How To Write A Program Verification And Programming Book

Transcription

1 Jose Bacelar Almeida Maria Joao Frade Jorge Sousa Pinto Simao Melo de Sousa Rigorous Software Development An Introduction to Program Verification & Springer

2 Contents 1 Introduction A Formal Approach to Software Engineering Test and Simulation-Based Reliability An Alternative Approach: Formal Methods Requirements: Functional, Security, and Safety Formal Methods and Industrial Norms From Classic Software Engineering to Formal Software Engineering This Book 11 References 12 2 An Overview of Formal Methods Tools and Techniques The Central Problem Some Existing Formal Methods Taxonomies This Overview Specifying and Analysing Model-Based Specification Algebraic Specification Declarative Modelling Specifying and Proving Logic in a Nutshell Proof Tools Model Checking Program Logics and Program Annotation Specifying and Deriving Refinement Extraction Execution Specifying and Transforming Conclusions Are Formal Methods Tools Ready for Industry? Is Industry Ready to Use Formal Methods? 39 ix

3 Conients 2.7 To Learn More 39 References 40 Prepositional Logic Syntax Semantics Proof System Soundness and Completeness Validity Checking: Semantic Methods Normal Forms in Propositional Logic Validity of CNF Formulas Satisfiability of CNF Formulas Validity Checking: Deductive Methods To Learn More Exercises 76 References 78 First-Order Logic Syntax Semantics Proof System Soundness and Completeness Validity Checking Negation and Prenex Normal Forms Herbrand/Skolem Normal Forms and Semi-Decidability Decidable Fragments Variations and Extensions First-Order Logic with Equality Many-Sorted First-Order Logic Second-Order Logic First-Order Theories Equality Natural Numbers Integers Arrays Other Theories Combining Theories To Learn More Exercises 124 References 127 Hoare Logic Annotated While Programs Program Seman tics The While'"'Programming Language Specifications and Hoare Triples 136

4 Contents xi 5.3 Loop Invariants Hoare Calculus The Whilearray Programming Language A Rule of Hoare Logic for Array Assignment Loop Termination and Total Correctness Adaptation To Learn More Exercises 155 References Generating Verification Conditions Mechanising Hoare Logic The Weakest Precondition Strategy An Architecture for Program Verification A VCGen Algorithm Calculating the Weakest Precondition Calculating Verification Conditions Putting It All Together Verification Conditions for Whilearray Programs To Learn More Exercises 178 References Safety Properties Error Semantics and Safe Programs While"" with Errors Safety-Sensitive Calculus and VCGen Safe Whileint Programs Bounded Arrays: The Whilearray N Language Safe Whilearray N Programs An Alternative Formalisation of Bounded Arrays To Learn More Exercises 193 References Procedures and Contracts Procedures and Recursion The "Notation Recursive Procedures Procedure Calls in System Contracts and Mutual Recursion Programming with Contracts Inference System for Parameterless Procedures Verification Conditions for Parameterless Procedures Frame Conditions Procedures with Parameters 208

5 xii Contents Parameters Passed by Value Parameters Passed by Reference Aliasing Return Values and Pure Functions To Learn More Exercises 226 References Specifying C Programs An Introduction to ACSL Array-Based Programs Using Axiomatics Function Calls State Labels and Behaviours To Learn More Exercises 239 References Verifying C Programs Safety Verification Arithmetic Overflow Safety Safety of Array Access Adding Loop Invariants Termination Checking and Loop Variants Safety of Function Calls Functional Correctness: Array Partitioning Functional Correctness: Multiset Preservation A Word of Caution Pointer Variables and Parameters Passed by Reference To Learn More Exercises 255 References 255 Index 258