Ralf Hinze - Böcker

String diagrams are powerful graphical methods for reasoning in elementary category theory. Written in an informal expository style, this book provides a self-contained introduction to these diagrammatic techniques, ideal for graduate students and researchers. Much of the book is devoted to worked examples highlighting how best to use string diagrams to solve realistic problems in elementary category theory. A range of topics are explored from the perspective of string diagrams, including adjunctions, monad and comonads, Kleisli and Eilenberg-Moore categories, and endofunctor algebras and coalgebras. Careful attention is paid throughout to exploit the freedom of the graphical notation to draw diagrams that aid understanding and subsequent calculations. Each chapter contains plentiful exercises of varying levels of difficulty, suitable for self-study or for use by instructors.

This book constitutes the refereed proceedings of the 12th International Conference on Mathematics of Program Construction, MPC 2015, held in Königswinter, Germany, in June/July 2015. Some typical areas are type systems, program analysis and transformation, programming-language semantics, security, and program logics.

A leitmotif in the evolution of programming paradigms has been the level and extent of parametrisation that is facilitated — the so-called genericity of the paradigm. The sorts of parameters that can be envisaged in a programming language range from simple values, like integers and ?oating-point numbers, through structured values, types and classes, to kinds (the type of types and/or classes).Datatype-generic programming is about parametrising programsby the structure of the data that they manipulate. Toappreciatethe importanceofdatatypegenericity,oneneedlooknofurther than the internet. The internet is a massive repository of structured data, but the structure is rarely exploited. For example, compression of data can be much more e?ective if its structure is known, but most compression algorithms regard the input data as simply a string of bits, and take no account of its internal organisation. Datatype-genericprogrammingisaboutexploitingthestructureofdatawhen it is relevant and ignoring it when it is not. Programming languages most c- monly used at the present time do not provide e?ective mechanisms for do- menting and implementing datatype genericity. This volume is a contribution towards improving the state of the art. The emergence of datatype genericity can be traced back to the late 1980s.