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A Featurebased Constraint System for Logic Programming with Entailment
, 1992
"... This paper presents the constraint system FT, which we feel is an intriguing alternative to Herbrand both theoretically and practically. As does Herbrand, FT provides a universal data structure based on trees. However, the trees of FT (called feature trees) are more general than the trees of Herbran ..."
Abstract

Cited by 69 (20 self)
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This paper presents the constraint system FT, which we feel is an intriguing alternative to Herbrand both theoretically and practically. As does Herbrand, FT provides a universal data structure based on trees. However, the trees of FT (called feature trees) are more general than the trees of Herbrand (called constructor trees), and the constraints of FT are finer grained and of different expressivity. The basic notion of FT are functional attributes called features, which provide for recordlike descriptions of data avoiding the overspecification intrinsic in Herbrand's constructorbased descriptions. The feature tree structure fixes an algebraic semantics for FT. We will also establish a logical semantics, which is given by three axiom schemes fixing the firstorder theory FT. FT is a constraint system for logic programming, providing a test for unsatisfiability, and a test for entailment between constraints, which is needed for advanced control mechanisms. The two major technical con...
FiniteTree Analysis for Constraint LogicBased Languages: The Complete Unabridged Version
, 2001
"... Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurscheck) and increased expressivity (cyclic terms can provide very efficient representations of grammars and other usef ..."
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Cited by 40 (16 self)
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Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurscheck) and increased expressivity (cyclic terms can provide very efficient representations of grammars and other useful objects). Unfortunately, the use of infinite rational trees has problems. For instance, many of the builtin and library predicates are illdefined for such trees and need to be supplemented by runtime checks whose cost may be significant. Moreover, some widelyused program analysis and manipulation techniques are correct only for those parts of programs working over finite trees. It is thus important to obtain, automatically, a knowledge of the program variables (the finite variables) that, at the program points of interest, will always be bound to finite terms. For these reasons, we propose here a new dataflow analysis, based on abstract interpretation, that captures such information. We present a parametric domain where a simple component for recording finite variables is coupled, in the style of the open product construction of Cortesi et al., with a generic domain (the parameter of the construction) providing sharing information. The sharing domain is abstractly specified so as to guarantee the correctness of the combined domain and the generality of the approach. This finitetree analysis domain is further enhanced by coupling it with a domain of Boolean functions, called finitetree dependencies, that precisely captures how the finiteness of some variables influences the finiteness of other variables. We also summarize our experimental results showing how finitetree analysis, enhanced with finitetree dependencies, is a practical means of obtaining precise finitenes...
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
 In Proceedings of the First International Conference on Principles and Practice of Constraint Programming
"... When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving metho ..."
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Cited by 26 (3 self)
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When combining languages for symbolic constraints, one is typically faced with the problem of how to treat "mixed" constraints. The two main problems are (1) how to define a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a "free amalgamated product" as a possible solution to the first problem. Subsequently, we define socalled simplycombinable structures (SCstructures). For SCstructures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SCstructures yields the free amalgamated product. The combination technique of [BS92, BaS94a] can be used to combine constraint solvers for (strong) SCstructures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras modulo equational theories, the class of SCstru...
A Feature Constraint System for Logic Programming with Entailment
 THEORETICAL COMPUTER SCIENCE
, 1992
"... We introduce a constraint system called FT. This system offers a theoretical and practical alternative to the usual Herbrand system of constraints over constructor trees. Like Herbrand, FT provides a universal data structure based on trees. However, the trees of FT (called feature trees) are more g ..."
Abstract

Cited by 16 (1 self)
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We introduce a constraint system called FT. This system offers a theoretical and practical alternative to the usual Herbrand system of constraints over constructor trees. Like Herbrand, FT provides a universal data structure based on trees. However, the trees of FT (called feature trees) are more general than the constructor trees of Herbrand, and the constraints of FT are of finer grain and of different expressiveness. The essential novelty of FT is provided by functional attributes called features which allow representing data as extensible records, a more flexible way than that offered by Herbrand's fixed arity constructors. The feature tree structure determines an algebraic semantics for FT. We establish a logical semantics thanks to three axiom schemes presenting the firstorder theory FT. We propose using FT as a constraint system for logic programming. We provide a test for constraint unsatisfiability, and a test for constraint entailment. The former corresponds to unification ...