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A Semantic Basis for the Termination Analysis of Logic Programs
 Journal of Logic Programming
, 1999
"... This paper presents a formal semantic basis for the termination analysis of logic programs. The semantics exhibits the termination properties of a logic program through its binary unfoldings  a possibly infinite set of binary clauses. Termination of a program P and goal G is determined by the abs ..."
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Cited by 100 (14 self)
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This paper presents a formal semantic basis for the termination analysis of logic programs. The semantics exhibits the termination properties of a logic program through its binary unfoldings  a possibly infinite set of binary clauses. Termination of a program P and goal G is determined by the absence of an infinite chain in the binary unfoldings of P starting with G. The result is of practical use as basing termination analysis on a formal semantics facilitates both the design and implementation of analyzers. A simple Prolog interpreter for binary unfoldings coupled with an abstract domain based on symbolic norm constraints is proposed as an implementation vehicle. We illustrate its application using two recently proposed abstract domains. Both techniques are implemented using a standard CLP(R) library. The combination of an interpreter for binary unfoldings and a constraint solver simplifies the design of the analyzer and improves its efficiency significantly. 1 Introduction This ...
Automatic Termination Analysis of Logic Programs
 Proceedings of the Fourteenth International Conference on Logic Programming
, 1997
"... This paper describes a system implemented in SICStus Prolog for automatically checking left termination of logic programs. Given a program and query, the system answers either that the query terminates or that there may be nontermination. The system can use any norm of a wide family of norms. It ca ..."
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Cited by 65 (3 self)
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This paper describes a system implemented in SICStus Prolog for automatically checking left termination of logic programs. Given a program and query, the system answers either that the query terminates or that there may be nontermination. The system can use any norm of a wide family of norms. It can handle automatically most of the examples found in the literature on termination of logic programs, and about half of the programs in the benchmarks of [5]. The algorithm employed by the system consists of three main parts: instantiation analysis (i.e., rigidity analysis), constraint inference, and construction of the querymapping pairs associated with the program and query. Each of these parts generalizes earlier work related to termination analysis. 1 Introduction Termination analysis of logic programs has been the focus of intensive research in recent years. Systems for automatic termination analysis are proposed, for example, in [15, 20, 22]. Methodologies and techniques for proving ...
Homeomorphic Embedding for Online Termination
 STATIC ANALYSIS. PROCEEDINGS OF SAS’98, LNCS 1503
, 1998
"... Recently wellquasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper, ..."
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Cited by 61 (8 self)
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Recently wellquasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of program analysis, specialisation and transformation techniques. In this paper,
Logic program specialisation through partial deduction: Control issues
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2002
"... Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It ..."
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Cited by 54 (12 self)
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Program specialisation aims at improving the overall performance of programs by performing source to source transformations. A common approach within functional and logic programming, known respectively as partial evaluation and partial deduction, is to exploit partial knowledge about the input. It is achieved through a wellautomated application of parts of the BurstallDarlington unfold/fold transformation framework. The main challenge in developing systems is to design automatic control that ensures correctness, efficiency, and termination. This survey and tutorial presents the main developments in controlling partial deduction over the past 10 years and analyses their respective merits and shortcomings. It ends with an assessment of current achievements and sketches some remaining research challenges.
Calculating Sized Types
 HigherOrder and Symbolic Computation
, 2001
"... Many program optimizations and analyses, such as arraybounds checking, termination analysis, etc, depend on knowing the size of a function's input and output. However, size information can be dicult to compute. Firstly, accurate size computation requires detecting a size relation between different ..."
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Cited by 52 (10 self)
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Many program optimizations and analyses, such as arraybounds checking, termination analysis, etc, depend on knowing the size of a function's input and output. However, size information can be dicult to compute. Firstly, accurate size computation requires detecting a size relation between different inputs of a function. Secondly, different optimizations and analyses may require slightly different size information, and thus slightly different computation. Literature in size computation has mainly concentrated on size checking, instead of size inference. In this paper, we provide a generic framework on which di erent size variants can be expressed and computed. We also describe an effective algorithm for inferring, instead of checking, size information. Size information are expressed in terms of Presburger formulae, and our algorithm utilizes the Omega Calculator to compute as exact a size information as possible, within the linear arithmetic capability.
