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22
ConstraintBased Type Inference for Guarded Algebraic Data Types
, 2003
"... Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch ..."
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Cited by 25 (3 self)
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Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch must be checked under di#erent typing assumptions. This mechanism allows exploiting the presence of dynamic tests in the code to produce extra static type information.
A constraintbased approach to guarded algebraic data types
 ACM Trans. Prog. Languages Systems
, 2007
"... We study HMG(X), an extension of the constraintbased type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (firstcla ..."
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Cited by 24 (0 self)
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We study HMG(X), an extension of the constraintbased type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (firstclass) phantom types, and equality qualified types, and are closely related to inductive types. Their characteristic property is to allow every branch of a case construct to be typechecked under different assumptions about the type variables in scope. We prove that HMG(X) is sound and that, provided recursive definitions carry a type annotation, type inference can be reduced to constraint solving. Constraint solving is decidable, at least for some instances of X, but prohibitively expensive. Effective type inference for guarded algebraic data types is left as an issue for future research.
The FirstOrder Theory of Ordering Constraints over Feature Trees
 Discrete Mathematics and Theoretical Computer Science
, 2001
"... The system FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the firstorder theory of FT and its fragments, both over finite trees and over possibly infinite trees. We prove that the firstor ..."
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Cited by 19 (5 self)
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The system FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. We investigate the firstorder theory of FT and its fragments, both over finite trees and over possibly infinite trees. We prove that the firstorder theory of FT is undecidable, in contrast to the firstorder theory of FT which is wellknown to be decidable. We determine the complexity of the entailment problem of FT with existential quantification to be PSPACEcomplete, by proving its equivalence to the inclusion problem of nondeterministic finite automata. Our reduction from the entailment problem to the inclusion problem is based on a new alogrithm that, given an existential formula of FT , computes a finite automaton which accepts all its logic consequences.
Complexity of Nonrecursive Logic Programs with Complex Values
 In Proceedings of the 17th ACM SIGACTSIGMODSIGART Symposium on Principles of Database Systems (PODS’98
, 1998
"... We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so we study the complexity of nonrecursive queries. By complex values we ..."
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Cited by 17 (2 self)
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We investigate complexity of the SUCCESS problem for logic query languages with complex values: check whether a query defines a nonempty set. The SUCCESS problem for recursive query languages with complex values is undecidable, so we study the complexity of nonrecursive queries. By complex values we understand values such as trees, finite sets, and multisets. Due to the wellknown correspondence between relational query languages and datalog, our results can be considered as results about relational query languages with complex values. The paper gives a complete complexity classification of the SUCCESS problem for nonrecursive logic programs over trees depending on the underlying signature, presence of negation, and range restrictedness. We also prove several results about finite sets and multisets. 1 Introduction A number of complexity results have been established for logic query languages. They are surveyed in [49, 18]. The major themes in these results are the complexity and expr...
Term algebras with length function and bounded quantifier alternation
 In Theorem Proving in HigherOrder Logics, volume 3223 of LNCS
, 2004
"... .)L: TA! Z. Formulae are formed from term literals and integerliterals using logical connectives and quantifications. Term literals are exactly ..."
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Cited by 11 (4 self)
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.)L: TA! Z. Formulae are formed from term literals and integerliterals using logical connectives and quantifications. Term literals are exactly
LISA: A Specification Language Based on WS2S
, 1998
"... We integrate two concepts from programming languages into a specification language based on WS2S, namely highlevel data structures such as records and recursivelydefined datatypes (WS2S is the weak secondorder monadic logic of two successors). Our integration is based on a new logic whose variabl ..."
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Cited by 10 (1 self)
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We integrate two concepts from programming languages into a specification language based on WS2S, namely highlevel data structures such as records and recursivelydefined datatypes (WS2S is the weak secondorder monadic logic of two successors). Our integration is based on a new logic whose variables range over recordlike trees and an algorithm for translating datatypes into tree automata. We have implemented LISA, a prototype system based on these ideas, which, when coupled with a decision procedure for WS2S like the MONA system, results in a verification tool that supports both highlevel specifications and complexity estimations for the running time of the decision procedure.
