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75
Type classes with functional dependencies
 ESOP/ETA (LNCS)
, 2000
"... Type classes in Haskell allow programmers to define functions that can be used on a set of different types, with a potentially different implementation in each case. For example, type classes are used to support equality and numeric types, and for monadic programming. A commonly requested extension ..."
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Cited by 153 (1 self)
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Type classes in Haskell allow programmers to define functions that can be used on a set of different types, with a potentially different implementation in each case. For example, type classes are used to support equality and numeric types, and for monadic programming. A commonly requested extension to support ‘multiple parameters ’ allows a more general interpretation of classes as relations on types, and has many potentially useful applications. Unfortunately, many of these examples do not work well in practice, leading to ambiguities and inaccuracies in inferred types and delaying the detection of type errors. This paper illustrates the kind of problems that can occur with multiple parameter type classes, and explains how they can be resolved by allowing programmers to specify explicit dependencies between the parameters. A particular novelty of this paper is the application of ideas from the theory of relational databases to the design of type systems.
Identifying the minimal transversals of a hypergraph and related problems
 SIAM Journal on Computing
, 1995
"... The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertic ..."
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Cited by 126 (7 self)
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The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be coNPcomplete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs, is shown to be computationally equivalent to transversal hypergraph recognition, i.e., given two hypergraphs H 1; H 2, decide if the sets in H 2 are all the minimal transversals of H 1. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size, but it is unknown whether an outputpolynomial algorithm exists for this problem. For several important subcases, for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs, we present outputpolynomial algorithms. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is pointed out by identifying important applications in database theory, Boolean switching theory, logic, and AI, particularly in modelbased diagnosis.
Testing implications of data dependencies
 ACM Transactions on Database Systems
, 1979
"... Presented is a computation methodthe chasefor testing implication of data dependencies by a set of data dependencies. The chase operates on tableaux similar to those of Aho, Sagiv, and Ullman. The chase includes previous tableau computation methods as special cases. By interpreting tableaux altern ..."
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Cited by 110 (3 self)
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Presented is a computation methodthe chasefor testing implication of data dependencies by a set of data dependencies. The chase operates on tableaux similar to those of Aho, Sagiv, and Ullman. The chase includes previous tableau computation methods as special cases. By interpreting tableaux alternately as mappings or as templates for relations, it is possible to test implication of join dependencies (including multivalued dependencies) and functional dependencies by a set of dependencies.
Computable Queries for Relational Databases
, 1980
"... this paper is to settle the question of maximal expressiveness of query languages. This is done in two steps. First, the set of computable queries is defined. These correspond to partial recursive functions which satisfy a consistency criterion reflecting the fact that the computation is on a data b ..."
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Cited by 83 (0 self)
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this paper is to settle the question of maximal expressiveness of query languages. This is done in two steps. First, the set of computable queries is defined. These correspond to partial recursive functions which satisfy a consistency criterion reflecting the fact that the computation is on a data base rather than, say, on a natural number
Mining Minimal NonRedundant Association Rules using Frequent Closed Itemsets
, 2000
"... The problem of the relevance and the usefulness of extracted association rules is of primary importance because, in the majority of cases, reallife databases lead to several thousands association rules with high condence and among which are many redundancies. Using the closure of the Galois con ..."
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Cited by 79 (6 self)
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The problem of the relevance and the usefulness of extracted association rules is of primary importance because, in the majority of cases, reallife databases lead to several thousands association rules with high condence and among which are many redundancies. Using the closure of the Galois connection, we dene two new bases for association rules which union is a generating set for all valid association rules with support and condence. These bases are characterized using frequent closed itemsets and their generators; they consist of the nonredundant exact and approximate association rules having minimal antecedents and maximal consequents, i.e. the most relevant association rules. Algorithms for extracting these bases are presented and results of experiments carried out on reallife databases show that the proposed bases are useful, and that their generation is not time consuming.
Monotonic Aggregation in Deductive Databases
 Journal of Computer and System Sciences
, 1992
"... We propose a semantics for aggregates in deductive databases based on a notion of minimality. Unlike some previous approaches, we form a minimal model of a program component including aggregate operators, rather than insisting that the aggregate apply to atoms that have been fully determined, or tha ..."
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Cited by 64 (3 self)
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We propose a semantics for aggregates in deductive databases based on a notion of minimality. Unlike some previous approaches, we form a minimal model of a program component including aggregate operators, rather than insisting that the aggregate apply to atoms that have been fully determined, or that aggregate functions are rewritten in terms of negation. In order to guarantee the existence of such a minimal model we need to insist that the domains over which we are aggregating are complete lattices, and that the program is in a sense monotonic. Our approach generalizes previous approaches based on the wellfounded semantics and various forms of stratification. We are also able to handle a large variety of monotonic (or pseudomonotonic) aggregate functions. 1 Introduction Deductive databases allow views to be defined using programs consisting of logical rules. Recently, a number of researchers have considered adding aggregation to the rule language. If the aggregation is applied in a...
