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.

This tutorial book presents six carefully revised lectures given at the Spring School on Datatype-Generic Programming, SSDGP 2006. This was held in Nottingham, UK, in April 2006. It was colocated with the Symposium on Trends in Functional Programming (TFP 2006), and the Conference of the Types Project (TYPES 2006). All the lectures have been subjected to thorough internal review by the editors and contributors, supported by independent external reviews.

Generic programming attempts to make programming more efficient by making it more general. This book is devoted to a novel form of genericity in programs, based on parameterizing programs by the structure of the data they manipulate.

The book presents the following four revised and extended chapters first given as lectures at the Generic Programming Summer School held at the University of Oxford, UK in August 2002:

- Generic Haskell: Practice and Theory

- Generic Haskell: Applications

- Generic Properties of Datatypes

- Basic Category Theory for Models of Syntax

Program construction is about turning specifications of computer software into implementations. Recent research aimed at improving the process of program construction exploits insights from abstract algebraic tools such as lattice theory, fixpoint calculus, universal algebra, category theory, and allegory theory.This textbook-like tutorial presents, besides an introduction, eight coherently written chapters by leading authorities on ordered sets and complete lattices, algebras and coalgebras, Galois connections and fixed point calculus, calculating functional programs, algebra of program termination, exercises in coalgebraic specification, algebraic methods for optimization problems, and temporal algebra.

This volume contains the proceedings of MPC 2000, the ?fth international c- ference on Mathematics of Program Construction. This series of conferences aims to promote the development of mathematical principles and techniques that are demonstrably useful and usable in the process of constructing c- puter programs (whether implemented in hardware or software). The focus is on techniques that combine precision with concision, enabling programs to be constructed by formal calculation. Within this theme, the scope of the series is very diverse, including programming methodology, program speci?cation and transformation, programming paradigms, programming calculi, and progr- ming language semantics. The quality of the papers submitted to the conference was in general very high. However, the number of submissions has decreased compared to the pre- ous conferences in the series. Each paper was refereed by at least ?ve and often more committee members. In order to maintain the high standards of the c- ference the committee took a stringent view on quality; this has meant that, in some cases, a paper was rejected even though there was a basis for a good c- ference or journal paper but the submitted paper did not meet the committee's required standards. In a few cases a good paper was rejected on the grounds that it did not 't within the scope of the conference.