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Reasoning about Termination of Pure Prolog Programs
 Information and Computation
, 1993
"... We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of ..."
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Cited by 130 (14 self)
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We provide a theoretical basis for studying termination of (general) logic programs with the Prolog selection rule. To this end we study the class of left terminating programs. These are logic programs that terminate with the Prolog selection rule for all ground goals. We offer a characterization of left terminating positive programs by means of the notion of an acceptable program that provides us with a practical method of proving termination. The method is illustrated by giving a simple proof of termination of the quicksort program for the desired class of goals. Then we extend this approach to the class of general logic programs by modifying the concept of acceptability. We prove that acceptable general programs are left terminating. The converse implication does not hold but we show that under the assumption of nonfloundering from ground goals every left terminating general program is acceptable. Finally, we prove that various ways of defining semantics coincide for acceptable gen...
SSemantics Approach: Theory and Applications
, 1994
"... The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semanticsbased program analysis. The approach leads to the intr ..."
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Cited by 126 (28 self)
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The paper is a general overview of an approach to the semantics of logic programs whose aim is finding notions of models which really capture the operational semantics, and are therefore useful for defining program equivalences and for semanticsbased program analysis. The approach leads to the introduction of extended interpretations which are more expressive than Herbrand interpretations. The semantics in terms of extended interpretations can be obtained as a result of both an operational (topdown) and a fixpoint (bottomup) construction. It can also be characterized from the modeltheoretic viewpoint, by defining a set of extended models which contains standard Herbrand models. We discuss the original construction modeling computed answer substitutions, its compositional version and various semantics modeling more concrete observables. We then show how the approach can be applied to several extensions of positive logic programs. We finally consider some applications, mainly in the area of semanticsbased program transformation and analysis.
An Overview of Temporal and Modal Logic Programming
 Proc. First Int. Conf. on Temporal Logic  LNAI 827
, 1994
"... . This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)mo ..."
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Cited by 65 (6 self)
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. This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion. Categories: Temporal and Modal Logic Programming. 1 Introduction In logic programming, a program is a set of Horn clauses representing our knowledge and assumptions about some problem. The semantics of logic programs as developed by van Emden and Kowalski [96] is based on the notion of the least (minimum) Herbrand model and its fixedpoint characterization. As logic programming has been applied to a growing number of problem domai...
A framework of directionality for proving termination of logic programs
 Proc. JICSLP
, 1992
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Transformation of Logic Programs
 Handbook of Logic in Artificial Intelligence and Logic Programming
, 1998
"... Program transformation is a methodology for deriving correct and efficient programs from specifications. In this chapter, we will look at the so called 'rules + strategies' approach, and we will report on the main techniques which have been introduced in the literature for that approach, i ..."
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Cited by 40 (4 self)
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Program transformation is a methodology for deriving correct and efficient programs from specifications. In this chapter, we will look at the so called 'rules + strategies' approach, and we will report on the main techniques which have been introduced in the literature for that approach, in the case of logic programs. We will also present some examples of program transformation, and we hope that through those examples the reader may acquire some familiarity with the techniques we will describe.
Constraintbased Termination Analysis of Logic Programs
 ACM Transactions on Programming Languages and Systems
, 1999
"... Current normbased automatic... In this paper we present a new termination analysis which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs. The proposed method is both efficient and precise. The use of constraint sets e ..."
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Cited by 35 (15 self)
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Current normbased automatic... In this paper we present a new termination analysis which integrates the various components and produces a set of constraints that, when solvable, identifies successful termination proofs. The proposed method is both efficient and precise. The use of constraint sets enables the propagation of information over all different phases while the need for multiple analyses is considerably reduced.
A Transformational Methodology for Proving Termination of Logic Programs
, 1991
"... this paper, we present a transformational approach for proving termination of logic programs by reducing the termination problem of logic programs to that of term rewriting systems. The termination problem of term rewriting systems has been well studied and many useful techniques and tools have been ..."
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Cited by 35 (5 self)
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this paper, we present a transformational approach for proving termination of logic programs by reducing the termination problem of logic programs to that of term rewriting systems. The termination problem of term rewriting systems has been well studied and many useful techniques and tools have been developed for proving termination of term rewriting systems. The prime motivation of our approach is to facilitate the use of this vast source of termination techniques and tools in proving termination of logic programs.
Algebra of logic programming
 International Conference on Logic Programming
, 1999
"... At present, the field of declarative programming is split into two main areas based on different formalisms; namely, functional programming, which is based on lambda calculus, and logic programming, which is based on firstorder logic. There are currently several language proposals for integrating th ..."
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Cited by 24 (4 self)
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At present, the field of declarative programming is split into two main areas based on different formalisms; namely, functional programming, which is based on lambda calculus, and logic programming, which is based on firstorder logic. There are currently several language proposals for integrating the expressiveness of these two models of computation. In this thesis we work towards an integration of the methodology from the two research areas. To this end, we propose an algebraic approach to reasoning about logic programs, corresponding to the approach taken in functional programming. In the first half of the thesis we develop and discuss a framework which forms the basis for our algebraic analysis and transformation methods. The framework is based on an embedding of definite logic programs into lazy functional programs in Haskell, such that both the declarative and the operational semantics of the logic programs are preserved. In spite of its conciseness and apparent simplicity, the embedding proves to have many interesting properties and it gives rise to an algebraic semantics of logic programming. It also allows us to reason about logic programs in a simple calculational style, using rewriting and the algebraic laws of combinators. In the embedding, the meaning of a logic program arises compositionally from the meaning of its constituent subprograms and the combinators that connect them. In the second half of the thesis we explore applications of the embedding to the algebraic transformation of logic programs. A series of examples covers simple program derivations, where our techniques simplify some of the current techniques. Another set of examples explores applications of the more advanced program development techniques from the Algebra of Programming by Bird and de Moor [18], where we expand the techniques currently available for logic program derivation and optimisation. To my parents, Sandor and Erzsebet. And the end of all our exploring Will be to arrive where we started And know the place for the first time.
On Proving Left Termination of Constraint Logic Programs
 ACM Transaction on Computational Logic
, 2001
"... The Constraint Logic Programming (CLP) Scheme merges logic programming with constraint solving over predefined domains. In this paper, we study proof methods for universal left termination of constraint logic programs. We provide a sound and complete characterization of left termination for ideal CL ..."
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Cited by 21 (8 self)
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The Constraint Logic Programming (CLP) Scheme merges logic programming with constraint solving over predefined domains. In this paper, we study proof methods for universal left termination of constraint logic programs. We provide a sound and complete characterization of left termination for ideal CLP languages which generalizes acceptability of logic programs. The characterization is then refined to the notion of partial acceptability, which is wellsuited for automatic modular inference. We describe a theoretical framework for automation of the approach, which is implemented. For nonideal CLP languages and without any assumption on their incomplete constraint solvers, even the most basic sound termination criterion from logic programming does not lift. We focus on a specific system, namely CLP(R), by proposing some additional conditions that make (partial) acceptability sound