The design and implementation of a relational programming system.

The declarative class of computer languages consists mainly of two paradigms - the logic and the functional. Much research has been devoted in recent years to the integration of the two with the aim of securing the advantages of both without retaining their disadvantages. To date this research has, arguably, been less fruitful than initially hoped. A large number of composite functional/logical languages have been proposed but have generally been marred by the lack of a firm, cohesive, mathematical basis. More recently new declarative paradigms, equational and constraint languages, have been advocated. These however do not fully encompass those features we perceive as being central to functional and logic languages. The crucial functional features are higher-order definitions, static polymorphic typing, applicative expressions and laziness. The crucial logic features are ability to reason about both functional and non-functional relationships and to handle computations involving search. This thesis advocates a new declarative paradigm which lies midway between functional and logic languages - the so-called relational paradigm. In a relationallanguage program and data alike are denoted by relations. All expressions are relations constructed from simpler expressions using operators which form a relational algebra. The impetus for use of relations in a declarative language comes from observations concerning their connection to functional and logic programming. Relations are mathematically more general than functions modelling non-functional as well as functional relationships. They also form the basis of many logic languages, for example, Prolog. This thesis proposes a new relational language based entirely on binary relations, named Drusilla. We demonstrate the functional and logic aspects of Drusilla. It retains the higher-order objects and polymorphism found in modern functional languages but handles non-determinism and models relationships between objects in the manner of a logic language with notion of algorithm being composed of logic and control elements. Different programming styles - functional, logic and relational- are illustrated. However, such expressive power does not come for free; it has associated with it a high cost of implementation. Two main techniques are used in the necessarily complex language interpreter. A type inference system checks programs to ensure they are meaningful and simultaneously performs automatic representation selection for relations. A symbolic manipulation system transforms programs to improve. efficiency of expressions and to increase the number of possible representations for relations while preserving program meaning

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

Refining Weakly Outermost-Needed Rewriting and Narrowing

Outermost-needed rewriting/narrowing is a sound and complete optimal demand-driven strategy for the class of inductively sequential constructor systems. Its parallel extension (known as weakly) deals with non-inductively sequential constructor systems. In this paper, we present natural rewriting, a suitable extension of (weakly) outermost-needed rewriting which is based on a refinement of the demandness notion associated to the latter, and we extend it to narrowing. Intuitively, natural rewriting (narrowing) always reduces (narrows) the most often demanded position in a term. We formalize the strategy for left-linear constructor systems though, for the class of inductively sequential constructor systems, natural rewriting (narrowing) behaves even better than outermost-needed rewriting (narrowing) in the avoidance of failing computations. With regard to inductively sequential constructor systems, we introduce a larger class of systems called inductively sequential preserving where natural rewriting and narrowing preserve optimality for sequential parts of the program. We also provide a prototype interpreter of natural rewriting and narrowing

Automated Reasoning

This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book

The design and implementation of a multiparadigm programming language.