Conditional functional dependencies for capturing data inconsistencies
 TODS
"... We propose a class of integrity constraints for relational databases, referred to as conditional functional dependencies (cfds), and study their applications in data cleaning. In contrast to traditional functional dependencies (fds) that were developed mainly for schema design, cfds aim at capturing ..."
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Cited by 32 (6 self)
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We propose a class of integrity constraints for relational databases, referred to as conditional functional dependencies (cfds), and study their applications in data cleaning. In contrast to traditional functional dependencies (fds) that were developed mainly for schema design, cfds aim at capturing the consistency of data by enforcing bindings of semantically related values. For static analysis of cfds we investigate the consistency problem, which is to determine whether or not there exists a nonempty database satisfying a given set of cfds, and the implication problem, which is to decide whether or not a set of cfds entails another cfd. We show that while any set of transitional fds is trivially consistent, the consistency problem is npcomplete for cfds, but it is in ptime when either the database schema is predefined or no attributes involved in the cfds have a finite domain. For the implication analysis of cfds, we provide an inference system analogous to Armstrong’s axioms for fds, and show that the implication problem is conpcomplete for cfds in contrast to the lineartime complexity for their traditional counterpart. We also present an algorithm for computing a minimal cover of a set of cfds. Since cfds allow data bindings, in some cases cfds may be physically large, complicating detection of constraint violations. We develop techniques for detecting cfd violations in sql as well as novel techniques for checking multiple
Mechanical Translation of Set Theoretic Problem Specifications Into Efficient RAM Code  A Case Study
 Proc. EUROCAL 85
, 1985
"... This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically de ..."
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Cited by 26 (8 self)
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This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically determined. The user is only required to supply the system with a formal problem specification, and is relieved of all responsibilities in the rest of the program development process. These results are obtained, in part, by greatly restricting the system to handle a class of determinate, set theoretic, tractable problems. The most essential transformational techniques that are used are fixed point iteration, finite differencing, and data structure selection. Rudimentary forms of these techniques have been implemented and used effectively in the RAPTS transformational programming system. This paper explains the conceptual underpinnings of our approach by considering the problem of attribute closure for relational databases and systematically deriving a program that implements a linear time solution. 1.
Achievements of relational database schema design theory revisited
 Semantics in Databases, volume LCNS 1358
, 1998
"... Database schema design is seen as to decide on formats for timevarying instances, on rules for supporting inferences and on semantic constraints. Schema design aims at both faithful formalization of the application and optimization at design time. It is guided by four heuristics: Separation of Asp ..."
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Cited by 26 (2 self)
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Database schema design is seen as to decide on formats for timevarying instances, on rules for supporting inferences and on semantic constraints. Schema design aims at both faithful formalization of the application and optimization at design time. It is guided by four heuristics: Separation of Aspects, Separation of Specializations, Inferential Completeness and Unique Flavor. A theory of schema design is to investigate these heuristics and to provide insight into how syntactic properties of schemas are related to worthwhile semantic properties, how desirable syntactic properties can be decided or achieved algorithmically, and how the syntactic properties determine costs of storage, queries and updates. Some wellknown achievements of design theory for relational databases are reviewed: normal forms, view support, deciding implications of semantic constraints, acyclicity, design algorithms removing forbidden substructures.
Functional Dependencies in Relational Databases: A Lattice Point of View
, 1992
"... A lattice theoretic approach is developed to study the properties of functional dependencies in relational databases. The particular attention is paid to the analysis of the semilattice of closed sets, the lattice of all closure operations on a given set and to a new characterization of normal form ..."
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Cited by 23 (2 self)
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A lattice theoretic approach is developed to study the properties of functional dependencies in relational databases. The particular attention is paid to the analysis of the semilattice of closed sets, the lattice of all closure operations on a given set and to a new characterization of normal form relation schemes. Relation schemes with restrictions on functional dependencies are also studied. 1. Introduction The relational datamodel was defined by E.F. Codd [14] in 1970, and it is still one of the most powerful database models. In this model a relation is a matrix (table) every row of which corresponds to a record and every column to an attribute. This model has been widely studied. One of the most important branches in the theory of relational databases is that dealing with the design of database schemes. This branch is based on the theory of dependencies and constraints. In this paper we study the functional dependencies. Informally, functional dependency means that some attribu...