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Twenty Five Years of Constructive Type Theory
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
Term Rewriting Systems
Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.
Selected Papers on Automath
The present volume contains a considered choice of the existing literature on Automath. Many of the papers included in the book have been published in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished. The aim of the editors is to present a representative selection of existing articles and reports and of material contained in dissertations, giving a compact and more or less complete overview of the work that has been done in the Automath research field, from the beginning to the present day. Six different areas have been distinguished, which correspond to Parts A to F of the book. These areas range from general ideas and motivation, to detailed syntactical investigations.
Introduction to Higher-Order Categorical Logic
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Lambda Calculus with Types
This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.
Processes, Terms and Cycles: Steps on the Road to Infinity
This Festschrift is dedicated to Jan Willem Klop on the occasion of his 60th birthday. The volume comprises a total of 23 scientific papers by close friends and colleagues, written specifically for this book. The papers are different in nature: some report on new research, others have the character of a survey, and again others are mainly expository. Every contribution has been thoroughly refereed at least twice. In many cases the first round of referee reports led to significant revision of the original paper, which was again reviewed. The articles especially focus upon the lambda calculus, term rewriting and process algebra, the fields to which Jan Willem Klop has made fundamental contributions.
The Beauty of Functional Code
This Festschrift has been published in honor of Rinus Plasmeijer, to celebrate the combined occasion of his 61st birthday and the 25th Symposium on Implementation and Application of Functional Languages, IFL 2013, held in Nijmegen, The Netherlands, in August 2013. Rinus Plasmeijer was the main designer of the lazy functional programming language "Clean" and has always been the leader of the associated research team. He has played a decisive role in making the Radboud University of Nijmegen an important center of research in functional programming by organizing and hosting the first few IFL symposia in Nijmegen. This Festschrift contains 19 scientific essays written by former PhD students of Rinus Plasmeijer and researchers in the field of functional programming who have collaborated with him. The authors write about the influence the beauty of functional programming has had or still has on their work.
Automata, Languages and Programming
In subvolume 27C1 magnetic and related properties of binary lanthanide oxides have been compiled. This subvolume covers data obtained since 1980 and can therefore be regarded as supplement to volume III/12c. While in the previous volume the majority of magnetic data was obtained either from magnetometric measurements or from neutron diffraction, for the present data the main emphasis is devoted to 'related' properties without which, however, the understanding of classical magnetic properties is impossible. A second part 27C2 will deal with binary oxides of the actinide elements.
Categorical Logic and Type Theory
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Higher Order Logic Theorem Proving and Its Applications
This volume presents the proceedings of the 7th International Workshop on Higher Order Logic Theorem Proving and Its Applications held in Valetta, Malta in September 1994. Besides 3 invited papers, the proceedings contains 27 refereed papers selected from 42 submissions. In total the book presents many new results by leading researchers working on the design and applications of theorem provers for higher order logic. In particular, this book gives a thorough state-of-the-art report on applications of the HOL system, one of the most widely used theorem provers for higher order logic.
