Program construction : calculating implementations from specifications

Unique approach tackles what most books don't-why maths and logic are fundamental tools for a programmer This comprehensive guide is a balanced combination of mathematical theory and the practice of programming Straightforward presentation of construction principles inlcuding: assignment axiom, sequential composition, case analysis, use of invariants and bound functions Includes a wide range of entertaining and challenging examples and exercises 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. Content: 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. Abstract: Unique approach tackles what most books don't-why maths and logic are fundamental tools for a programmer. This comprehensive guide is a balanced combination of mathematical theory and the practice of programming. Straightforward presentation of construction principles including: assignment axiom, sequential composition, case analysis, use of invariants and bound functions. Includes a wide range of entertaining and challenging examples and exercises Most texts on logic or discrete math fail to show why math and logic are fundamental tools for programmers. Program Construction illustrates the importance of math and logic to programming, providing a complete, self-contained account of the principles of logical reasoning. Designed specifically so users can construct programs that meet their specifications, the book details program construction principles in a straightforward fashion, avoiding overly complicated theory, and then illustrating each with convincing examples.