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. Language: English