This collection of original research papers assesses and summarizes the impact of types on logic programming. Type theory is a well-established branch of theoretical computer science that has played an important role in the development of imperative and functional programming languages. This collection of original research papers assesses and summarizes the impact of types on logic programming. It covers all of the major themes in this burgeoning field, including simple types, regular tree types, polymorphic types, subtypes, and dependent types. Language design issues as well as semantics, pragmatics, and applications of types are discussed.The benefits that type considerations have to offer logic programming are being increasingly realized: through type checking many errors can be caught before a program is run, resulting in more reliable programs; types form an expressive basis for module systems, since they prescribe a machine-verifiable interface for the code encapsulated within a module; and types may be used to improve performance of code generated by a compiler. The research in this collection describes these benefits as well as important differences in the impact of types in functional and logic programming.

This book constitutes the refereed proceedings of the 10th International Symposium on Functional and Logic Programming, FLOPS 2010, held in Sendai, Japan, in April 2010. The 21 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 49 submissions. The papers are organized in topical sections on types; program analysis and transformation; foundations; logic programming; evaluation and normalization; term rewriting; and parallelism and control.

A new edition of a book, written in a humorous question-and-answer style, that shows how to implement and use an elegant little programming language for logic programming. The goal of this book is to show the beauty and elegance of relational programming, which captures the essence of logic programming. The book shows how to implement a relational programming language in Scheme, or in any other functional language, and demonstrates the remarkable flexibility of the resulting relational programs. As in the first edition, the pedagogical method is a series of questions and answers, which proceed with the characteristic humor that marked The Little Schemer and The Seasoned Schemer. Familiarity with a functional language or with the first five chapters of The Little Schemer is assumed. For this second edition, the authors have greatly simplified the programming language used in the book, as well as the implementation of the language. In addition to revising the text extensively, and simplifying and revising the “Laws” and “Commandments,” they have added explicit “Translation” rules to ease translation of Scheme functions into relations.

This volume contains the papers presented at the 4th Fuji International S- posium on Functional and Logic Programming (FLOPS’99) held in Tsukuba, Japan, November 11–13, 1999, and hosted by the Electrotechnical Laboratory (ETL). FLOPS is a forum for presenting and discussing all issues concerning functional programming, logic programming, and their integration. The sym- sium takes place about every 1.5 years in Japan. Previous FLOPS meetings were held in Fuji Susuno (1995), Shonan Village (1996), and Kyoto (1998). 1 There were 51 submissions from Austria ( ),Belgium (2),Brazil(3),China 3 3 1 7 (1), Denmark (2), France (3 ), Germany (8), Ireland (1), Israel ( ), Italy (1 ), 4 3 12 1 Japan (9 ), Korea (1), Morocco (1), The Netherlands (1), New Zealand (1), 3 1 1 3 5 Portugal ( ), Singapore ( ), Slovakia (1), Spain (4 ), Sweden (1), UK (4 ), 2 3 4 6 1 and USA (2 ), of which the program committee selected 21 for presentation. In 4 addition, this volume contains full papers by the two invited speakers, Atsushi Ohori and Mario Rodr ́?guez-Artalejo.

This volume contains the papers which have been accepted for presentation atthe Third International Symposium on Programming Language Implementation andLogic Programming (PLILP '91) held in Passau, Germany, August 26-28, 1991. The aim of the symposium was to explore new declarative concepts, methods and techniques relevant for the implementation of all kinds of programming languages, whether algorithmic or declarative ones. The intention was to gather researchers from the fields of algorithmic programming languages as well as logic, functional and object-oriented programming. This volume contains the two invited talks given at the symposium by H. Ait-Kaci and D.B. MacQueen, 32 selected papers, and abstracts of several system demonstrations. The proceedings of PLILP '88 and PLILP '90 are available as Lecture Notes in Computer Science Volumes 348 and 456.

This book constitutes the refereed proceedings of the 5th International Symposium on Functional and Logic Programming, FLOPS 2001, held in Tokyo, Japan in March 2001. The 21 revised full papers presented together with three invited papers were carefully reviewed and selected from 40 submissions. The book offers topical sections on functional programming, logic programming, functional logic programming, types, program analysis and transformation, and Lambda calculus.

Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called λProlog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and λ-terms and π-calculus expressions can be encoded in λProlog.

This book constitutes the refereed proceedings of the 6th International Symposium on Functional and Logic Programming, FLOPS 2002, held in Aizu, Japan, in September 2002. The 15 revised full papers presented together with 3 full invited papers were carefully reviewed and selected from 27 submissions. The papers are organized in topical sections on constraint programming, program transformation and analysis, semantics, rewriting, compilation techniques, and programming methodology.

Agda is an advanced programming language based on Type Theory. Agda's type system is expressive enough to support full functional verification of programs, in two styles. In external verification, we write pure functional programs and then write proofs of properties about them. The proofs are separate external artifacts, typically using structural induction. In internal verification, we specify properties of programs through rich types for the programs themselves. This often necessitates including proofs inside code, to show the type checker that the specified properties hold. The power to prove properties of programs in these two styles is a profound addition to the practice of programming, giving programmers the power to guarantee the absence of bugs, and thus improve the quality of software more than previously possible. Verified Functional Programming in Agda is the first book to provide a systematic exposition of external and internal verification in Agda, suitable for undergraduate students of Computer Science. No familiarity with functional programming or computer-checked proofs is presupposed. The book begins with an introduction to functional programming through familiar examples like booleans, natural numbers, and lists, and techniques for external verification. Internal verification is considered through the examples of vectors, binary search trees, and Braun trees. More advanced material on type-level computation, explicit reasoning about termination, and normalization by evaluation is also included. The book also includes a medium-sized case study on Huffman encoding and decoding.