Computing Nonground Representations of Stable Models
 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR97), number 1265 in Lecture Notes in Computer Science
, 1997
"... Turi [20] introduced the important notion of a constrained atom: an atom with associated equality and disequality constraints on its arguments. A set of constrained atoms is a constrained interpretation. ..."
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Cited by 9 (0 self)
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Turi [20] introduced the important notion of a constrained atom: an atom with associated equality and disequality constraints on its arguments. A set of constrained atoms is a constrained interpretation.
Ordering Constraints over Feature Trees Expressed in Secondorder Monadic Logic
 Information and Computation
, 1998
"... The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the firstorder theory of FT is well understood, only few decidability results are known for the firstorder theory of FT . We introduc ..."
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Cited by 8 (4 self)
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The language FT of ordering constraints over feature trees has been introduced as an extension of the system FT of equality constraints over feature trees. While the firstorder theory of FT is well understood, only few decidability results are known for the firstorder theory of FT . We introduce a new method for proving the decidability of fragments of the firstorder theory of FT . This method is based on reduction to second order monadic logic that is decidable according to Rabin's famous tree theorem. The method applies to any fragment of the firstorder theory of FT for which one can change the model towards sufficiently labeled feature trees  a class of trees that we introduce. As we show, the first ordertheory of ordering constraints over sufficiently labeled feature trees is equivalent to secondorder monadic logic (S2S for infinite and WS2S for finite feature trees). We apply our method for proving that entailment of FT with existential quantifiers j 1 j=9x 1 : : :9x n j 2 is decidable. Previous results were restricted to entailment without existential quantifiers which can be solved in cubic time. Meanwhile, entailment with existential quantifiers has been shown PSPACEcomplete (for finite and infinite feature trees respectively).
Expressiveness of Full First Order Constraints in the Algebra of Finite or Infinite Trees
, 2000
"... We are interested in the expressiveness of constraints represented by general first order formulae, with equality as unique relational symbol and functional symbols taken from an infinite set F. The chosen domain is the set of trees whose nodes, in possibly in nite number, are labeled by elements of ..."
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Cited by 7 (0 self)
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We are interested in the expressiveness of constraints represented by general first order formulae, with equality as unique relational symbol and functional symbols taken from an infinite set F. The chosen domain is the set of trees whose nodes, in possibly in nite number, are labeled by elements of F . The operation linked to each element f of F is the mapping (a1 , ..., an ) 7! b, where b is the tree whose initial node is labeled f and whose sequence of daughters is a1 , ..., an . We first consider constraints involving long alternated sequences of quantifiers 9898 . . . . We show how to express winning positions of twopartners games with such constraints and apply our results to two examples. We then construct a family of strongly expressive constraints, inspired by a constructive proof of a complexity result by Pawel Mielniczuk. This family involves the huge number (k), obtained by evaluating top down a power tower of 2's, of height k. With elements of this family, of sizes at most proportional to k, we de ne a nite tree having (k) nodes, and we express the result of a Prolog machine executing at most (k) instructions. By replacing the Prolog machine by a Turing machine we rediscover the following result of Sergei Vorobyov: the complexity of an algorithm, deciding whether a constraint without free variables is true, cannot be bounded above by a function obtained by nite composition of elementary functions including exponentiation. Finally, taking advantage of the fact that we have at our disposal an algorithm for solving such constraints in all their generality, we produce a set of benchmarks for separating feasible examples from purely speculative ones. Among others we solve constraints involving alternated sequences of more than 160 quantifiers.
SchemaBased Independence Analysis for XML Updates
"... Queryupdate independence analysis is the problem of determining whether an update affects the results of a query. Queryupdate independence is useful for avoiding recomputation of materialized views and may have applications to access control and concurrency control. This paper develops static anal ..."
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Cited by 7 (1 self)
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Queryupdate independence analysis is the problem of determining whether an update affects the results of a query. Queryupdate independence is useful for avoiding recomputation of materialized views and may have applications to access control and concurrency control. This paper develops static analysis techniques for queryupdate independence problems involving core XQuery queries and updates with a snapshot semantics (based on the W3C XQuery Update Facility proposal). Our approach takes advantage of schema information, in contrast to previous work on this problem. We formalize our approach, sketch a proof of correctness, and report on the performance and accuracy of our implementation. 1.