Program Construction: Calculating Implementations from Specifications

The ever-increasing dependence of our lives and livelihoods on the correct functioning of computer software means that logic and program correctness are core elements of all good computer science degrees. This book presents both these topics in one self-contained text.

The focus of the book is on "correct-by-construction" program design -- the discipline of calculating programs from their specifications. Modern, calculational logic is introduced in combination with key program construction principles, such as the assignment axiom, loop invariants and bound functions. This material is intertwined with motivational discussion, programming examples and challenging problem-solving exercises, bringing the book alive for its intended audience, undergraduates in computer science and mathematics, as well as professional programmers wishing to further develop their programming skills.

The book covers the elements of logic and program correctness that form the foundations of further study --- the logical connectives and their algebraic properties, induction, quantifiers and program construction rules. Substantial examples of program construction are included. Many exercises are provided, all with detailed solutions.

Table of Contents

Preface.

A Science of Computing.

A Searching Problem and Its Solution.

Calculational Proof.

Implementation Issues.

Calculational Logic: Part 1.

Number Conversion.

Calculational Logic: Part 2.

Maximum and Minimum.

The Assignment Statement.

Sequential Composition and Conditional Statements.

Quantifiers.

Inductive Proofs and Constructions.

Iteration.

Sorting and Searching Algorithms.

Remainder Computation.

Cyclic Codes.

Appendix.

Solutions to Exercises.

References.

Glossary of Symbols.

Index.