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11
On the theory of structural subtyping
, 2003
"... We show that the firstorder theory of structural subtyping of nonrecursive types is decidable. Let Σ be a language consisting of function symbols (representing type constructors) and C a decidable structure in the relational language L containing a binary relation ≤. C represents primitive types; ..."
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Cited by 18 (8 self)
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We show that the firstorder theory of structural subtyping of nonrecursive types is decidable. Let Σ be a language consisting of function symbols (representing type constructors) and C a decidable structure in the relational language L containing a binary relation ≤. C represents primitive types; ≤ represents a subtype ordering. We introduce the notion of Σtermpower of C, which generalizes the structure arising in structural subtyping. The domain of the Σtermpower of C is the set of Σterms over the set of elements of C. We show that the decidability of the firstorder theory of C implies the decidability of the firstorder theory of the Σtermpower of C. This result implies the decidability of the firstorder theory of structural subtyping of nonrecursive types.
C.: Partial Constraint Checking for Context Consistency in Pervasive Computing
 ACM Trans. on Software Engineering and Methodology 19(3), Article 9
, 2010
"... Pervasive computing environments typically change frequently in terms of available resources and their properties. Applications in pervasive computing use contexts to capture these changes and adapt their behaviors accordingly. However, contexts available to these applications may be abnormal or imp ..."
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Cited by 10 (6 self)
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Pervasive computing environments typically change frequently in terms of available resources and their properties. Applications in pervasive computing use contexts to capture these changes and adapt their behaviors accordingly. However, contexts available to these applications may be abnormal or imprecise due to environmental noises. This may result in context inconsistencies, which imply that contexts conflict with each other. The inconsistencies may set such an application into a wrong state or lead the application to misadjust its behavior. It is thus desirable to detect and resolve the context inconsistencies in a timely way. One popular approach is to detect context inconsistencies when contexts breach certain consistency constraints. Existing constraint checking techniques recheck the entire expression of each affected consistency constraint upon context changes. When a changed context affects only a constraint’s subexpression, rechecking the entire expression can adversely delay the detection of other context inconsistencies. This article proposes a rigorous approach to identifying the parts of previous checking results that are reusable without entire rechecking. We evaluated our work on the Cabot middleware through both simulation experiments and a case study. The experimental results reported that our approach achieved over a fifteenfold
NonStructural Subtype Entailment in Automata Theory
, 2003
"... Decidability of nonstructural subtype entailment is a longstanding open problem in programming language theory. In this paper, we apply automata theoretic methods to characterize the problem equivalently by using regular expressions and word equations. This characterization induces new results on ..."
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Cited by 8 (3 self)
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Decidability of nonstructural subtype entailment is a longstanding open problem in programming language theory. In this paper, we apply automata theoretic methods to characterize the problem equivalently by using regular expressions and word equations. This characterization induces new results on nonstructural subtype entailment, constitutes a promising starting point for further investigations on decidability, and explains for the first time why the problem is so difficult. The difficulty is caused by implicit word equations that we make explicit.
Tree Extension Algebras: Logics, Automata, and Query Languages
 In Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science (LICS
, 2002
"... We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T T , holding if and only if every branch of T extends to a branch of T , unary nodetests, and a binary relation checking if the domains of two trees are equal. We show ..."
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Cited by 8 (1 self)
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We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T T , holding if and only if every branch of T extends to a branch of T , unary nodetests, and a binary relation checking if the domains of two trees are equal. We show that from such a formula one can generate a tree automaton that accepts the set of tuples of trees defined by the formula, and conversely that every automaton over treetuples is captured by such a formula. We look at the fragment with only extension inequalities and leaf tests, and show that it corresponds to a new class of automata on tree tuples, which is strictly weaker then general treetuple automata. We use the automata representations to show separation and expressibility results for formulae in the logic. We then turn to relational calculi over the logic defined here: that is, from constraints we extend to queries that have secondorder parameters for a finite set of tree tuples. We give normal forms for queries, and use these to get bounds on the data complexity of query evaluation, showing that while general query evaluation is unbounded within the polynomial hierarchy, generic query evaluation has very low complexity, giving strong bounds on the expressive power of relational calculi with tree extension constraints. We also give normal forms for safe queries in the calculus.
Logical definability and query languages over ranked and unranked trees
 ACM TOCL
"... We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T ≺ T ′ , holding if and only if every branch of T extends to a branch of T ′, unary nodetests, and a binary relation checking if the domains of two trees are equal. We conside ..."