by Chi-keung Luk.Thesis (M.Phil.)--Chinese University of Hong Kong, 1993.Includes bibliographical references (leaves 169-174).Preface --- p.xiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Programming Languages --- p.2Chapter 1.2 --- Programming Paradigms --- p.2Chapter 1.2.1 --- What is a programming paradigm --- p.2Chapter 1.2.2 --- Which came first? Languages or paradigms? --- p.2Chapter 1.2.3 --- Overview of some paradigms --- p.4Chapter 1.2.4 --- A spectrum of paradigms --- p.6Chapter 1.2.5 --- Mulitparadigm systems --- p.7Chapter 1.3 --- The Objectives of this research --- p.8Chapter 2 --- "Studies of the object-oriented, the logic and the functional paradigms" --- p.10Chapter 2.1 --- The Object-Oriented Paradigm --- p.10Chapter 2.1.1 --- Basic components --- p.10Chapter 2.1.2 --- Motivations --- p.11Chapter 2.1.3 --- Some related issues --- p.12Chapter 2.1.4 --- Computational models for object-oriented programming --- p.16Chapter 2.2 --- The Functional Paradigm --- p.18Chapter 2.2.1 --- Basic concepts --- p.18Chapter 2.2.2 --- Lambda calculus --- p.20Chapter 2.2.3 --- The characteristics of functional programs --- p.21Chapter 2.2.4 --- Practicality of functional programming --- p.25Chapter 2.3 --- The Logic Paradigm --- p.28Chapter 2.3.1 --- Relations --- p.28Chapter 2.3.2 --- Logic programs --- p.29Chapter 2.3.3 --- The opportunity for parallelism --- p.30Chapter 2.4 --- Summary --- p.31Chapter 3 --- A survey of some existing multiparadigm languages --- p.32Chapter 3.1 --- Logic + Object-Oriented --- p.33Chapter 3.1.1 --- LogiC++ --- p.33Chapter 3.1.2 --- Intermission --- p.34Chapter 3.1.3 --- Object-Oriented Programming in Prolog (OOPP) --- p.36Chapter 3.1.4 --- Communication Prolog Unit (CPU) --- p.37Chapter 3.1.5 --- DLP --- p.37Chapter 3.1.6 --- Representing Objects in a Logic Programming Language with Scoping Constructs (OLPSC) --- p.39Chapter 3.1.7 --- KSL/Logic --- p.40Chapter 3.1.8 --- Orient84/K --- p.41Chapter 3.1.9 --- Vulcan --- p.42Chapter 3.1.10 --- The Bridge approach --- p.43Chapter 3.1.11 --- Discussion --- p.44Chapter 3.2 --- Functional + Object-Oriented --- p.46Chapter 3.2.1 --- PROOF --- p.46Chapter 3.2.2 --- A Functional Language with Classes (FLC) --- p.47Chapter 3.2.3 --- Common Lisp Object System (CLOS) --- p.49Chapter 3.2.4 --- FOOPS --- p.50Chapter 3.2.5 --- Discussion --- p.51Chapter 3.3 --- Logic + Functional --- p.52Chapter 3.3.1 --- HOPE --- p.52Chapter 3.3.2 --- FUNLOG --- p.54Chapter 3.3.3 --- F* --- p.55Chapter 3.3.4 --- LEAF --- p.56Chapter 3.3.5 --- Applog --- p.57Chapter 3.3.6 --- Discussion --- p.58Chapter 3.4 --- Logic + Functional + Object-Oriented --- p.61Chapter 3.4.1 --- Paradise --- p.61Chapter 3.4.2 --- LIFE --- p.62Chapter 3.4.3 --- UNIFORM --- p.63Chapter 3.4.4 --- G --- p.64Chapter 3.4.5 --- FOOPlog --- p.66Chapter 3.4.6 --- Logic and Objects (L&O) --- p.66Chapter 3.4.7 --- Discussion --- p.67Chapter 4 --- The design of a multiparadigm language I --- p.70Chapter 4.1 --- An Object-Oriented Framework --- p.71Chapter 4.1.1 --- A hierarchy of classes --- p.71Chapter 4.1.2 --- Program structure --- p.71Chapter 4.1.3 --- Parametric classes --- p.72Chapter 4.1.4 --- Inheritance --- p.73Chapter 4.1.5 --- The meanings of classes and methods --- p.75Chapter 4.1.6 --- Objects and messages --- p.75Chapter 4.2 --- The logic Subclasses --- p.76Chapter 4.2.1 --- Syntax --- p.76Chapter 4.2.2 --- Distributed inference --- p.76Chapter 4.2.3 --- Adding functions and expressions to logic programs --- p.77Chapter 4.2.4 --- State modelling --- p.79Chapter 4.3 --- The functional Subclasses --- p.80Chapter 4.3.1 --- The syntax of functions --- p.80Chapter 4.3.2 --- Abstract data types --- p.81Chapter 4.3.3 --- Augmented list comprehensions --- p.82Chapter 4.4 --- The Semantic Foundation of I Programs --- p.84Chapter 4.4.1 --- T1* : Transform functions into Horn clauses --- p.84Chapter 4.4.2 --- T2*: Transform object-oriented features into pure logic --- p.85Chapter 4.5 --- Exploiting Parallelism in I Programs --- p.89Chapter 4.5.1 --- Inter-object parallelism --- p.89Chapter 4.5.2 --- Intra-object parallelism --- p.92Chapter 4.6 --- Discussion --- p.96Chapter 5 --- An implementation of a prototype of I --- p.99Chapter 5.1 --- System Overview --- p.99Chapter 5.2 --- I-to-Prolog Translation --- p.101Chapter 5.2.1 --- Pass 1 - lexical and syntax analysis --- p.101Chapter 5.2.2 --- Pass 2 - Class Table Construction and Semantic Checking --- p.101Chapter 5.2.3 --- Pass 3 - Determination of Multiple Inheritance Precedence --- p.105Chapter 5.2.4 --- Pass 4 - Translation of the directive part --- p.110Chapter 5.2.5 --- Pass 5 - Creation of Prolog source code for an I object --- p.110Chapter 5.2.6 --- Using expressions in logic methods --- p.112Chapter 5.3 --- I-to-LML Translation --- p.114Chapter 5.4 --- The Run-time Handler --- p.117Chapter 5.4.1 --- Object Management --- p.118Chapter 5.4.2 --- Process Management and Message Passing --- p.121Chapter 6 --- Some applications written in I --- p.125Chapter 6.1 --- Modeling of a State Space Search --- p.125Chapter 6.2 --- A Solution to the N-queen Problem --- p.129Chapter 6.3 --- Object-Oriented Modeling of a Database --- p.131Chapter 6.4 --- A Simple Expert System --- p.133Chapter 6.5 --- Summary --- p.138Chapter 7 --- Conclusion and future work --- p.139Chapter 7.1 --- Conclusion --- p.139Chapter 7.2 --- Future Work --- p.141Chapter A --- Language manual --- p.146Chapter A.1 --- Introduction --- p.146Chapter A.2 --- Syntax --- p.146Chapter A.2.1 --- The lexical specification --- p.146Chapter A.2.2 --- The syntax specification --- p.149Chapter A3 --- Classes --- p.152Chapter A.4 --- Object Creation and Method Invocation --- p.153Chapter A.5 --- The logic Subclasses --- p.155Chapter A.6 --- The functional Subclasses --- p.156Chapter A.7 --- Types --- p.158Chapter A.8 --- Mutable States --- p.158Chapter B --- User's guide --- p.160Chapter B.1 --- System Calls --- p.160Chapter B.2 --- Configuration Parameters --- p.162Chapter B.3 --- Errors --- p.163Chapter B.4 --- Implementation Limits --- p.164Chapter B.5 --- How to install the system --- p.164Chapter B.6 --- How to use the system --- p.164Chapter B.7 --- How to recompile the system --- p.166Chapter B.8 --- Directory arrangement --- p.167Chapter C --- List of publications --- p.168Bibliography --- p.16

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Proceedings of the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), 10-11 July 2017, Nottingham Conference Centre, Nottingham Trent University

This book contains the abstracts and papers presented at the Eleventh UK Conference on Boundary Integral Methods (UKBIM 11), held at Nottingham Trent University in July 2017. The work presented at the conference, and published in this volume, demonstrates the wide range of work that is being carried out in the UK, as well as from further afield