The Science of Programming

0. Why Use Logic? Why Prove Programs Correct?.- I. Propositions and Predicates.- 1. Propositions.- 2. Reasoning using Equivalence Transformations.- 3. A Natural Deduction System.- 4. Predicates.- 5. Notations and Conventions for Arrays.- 6. Using Assertions to Document Programs.- II. The Semantics of a Small Language.- 7. The Predicate Transformer wp.- 8. The Commands skip, abort and Composition.- 9. The Assignment Command.- 10. The Alternative Command.- 11. The Iterative Command.- 12. Procedure Call.- III. The Development of Programs.- 13. Introduction.- 14. Programming as a Goal-Oriented Activity.- 15. Developing Loops from Invariants and Bounds.- 16. Developing Invariants.- 17. Notes on Bound Functions.- 18. Using Iteration Instead of Recursion.- 19. Efficiency Considerations.- 20. Two Larger Examples of Program Development.- 21. Inverting Programs.- 22. Notes on Documentation.- 23. Historical Notes.- Appendix 1. Backus-Naur Form.- Appendix 2. Sets, Sequences, Integers and Real Numbers.- Appendix 3. Relations and Functions.- Appendix 4. Asymptotic Execution Time Properties.- Answers to Exercises.- References.