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Cited by 7 (4 self)
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We study relations on trees defined by firstorder constraints over a vocabulary that includes the tree extension relation T ≺ T ′ , holding if and only if every branch of T extends to a branch of T ′, unary nodetests, and a binary relation checking if the domains of two trees are equal. We consider both ranked and unranked trees. These are trees with and without a restriction on the number of children of nodes. We adopt the modeltheoretic approach to tree relations and study relations definable over the structure consisting of the set of all trees and the above predicates. We relate definability of sets and relations of trees to computability by tree automata. We show that some natural restrictions correspond to familiar logics in the more classical setting, where every tree is a structure over a fixed vocabulary, and to logics studied in the context of XML pattern languages. We then look at relational calculi over collections of trees, and obtain quantifierrestriction results that give us bounds on the expressive power and complexity. As unrestricted relational calculi can express problems complete for each level of the polynomial hierarchy, we look at their restrictions, corresponding to the restricted logics over the family of all unranked trees, and find several calculi with low (NC 1) data complexity, while still expressing properties important for database and
A flowbased approach for variant parametric types
 In Proceedings of the 2006 ACM SIGPLAN Conference on ObjectOriented Programming, Systems, Languages & Applications (OOPSLA‘06
, 2006
"... A promising approach for typesafe generic codes in the objectoriented paradigm is variant parametric type, which allows covariant and contravariant subtyping on fields where appropriate. Previous approaches formalise variant type as a special case of the existential type system. In this paper, we p ..."
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Cited by 6 (0 self)
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A promising approach for typesafe generic codes in the objectoriented paradigm is variant parametric type, which allows covariant and contravariant subtyping on fields where appropriate. Previous approaches formalise variant type as a special case of the existential type system. In this paper, we present a new framework based on flow analysis and modular type checking to provide a simple but accurate model for capturing generic types. Our scheme stands to benefit from past (and future) advances in flow analysis and subtyping constraints. Furthermore, it fully supports casting for variant types with a special reflection mechanism, called cast capture, to handle objects with unknown types. We have built a constraintbased type checker and have proven its soundness. We have also successfully annotated a suite of Java libraries and client code with our flowbased variant type system.
Complexity of Subtype Satisfiability over Posets
 in "14th European Symposium on Programming", LNCS
, 2005
"... Subtype satisfiability is an important problem for designing advanced subtype systems and subtypebased program analysis algorithms. The problem is well understood if the atomic types form a lattice. However, little is known about subtype satisfiability over posets. In this paper, we investigate alg ..."
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Cited by 5 (0 self)
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Subtype satisfiability is an important problem for designing advanced subtype systems and subtypebased program analysis algorithms. The problem is well understood if the atomic types form a lattice. However, little is known about subtype satisfiability over posets. In this paper, we investigate algorithms for and the complexity of subtype satisfiability over general posets. We present a uniform treatment of different flavors of subtyping: simple versus recursive types and structural versus nonstructural subtype orders. Our results are established through a new connection of subtype constraints and modal logic. As a consequence, we settle a problem left open by Tiuryn and Wand in 1993. 1
Internship report: Uniform and nonstructural subtyping
"... We expose a new approach to tackle nonstructural subtyping problems. We introduce uniform subtyping as a means to capture some properties of nonstructural subtyping. In the uniform theory, we show that the validity of a firstorder sentence is decidable, and entailment is PSPACEhard. In addition, ..."
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We expose a new approach to tackle nonstructural subtyping problems. We introduce uniform subtyping as a means to capture some properties of nonstructural subtyping. In the uniform theory, we show that the validity of a firstorder sentence is decidable, and entailment is PSPACEhard. In addition, we give decidable approximations to entailment and subtyping constrained types — two problems which are still open in the nonstructural theory. Contents 1
Subtype Constraints in Modal Logic
, 2005
"... We establish a new relationship between subtype constraints and modal logic. It implies uniformly that satisfiability of structural subtype constraints with ordered constants, function and recursive types is DEXPTIMEcomplete, and PSPACEcomplete without recursive types. This answers an open questio ..."
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We establish a new relationship between subtype constraints and modal logic. It implies uniformly that satisfiability of structural subtype constraints with ordered constants, function and recursive types is DEXPTIMEcomplete, and PSPACEcomplete without recursive types. This answers an open question raised by Tiuryn and Wand in 1993, and yields a new simpler proof to a result of Tiuryn and Frey at the same time.