Isabelle/HOL：高阶逻辑推导引擎证明

This textbook-like tutorial is a self-contained introduction to interactive proof, specification, and verification in higher-order logic, using the proof assistant Isabelle 2002. In contrast to existing Isabelle documentation, this book provides a direct route into higher-order logic by bypassing first-order logic and minimizing discussion of meta-theory.
　　Isabelle is a generic system for implementing logical formalisms, and Isabelle/HOL is the specialization of Isabelle for higher-order logic; this theorem prover is well suited as a specification and verification system.

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This textbook-like tutorial is a self-contained introduction to interactive proof, specification, and verification in higher-order logic, using the proof assistant Isabelle 2002. In contrast to existing Isabelle documentation, this book provides a direct route into higher-order logic by bypassing first-order logic and minimizing discussion of meta-theory.
Isabelle is a generic system for implementing logical formalisms, and Isabelle/HOL is the specialization of Isabelle for higher-order logic; this theorem prover is well suited as a specification and verification system.

Part I. Elementary Techniques
　1 Basics
　　1.1 Introduction
　　1.2 Theories
　　1.3 Types, Terms, and Formulae
　　1.4 Variables
　　1.5 Interaction and Interfaces
　　1.6 Getting Started
　2 Functional Programming in HOL
　　2.1 An Introductory Theory
　　2.2 An Introductory Proof
　　2.3 Some Helpful Commands
　　2.4 Datatypes
2.4.1 Lists
2.4.2 The General Format
2.4.3 Primitive Recursion
2.4.4 Case Expressions
2.4.5 Structural Induction and Case Distinction ..
2.4.6 Case Study: Boolean Expressions
2.5 Some Basic Types
2.5.1 Natural Numbers
2.5.2 Pairs
2.5.3 Datatype opt, ion
　　2.6 Definitions
2.6.1 Type Synonyms
2.6.2 Constant Definitions
　　2.7 The Definitional Approach
　3　More Functional Programming
　　3.1 Simplification
3.1.1 What Is Simplification?
3.1.2 Simplification Rules
3.1.3 The simp Method
　　　3.1.4 Adding and Deleting Simplification Rules
　　　3.1.5 Assumptions
　　　3.1.6 Rewriting with Definitions
　　　3.1.7 Simplifying let-Expressions
　　　3.1.8 Conditional Simplification Rules
　　　3.1.9 Automatic Case Splits
　　　3.1.10 Tracing
　　3.2　Induction Heuristics
　　3.3　Case Study: Compiling Expressions
　　3.4 Advanced Datatypes
　　　3.4.1 Mutual Recursion
　　　3.4.2 Nested Recursion
　　　3.4.3 The Limits of Nested Recursion
　　　3.4.4 Case Study: Tries
　　3.5　Total Recursive Functions
　　　3.5.1 Defining Recursive Functions
　　　3.5.2 Proving Termination
　　　3.5.3 Simplification and Recursive Functions
　　　3.5.4 Induction and Recursive Functions
　4　Presenting Theories
　　4.1 Concrete Syntax
4.1.1 Infix Annotations
4.1.2 Mathematical Symbols
4.1.3 Prefix Annotations
4.1.4 Syntax Translations
　　4.2 Document Preparation
　　　4.2.1 Isabelle Sessions
　　　4.2.2 Structure Markup
　　　4.2.3 Formal Comments and Antiquotations
　　　4.2.4 Interpretation of Symbols
　　　4.2.5 Suppressing Output
Part II. Logic and Sets
　5　The Rules of the Game
5.1 Natural Deduction
5.2 Introduction Rules
5.3 Elimination Rules
5.4 Destruction Rules: Some Examples
5.5 Implication
5.6 Negation
5.7 Interlude: The Basic Methods for Rules
5.8 Unification and Substitution
　　　……
A.Appendix
Part Ⅲ Advanced Material
Bibliography
Index