Termination of Nested and Mutually Recursive Algorithms
, 1996
"... This paper deals with automated termination analysis for functional programs. Previously developed methods for automated termination proofs of functional programs often fail for algorithms with nested recursion and they cannot handle algorithms with mutual recursion. We show that termination proofs ..."
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Cited by 39 (9 self)
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This paper deals with automated termination analysis for functional programs. Previously developed methods for automated termination proofs of functional programs often fail for algorithms with nested recursion and they cannot handle algorithms with mutual recursion. We show that termination proofs for nested and mutually recursive algorithms can be performed without having to prove the correctness of the algorithms simultaneously. Using this result, nested and mutually recursive algorithms do no longer constitute a special problem and the existing methods for automated termination analysis can be extended to nested and mutual recursion in a straightforward way. We give some examples of algorithms whose termination can now be proved automatically (including wellknown challenge problems such as McCarthy's f_91 function).
Solving HigherOrder Equations: From Logic to Programming
, 1995
"... Higherorder constructs provide the necessary level of abstraction for concise and natural formulations in many areas of computer science. We present constructive methods for higherorder equational reasoning with applications ranging from theorem proving to novel programming concepts. A major probl ..."
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Cited by 36 (9 self)
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Higherorder constructs provide the necessary level of abstraction for concise and natural formulations in many areas of computer science. We present constructive methods for higherorder equational reasoning with applications ranging from theorem proving to novel programming concepts. A major problem of higherorder programming is the undecidability of higherorder unification. In the first part, we develop several classes with decidable secondorder unification. As the main result, we show that the unification of a linear higherorder pattern s with an arbitrary secondorder term that shares no variables with s is decidable and finitely solvable. This is the unification needed for secondorder functionallogic programming. The second main contribution is a framework for solving higherorder equational problems by narrowing. In the firstorder case, narrowing is the underlying computation rule for the integration of logic programming and functional programming. We argue that there are...
Logic programming revisited: logic programs as inductive definitions
 ACM Transactions on Computational Logic
, 2001
"... Logic programming has been introduced as programming in the Horn clause subset of first order logic. This view breaks down for the negation as failure inference rule. To overcome the problem, one line of research has been to view a logic program as a set of iffdefinitions. A second approach was to ..."
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Cited by 35 (21 self)
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Logic programming has been introduced as programming in the Horn clause subset of first order logic. This view breaks down for the negation as failure inference rule. To overcome the problem, one line of research has been to view a logic program as a set of iffdefinitions. A second approach was to identify a unique canonical, preferred or intended model among the models of the program and to appeal to common sense to validate the choice of such model. Another line of research developed the view of logic programming as a nonmonotonic reasoning formalism strongly related to Default Logic and Autoepistemic Logic. These competing approaches have resulted in some confusion about the declarative meaning of logic programming. This paper investigates the problem and proposes an alternative epistemological foundation for the canonical model approach, which is not based on common sense but on a solid mathematical information principle. The thesis is developed that logic programming can be understood as a natural and general logic of inductive definitions. In particular, logic programs with negation represent nonmonotone inductive definitions. It is argued that this thesis results in an alternative justification of the wellfounded model as the unique intended model of the logic program. In addition, it equips logic programs with an easy to comprehend meaning
Inferring Leftterminating Classes of Queries for Constraint Logic Programs
 Proc. JICSLP'96
, 1996
"... This paper presents an approach for universal lefttermination of constraint logic programs, based on approximations. An approximation is basically an algebraic morphism between two constraint structures. By moving from the original domain to natural numbers, we compute interargument relations and ..."
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Cited by 34 (14 self)
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This paper presents an approach for universal lefttermination of constraint logic programs, based on approximations. An approximation is basically an algebraic morphism between two constraint structures. By moving from the original domain to natural numbers, we compute interargument relations and some control information about a program. By moving from the natural numbers to the booleans, we compute a boolean term called a termination condition such that if the boolean approximation of a goal entails the termination condition, then the Prolog computation tree for that goal is finite.
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 34 (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.