Bidirectional transformations (BX) are means of maintaining consistency between multiple information sources: when one source is edited, the others may need updating to restore consistency. BX have applications in databases, user interface design, model-driven development, and many other domains. This volume represents the lecture notes from the Summer School on Bidirectional Transformations, held in Oxford, UK, in July 2016. The school was one of the final activities on the project "A Theory of Least Change for Bidirectional Transformations", running at the University of Oxford and the University of Edinburgh from 2013 to 2017 and funded by the UK Engineering and Physical Sciences Research Council. The five chapters included in this volume are a record of most of the material presented at the summer school. After a comprehensive introduction to bidirectional transformations, they deal with triple graph grammars, modular edit lenses, putback-based bidirectional programming, and engineering of bidirectional transformations.

Generic programming is about making programs more adaptable by making them more general. Generic programs often embody non-traditional kinds of polymorphism; ordinary programs are obtained from them by suitably instantiating their parameters. In contrast with normal programs, the parameters of a generic program are often quite rich in structure; for example, they may be other programs, types or type constructors, class hierarchies, or even programming paradigms. Generic programming techniques have always been of interest, both to practitioners and to theoreticians, but only recently have generic programming techniques become a specific focus of research in the functional and object-oriented programming language communities. Generic Programming comprises the edited proceedings of the Working Conference on Generic Programming, which was sponsored by the International Federation for Information Processing (IFIP) and held in Dagstuhl, Germany in July 2002. With contributions from leading researchers around the world, this volume captures the state of the art in this important emerging area.

Generic programming is about making programs more widely applicable via exotic kinds of parametrization---not just along the dimensions of values or of types, but also of things such as the shape of data, algebraic structures, strategies, computational paradigms, and so on. Indexed programming is a lightweight form of dependently typed programming, constraining flexibility by allowing one to state and check relationships between parameters: that the shapes of two arguments agree, that an encoded value matches some type, that values transmitted along a channel conform to the stated protocol, and so on. The two forces of genericity and indexing balance each other nicely, simultaneously promoting and controlling generality. The 5 lectures included in this book stem from the Spring School on Generic and Indexed Programming, held in Oxford, UK, in March 2010 as a closing activity of the generic and indexed programming project at Oxford which took place in the years 2006-2010.

This book constitutes the refereed proceedings of the 11th International Conference on Mathematics of Program Construction, MPC 2012, held in Madrid, Spain, in June 2012. The 13 revised full papers presented together with three invited talks were carefully reviewed and selected from 27 submissions. The papers are organized in topical sections on security and information flow, synchronous and real-time systems, algorithms and games, program calculi, tool support, algebras and datatypes, and categorical functional programming.

This volume contains the proceedings of TFM2009, the Second International FME Conference on Teaching Formal Methods, organized by the Subgroup of Education of the Formal Methods Europe (FME) association. The conference took place as part of the ?rst Formal Methods Week (FMWeek), held in Ei- hoven, The Netherlands, in November 2009. TFM2009 was a one-day forum in which to explore the successes and fa- ures of formal method (FM) education, and to promote cooperative projects to further educationand training in FMs. The organizersgatheredlecturers,tea- ers,andindustrialpartnersto discusstheir experience,presenttheir pedagogical methodologies, and explore best practices. Interest in FM teaching is growing. TFM2009 followed in a series of events on teaching FMs which includes two BCS-FACS TFM workshops (Oxford in 2003, and London in 2006), the TFM2004 conference (Ghent, 2004, with p- ceedings published as Springer LNCS Volume 3294), the FM-Ed 2006 workshop (Hamilton, co-located with FM2006), FORMED (Budapest, at ETAPS2008), and FMET2008 (Kitakyushu, co-located with ICFEM2008). FMs have an important role to play in the development of complex c- puting systems-a role acknowledged in industrial standards such as IEC61508 and ISO/IEC15408, and in the increasing use of precise modelling notations, semantic markup languages, and model-driven techniques. There is a growing need for software engineers who can work e?ectively with simple, mathematical abstractions, and with practical notions of inference and proof.

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.

This book constitutes the refereed proceedings of the 6th International Conference on Integrated Formal Methods, IFM 2007, held in Oxford, UK in July 2007.

The 32 revised full papers presented together with 1 invited paper were carefully reviewed and selected from 85 submissions. The papers address all aspects of formal methods integration, including of a process of analysis or design application of formal methods to analysis or design, extension of one method, based upon the inclusion of ideas or concepts from others, informal or semi-formal modelling languages, tools, or techniques, and semantic integration or practical application.

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

Generic programming is about making programs more adaptable by making them more general. Generic programs often embody non-traditional kinds of polymorphism; ordinary programs are obtained from them by suitably instantiating their parameters. In contrast with normal programs, the parameters of a generic program are often quite rich in structure; for example, they may be other programs, types or type constructors, class hierarchies, or even programming paradigms.

Generic programming techniques have always been of interest, both to practitioners and to theoreticians, but only recently have generic programming techniques become a specific focus of research in the functional and object-oriented programming language communities.

Generic Programming comprises the edited proceedings of the Working Conference on Generic Programming, which was sponsored by the International Federation for Information Processing (IFIP) and held in Dagstuhl, Germany in July 2002. With contributions from leading researchers around the world, this volume captures the state of the art in this important emerging area.

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 book constitutes the thoroughly refereed post-conference proceedings of the Third International Symposium on Foundations of Health Information Engineering and Systems, FHIES 2013, held in Macau, China, in August 2013. The 19 revised full papers presented together with 1 invited talk in this volume were carefully reviewed and selected from 22 submissions. The papers are organized in following subjects: panel position statements, pathways, generation and certification, interoperability, patient safety, device safety, formal methods and HIV/AIDS and privacy.

This book is devoted to five main principles of algorithm design: divide and conquer, greedy algorithms, thinning, dynamic programming, and exhaustive search. These principles are presented using Haskell, a purely functional language, leading to simpler explanations and shorter programs than would be obtained with imperative languages. Carefully selected examples, both new and standard, reveal the commonalities and highlight the differences between algorithms. The algorithm developments use equational reasoning where applicable, clarifying the applicability conditions and correctness arguments. Every chapter concludes with exercises (nearly 300 in total), each with complete answers, allowing the reader to consolidate their understanding and apply the techniques to a range of problems. The book serves students (both undergraduate and postgraduate), researchers, teachers, and professionals who want to know more about what goes into a good algorithm and how such algorithms can be expressed in purely functional terms.