## Isabelle/HOL: A Proof Assistant for Higher-Order LogicThis volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst 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. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages. |

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### Contents

1The Basics | 3 |

2 Functional Programming in HOL | 9 |

3 More Functional Programming | 27 |

4 Presenting Theories | 53 |

5 The Rules of the Game | 67 |

6 Sets Functions and Relations | 105 |

7 Inductively Defined Sets | 127 |

8 More about Types | 146 |

9 Advanced Simplification Recursion and Induction | 175 |

Verifying a Security Protocol | 195 |

A Appendix | 206 |

209 | |

213 | |

### Other editions - View all

Isabelle/HOL: A Proof Assistant for Higher-Order Logic Tobias Nipkow,Lawrence C. Paulson,Markus Wenzel No preview available - 2002 |

Isabelle/HOL: A Proof Assistant for Higher-Order Logic Tobias Nipkow,Lawrence C. Paulson,Markus Wenzel No preview available - 2014 |

### Common terms and phrases

aexp apply assumption apply blast apply erule apply rule apply simp apply(auto apply(induct_tac apply(simp argument arity auto automatically axioms bool bound variables classical reasoner command conclusion constant constdefs constructors consts Crypt pubK datatype declaration defined drule mp elimination rule equation evala example expressions formula functional programming goal gterms F higher-order logic ifex induction hypothesis induction rule inductive definition infix instantiated intro introduction rule Isabelle Isabelle’s Isabelle/HOL itrev knows Spy LATEX lemma logic map_bt method model checking natural deduction natural numbers Nonce notation ns_public operations ordrel overloaded premise primrec proof protocol prove recdef record recursive call recursive functions replaced result rev xs rewrite rules rule induction schematic variables Sect simp add simp_all simplification rule split subgoal subst Suc Suc symbols syntax term theorem theory tion transitive closure trev trivial universal quantifier well_formed_gterm well-founded relation Xcoord