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1

Modeling Contexts with Dependent Types

Dapoigny R., Barlatier P.

Fundamenta Informaticae

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2010

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Vol. 104, nr 4

293-327

EN

In the area of knowledge representation, a challenging topic is the formalization of context knowledge on the basis of logical foundations and ontological semantics. However, most attempts to provide a formal model of contexts suffer from a number of difficulties, such as limited expressiveness of representation, restricted variable quantification, lack of (meta) reasoning about properties, etc. In addition, type theory originally developed for formal modeling of mathematics has also been successfully applied to the correct specification of programs and in the semantics of natural language. In this paper, we suggest a type theoretical approach to the problem of context and action modeling. Type theory is used both for representing the system’s knowledge of the discourse domain and for reasoning about it. For that purpose, we extend an existing dependent type theory having nice properties, with context-based rules and appropriate inductive types. We claim that the resulting theory exploiting the power of dependent types is able to provide a very expressive system together with a unified theory allowing higher-order reasoning.

2

Types for Active Objects with Static Deadlock Prevention

Puntigam F., Peter Ch.

Fundamenta Informaticae

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2001

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Vol. 48, nr 4

315-341

EN

Process types statically ensure the acceptability of all messages sent to an object even if the set of acceptable messages changes dynamically. As proposed so far, process types do not ensure the return of answers; deadlocks may prevent objects from behaving as expected. In this article we propose an object calculus with types distinguishing between obligatory messages (that must be sent, for example, as answer to a question) and optional messages (that can, but need not be sent). A type checker enforces the sending of obligatory messages and ensures that obligatory messages are not suppressed by deadlocks. The proposed type concept supports subtyping.

3

A foundation for refining concurrent objects

Büchi M., Sekerinski E.

Fundamenta Informaticae

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2000

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Vol. 44, Nr 1,2

25-61

EN

We study the notion of class refinement in a concurrent object-oriented setting. Our model is based on a combination of action systems and classes. An action system describes the behavior of a concurrent, distributed, or interactive system in terms of the atomic actions that can take place during the execution of the system. Classes serve as templates for creating objects. To express concurrency with objects, we add actions to classes. We define class refinement based on trace refinement of action systems. Additionally, we give a simulation-based proof rule. We show that the easier to apply simulation rule implies the trace-based definition of class refinement. Class refinement embraces algorithmic refinement, data refinement, and atomicity refinement. Atomicity refinement allows us to split large atomic actions into several smaller ones. Thereby, it paves the way for more parallelism. We investigate the special case of atomicity refinement by early returns in methods.

4

A subtyping for extensible, incomplete objects

Bono V., Bugliesi M., Dezani-Ciancaglini M., Liquori L.

Fundamenta Informaticae

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1999

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Vol. 38, Nr 4

325-364

EN

We extend the type system for the Lambda Calculus of Objects with a mechanism of width subtyping and a treatment of incomplete objects. The main novelties over previous work are the use of subtype-bounded quantification to capture a new and more direct rendering of MyType polymorphism, and a uniform treatment for other features that were accounted for via different systems in subsequent extensions. The new system provides for (i) appropriate type specialization of inherited methods, (ii) static detection of errors, (iii) width subtyping compatible with object extension, and (iv) sound typing for partially specified objects.

5

Coinductive axiomatization of recursive type equality and subtyping

Brandt M., Henglein F.

Fundamenta Informaticae

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1998

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Vol. 33, nr 4

309-338

EN

We present new sound and complete axiomatizations of type equality and subtype inequality for a first-order type language with regular recursive types. The rules are motivated by coinductive characterizations of type containment and type equality via simulation and bisimulation, respectively. The main novelty of the axiomatization is the fixpoint rule (or coinduction principle). It states that from A,Pý P one may deduce Aý P, where P is either a type equality t = t1 or type containment t