The Design of Well-Structured and Correct Programs

1 Introducing Top-down Design.- 1.1 The Idea of Top-down Design.- 1.2 An Example: The Greatest Common divisor.- 1.3 Programming Language and Machine Language.- 2 Basic Compositions of Actions and Their Proof Rules.- 2.1 Relations for Program Correctness.- 2.2 Logical Formulas and Pascal Expressions.- 2.3 Proof Rules for Simple Statements.- 2.4 Compound and Conditional Statements.- 2.5 Repetitive Statements.- 2.6 Summary of Basic Proof Rules.- 2.7 Using the Basic Proof Rules.- 2.8 Correct Termination of Algorithms.- Exercises.- 3 Data Types.- 3.1 Introduction.- 3.2 A Primer on Set Theory.- 3.3 Scalar Types and Simple Types.- 3.4 Arrays, Records, and Files.- 3.5 Processing Arrays.- 3.6 Processing Files and Records.- 3.7 Set Manipulation in Pascal.- Exercises.- 4 Developing Programs with Proofs of Correctness.- 4.1 Introduction.- 4.2 Squares and Palindromes.- 4.3 Sorting Arrays and Files.- 4.4 Manipulating Sets.- Exercises.- 5 Procedures and Functions.- 5.1 Procedures and Functions.- 5.3 Functions and Their Proof of Correctness.- 5.4 Proofs of Correctness of Procedures.- Exercises.- 6 Recursion.- 6.1 Introduction.- 6.2 Design and Correctness of Recursive Procedures.- 6.3 Recursive Data Types.- 6.4 Recursive Algorithms and Recursive Data Structures.- Exercises.- 7 Programming with and without Gotos.- 7.1 Goto Statements.- 7.2 Proof Rules for Gotos.- 7.3 Return Exits and the Algorithm Find.- 7.4 Failure Exits and the Algorithm Lookup.- 7.5 Loops with Exits in the Middle.- Exercises.- References.- Appendixes.- Index of Algorithms.- Author Index.