Design and Analysis of Algorithms

Chapter 6

Proof Rules—Basics

Objectives

After reading this chapter, you should understand:

• The importance of Proof Rules (Axiomatic Semantics) in Program Verification
• Assertions and their role
• Proof Rules and their Notation
• How Proof Rules are specified for standard High Level Language constructs
• How to ensure correct Termination of Programs
• Program Transformation: Why and How
• Proof Rules for Procedures and Functions

Chapter Outline

6.1 Introduction

6.2 Computer Model for Program Execution

6.3 Assertions at Input and Output of Blocks

6.3.1 Symbolic Execution

6.4 Proof Rules

6.4.1 Compound Statements

6.4.2 Conditional Statements

6.4.3 Case Statements

6.4.4 Repetitive Statements

6.4.5 Repeat-Until Statement

6.4.6 Example: The Division Algorithm ...