevant to the conjecture to prove and delegates the problem to first- order resolution provers and SMT solvers.
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• 2015
The semantics of FOL can be described in the meta-language of higher-order logic (HOL) and one can prove sentences in FOL valid using the formalized FOL semantics.
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• 2016
We present a short proof of the Church-Rosser property for the lambda-calculus enjoying two distinguishing features: firstly, it employs the Z-property, resulting in a short and elegant proof; and
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IWIL@LPAR
• 2017
Modifications to the higher-order automated theorem prover Leo-III are presented for turning it into a reasoning system for rank-1 polymorphic HOL and a suitable paramodulation-based calculus are sketched.
The aim of this paper is to encourage the development of personal proof assistants and semi-automated provers for a variety of modal logics.
• Computer Science
• 2018
This work shows work in progress on certifying soundness of this system in the interactive proof assistant Isabelle, and establishes an outline for future work such as a certiﬁed completeness proof of the axiomatic system in Isabelle.
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High. Order Symb. Comput.
• 2008
Techniques that support the expression of functional programs as logical functions are discussed, including those that can be automatically proved and those that have difficult termination proofs.
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Arch. Formal Proofs
• 2021
This work formalizes this metalogic and the language of proof terms in Isabelle/HOL, defines an executable (but inefficient) proof term checker and proves the correctness of all the proofs in those theories.