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The volume is organized into three parts: elementary techniques for modeling functional programs and mastering induction combined with automation; logic and set-oriented tactics for selective rule application, inductive set definitions, and applications like model checking; and advanced material covering numbers, records, overloading, and extended verification work including a security protocol. 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Paulson Markus Wenzel  \nIsabelle  \nHOL  \n=  \n→  \nλ  \n∀  \nβ  \nα  \nA Proof Assistant for Higher-Order Logic  \nDecember 12, 2021  \nSpringer-Verlag  \nBerlin Heidelberg NewYork London Paris Tokyo HongKong Barcelona Budapest  \nPreface  \nThis volume is a self-contained introduction to interactive proof in higherorder logic (HOL), using the proof assistant Isabelle. It is written for potential users rather than for our colleagues in the research world.  \nThe book has three parts.  \n– The first part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion.  \n– The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes Isabelle/HOL’s treatment of sets, functions and relations and explains how to define sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.  \n– The third part, Advanced Material, describes a variety of other topics. Among these are the real numbers, records and overloading. Advanced techniques for induction and recursion are described. A whole chapter is devoted to an extended example: the verification of a security protocol.  \nThe typesetting relies on Wenzel’s theory presentation tools. An annotated source file is run, typesetting the theory in the form of a LATEX source file. This book is derived almost entirely from output generated in this way. The final chapter of Part I explains how users may produce their own formal documents in a similar fashion.  \nIsabelle’s web site 1 contains links to the download area and to documentation and other information. The classic Isabelle user interface is Proof General / Emacs by David Aspinall’s. This book says very little about Proof General, which has its own documentation.  \nThis tutorial owes a lot to the constant discussions with and the valuable feedback from the Isabelle group at Munich: Stefan Berghofer, Olaf M¨uller, Wolfgang Naraschewski, David von Oheimb, Leonor Prensa Nieto, Cornelia Pusch, Norbert Schirmer and Martin Strecker. Stephan Merz was also kind  \n1 [https://isabelle.in.tum.de/](https://isabelle.in.tum.de/)  \niv Preface  \nenough to read and comment on a draft version. We received comments from Stefano Bistarelli, Gergely Buday, John Matthews and Tanja Vos.  \nThe research has been funded by many sources, including the dfg grants NI 491/2, NI 491/3, NI 491/4, NI 491/6, bmbf project Verisoft, the epsrc grants GR/K57381, GR/K77051, GR/M75440, GR/R01156/01 GR/S57198/01 and by the esprit working groups 21900 and IST-1999-29001 (the Types project) .  \nTable of Contents  \nPart I. Elementary Techniques  \n1. The Basics : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3  \n1.1 Introduction ........................................... 3  \n1.2 Theories ............................................... 4  \n1.3 Types, Terms and Formulae ............................. 4  \n1.4 Variables .............................................. 7  \n1.5 Interaction and Interfaces ............................... 7  \n1.6 Getting Started ........................................ 8  \n2. Functional Programming in HOL : : : : : : : : : : : : : : : : : : : : : : : : : 9  \n2.1 An Introductory Theory ................................. 9  \n2.2 Evaluation ............................................. 11  \n2.3 An Introductory Proof .................................. 12  \n2.4 Some Helpful Commands ................................ 16  \n2.5 Datatypes ............................................. 16  \n2.5.1 Lists ............................................ 17  \n2.5.2 The General Format ....................","cbCaiuZpNojOl42c","https://ap.wps.com/l/cbCaiuZpNojOl42c","pdf",1354663,221,"English","# Part I. Elementary Techniques\n## The Basics\n## Functional Programming in HOL\n## An Introductory Theory\n## More Functional Programming\n## Simplification\n## Induction Heuristics","[{\"question\":\"What is the purpose of this book and who is it written for?\",\"answer\":\"It provides a self-contained introduction to interactive proof in higher-order logic using Isabelle, written for potential users rather than research specialists.\"},{\"question\":\"How is the book structured across its three parts?\",\"answer\":\"Part I covers elementary techniques for modeling functional programs in HOL; Part II focuses on logic and sets, including lower-level tactics and inductive set definitions; Part III presents advanced topics such as real numbers, records, overloading, and induction/recursion techniques.\"},{\"question\":\"What kinds of examples and applications are included?\",\"answer\":\"Examples include nested and mutual recursion, inductive definitions, model checking, formal languages, and an extended security-protocol verification chapter.\"}]","A Proof Assistant for Higher-Order Logic - Preface and Table of Contents | PDF",557]