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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.
Ordering Constraints over Feature Trees
, 1999
"... Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular ..."
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Cited by 14 (5 self)
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Feature trees are the formal basis for algorithms manipulating record like structures in constraint programming, computational linguistics and in concrete applications like software configuration management. Feature trees model records, and constraints over feature trees yield extensible and modular record descriptions. We introduce the constraint system FT of ordering constraints interpreted over feature trees. Under the view that feature trees represent symbolic information, the relation corresponds to the information ordering ("carries less information than"). We present two algorithms in cubic time, one for the satisfiability problem and one for the entailment problem of FT . We show that FT has the independence property. We are thus able to handle negative conjuncts via entailment and obtain a cubic algorithm that decides the satisfiability of conjunctions of positive and negated ordering constraints over feature trees. Furthermore, we reduce the satisfiability problem of Dorre's weak subsumption constraints to the satisfiability problem of FT and improve the complexity bound for solving weak subsumption constraints from O(n^5) to O(n³).
Functions as Passive Constraints in LIFE
 ACM Transactions on Programming Languages and Systems
, 1994
"... LIFE is an experimental programming language proposing to integrate logic programming, functional programming, and objectoriented programming. It replaces firstorder terms with ψterms, data structures which allow computing with partial information. These are approximation structures denoting se ..."
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Cited by 12 (4 self)
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LIFE is an experimental programming language proposing to integrate logic programming, functional programming, and objectoriented programming. It replaces firstorder terms with ψterms, data structures which allow computing with partial information. These are approximation structures denoting sets of values. LIFE further enriches the expressiveness of ψterms with functional dependency constraints. We must explain the meaning and use of functions in LIFE declaratively as solving partial information constraints. These constraints do not attempt to generate their solutions but behave as demons filtering out anything else.
Simple type inference for structural polymorphism
 In: The Ninth International Workshop on Foundations of ObjectOriented Languages
, 2002
"... We propose a new way to mix constrained types and type inference, where the interaction between the two is minimal. By using local constraints embedded in types, rather than the other way round, we obtain a system which keeps the usual structure of an HindleyMilner type system. In practice, this me ..."
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Cited by 8 (4 self)
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We propose a new way to mix constrained types and type inference, where the interaction between the two is minimal. By using local constraints embedded in types, rather than the other way round, we obtain a system which keeps the usual structure of an HindleyMilner type system. In practice, this means that it is easy to introduce local constraints in existing type inference algorithms. Eventhough our system is notably weaker than general constraintbased type systems, making it unable to handle subtyping for instance, it is powerful enough to accomodate many features, from simple polymorphic records à la Ohori to Objective Caml’s polymorphic variants, and accurate typing of pattern matching (i.e. polymorphic message dispatch), all these through tiny variations in the constraint part of the system. 1.
Entailment and Disentailment of OrderSorted Feature Constraints
 In Proceedings of the Fourth International Conferenceon Logic Programmingand Automated Reasoning, Andrei Voronkov
, 1993
"... LIFE uses matching on ordersorted feature structures for passing arguments to functions. As opposed to unication which amounts to normalizing a conjunction of constraints, solving a matching problem consists of deciding whether a constraint (guard) or its negation are entailed by the context. We gi ..."
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Cited by 6 (3 self)
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LIFE uses matching on ordersorted feature structures for passing arguments to functions. As opposed to unication which amounts to normalizing a conjunction of constraints, solving a matching problem consists of deciding whether a constraint (guard) or its negation are entailed by the context. We give a complete and consistent set of rules for entailment and disentailment of ordersorted feature constraints. These rules are directly usable for relative simplification, a general prooftheoretic method for proving guards in concurrent constraint logic languages using guarded rules.
Type Inference for FirstClass Messages with Feature Constraints
 International Journal of Foundations of Computer Science
, 1998
"... We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for firstclass messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by firstclass feature tree" y, in contrast to the standard selection con ..."
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Cited by 5 (0 self)
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We present a constraint system OF of feature trees that is appropriate to specify and implement type inference for firstclass messages. OF extends traditional systems of feature constraints by a selection constraint xhyiz "by firstclass feature tree" y, in contrast to the standard selection constraint x[ f ]y "by fixed feature" f . We investigate the satisfiability problem of OF and show that it can be solved in polynomial time, and even in quadratic time in an important special case. We compare OF with Treinen's constraint system EF of feature constraints with firstclass features, which has an NPcomplete satisfiability problem. This comparison yields that the satisfiability problem for OF with negation is NPhard. Based on OF we give a simple account of type inference for firstclass messages in the spirit of Nishimura's recent proposal, and we show that it has polynomial time complexity: We also highlight an immediate extension that is desirable but makes type inference NPhard.
Feature Automata and Sets of Feature Trees
, 1993
"... Feature trees generalize firstorder trees (which are called ground terms in the general framework of universal algebra). Namely, argument positions become keywords ("features") from an infinite symbol set F. A constructor symbol becomes a node symbol that can occur with arbitrary and arbitrarily ma ..."
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Feature trees generalize firstorder trees (which are called ground terms in the general framework of universal algebra). Namely, argument positions become keywords ("features") from an infinite symbol set F. A constructor symbol becomes a node symbol that can occur with arbitrary and arbitrarily many argument positions. Feature trees are used to model flexible records; the assumption that F is infinite accounts for dynamic record field additions. We develop a universal algebra framework for feature trees. We extend the classical setdefining notions: automata, regular expressions and equational systems, and show that they coincide. This extension of the regular theory of trees requires new notions and proofs. Roughly, a feature automaton reads a feature tree in two directions: along its branches and along the list of the direct descendants of each node. The second direction corresponds to an automaton on a commutative monoid (over an infinite alphabet). One motivation for this work st...