At least four research fields detennine the theoretical background of specification and deduction in computer science: recursion theory, automated theorem proving, abstract data types and tenn rewriting systems. As these areas approach each other more and more, the strong distinctions between functional and relational views, deductive and denotational approaches as well as between specification and programming are relieved in favour of their integration. The book will not expose the lines of this development; conversely, it starts out from the nucleus of Hom clause logic and brings forth both known and unknown results, most of which affect more than one of the fields mentioned above. Chapter 1 touches on historical issues of specification and prototyping and delimits the topics handled in this book from others which are at the core of related work. Chapter 2 provides the fundamental notions and notations needed for the presentation and interpretation of many-sorted Horn clause theories with equality. Chapter 3 supplies a number of sample Hom clause specifications ranging from arithmetic through string manipulation to higher data structures and interpreters of programming languages. Some of these examples serve as a reference to illustrate definitions and results, others may throw a light on the strong link between specifications and programs, which are executed by applying deduction rules. Thus we have included examples of how to use program trans/ormation methods in specification design.

Klappentext

This book presents a unifying approach to semantical concepts and deductive methods used in recursive, equational and logic programming, data type specification and automated theorem-proving. The common background is Horn logic with equality. Although this logic does not cover the full first-order logic, it supplies us with a language that allows "natural" problem specifications, offers several semantical views (functional, relational, inductive, behavioural, etc.) and puts at our disposal a number of more or less special-purpose deductive methods, which can be used as rapid prototyping tools. The Horn clause calculus serves as the interface between the model-theoretic concepts of initial semantics, final semantics and internalized logic on one hand and deductive methods based on resolution, paramodulation, reduction and narrowing on the other hand. This contrasts previous approaches, which equip each semantical concept with its own calculus or, conversely, build a particular semantics upon each deductive method. Here the author starts out from the Horn clause calculus and develops individual concepts, results and procedures in a way that clearly delimits their respective purposes from each other. The unifying approach also brings about new variants or generalizations of known results and admits comparable arguments in soundness and completeness proofs.

Inhalt
1 Introduction.- 2 Basic Notions.- 2.1 Preliminaries.- 2.2 The Syntax of Specifications.- 2.3 Models of a Specification.- 3 Sample Specifications.- 3.1 Boolean Algebra.- 3.2 Arithmetic.- 3.3 Program Transformations.- 3.4 A Store-based Language Interpreter.- 3.5 Binary Numbers.- 3.6 Decoding Binary Numbers.- 3.7 Sequences.- 3.8 Palindromes.- 3.9 Sorting.- 3.10 Unordered Combinations.- 3.11 Binary Trees.- 3.12 Search Trees.- 3.13 2-3 Trees.- 3.14 Tree Domains.- 3.15 A Stream Language Interpreter.- 4 Models and Theories.- 4.1 Introduction.- 4.2 The Horn Clause Calculus.- 4.3 Initial Semantics.- 4.4 Initial Correctness.- 4.5 Final Semantics.- 4.6 Final Correctness.- 4.7 The Refutation of Inductive Theorems.- 4.8 Internalized Logic.- 4.9 Horn Clause Versus Sequent Logic.- 4.10 Bibliographic Notes.- 5 Resolution and Paramodulation.- 5.1 Introduction.- 5.2 Resolution.- 5.3 Paramodulation.- 5.4 Most General Unification.- 5.5 Lazy Resolution.- 5.6 Bibliographic Notes.- 6 The Relevance of Constructors.- 6.1 Introduction.- 6.2 Partial Semantics.- 6.3 Inductionless Induction.- 6.4 Bibliographic Notes.- 7 Reduction.- 7.1 Introduction.- 7.2 The Classical Approach.- 7.3 The Congruence Class Approach.- 7.4 The Normal Form Approach.- 7.5 The Weak Normal Form Approach.- 7.6 From Equations to Horn Clauses.- 7.7 Term and Goal Reduction.- 7.8 Confluence Properties.- 7.9 Strategy-controlled Reduction.- 7.10 Basic Reduction.- 7.11 Bibliographic Notes.- 8 Narrowing.- 8.1 Introduction.- 8.2 The Narrowing Calculus.- 8.3 Strategy-controlled Narrowing.- 8.4 Narrowing Strategies.- 8.5 Ground Term Generating Term Sets.- 8.6 Basic Narrowing.- 8.7 Reduced Narrowing.- 8.8 Reduced Basic Narrowing.- 8.9 Optimized Narrowing.- 8.10 Optimizing Functions.- 8.11 Lazy Narrowing.- 8.12 Bibliographic Notes.- 9 Church-Rosser Criteria.- 9.1 Introduction.- 9.2 Fully Parallel and Overlapping Reductions.- 9.3 Convergence Properties.- 9.4 Critical Pairs.- 9.5 Confluence of NAX.- 9.6 Strong Confluence of NAX.- 9.7 Confluence of ~NAX.- 9.8 BAX-compatibilityof NAX.- 9.9 An Algorithm for Church-Rosser Proofs.- 9.10 Bibliographic Notes.- References.- Notation Index.- Definition Index.