Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. Lengauer C.B. Jones, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by a translation from programs to verification conditions, thus following the approach ESC Modula 3. Verification conditions are expressed in first order predicate calculus. Thus, we do not need any special logics, like separation logics (e.g. 0] or coalgebras as used in the LOOP project [8], to reason about pointer structures and updates. This makes our approach more amenable to further studies on heap strutures and confinement. Modularity. The proposed technique is modular in that one can verify software units (say, methods, classes, or small sets of classes) separately and ....

Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Academic Publications, 1996.

....PVS. After type checking, the user can state the properties (s)he would like to prove about these Java classes, and subsequently (try to) prove them, using the full power of PVS. The underlying Java semantics that is used in the automatic translation is based on so called coalgebras [JR97,Rei95,Jac96] These are special functions, which are useful for describing state based dynamical systems. In the theory of coalgebras there are standard notions of invariance and bisimulation. Java classes are translated into coalgebras, acting on a single (global) memory (type) consisting of an innite ....

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83103. Kluwer Acad. Publ., 1996.

.... as a Modality 1 Introduction The notions of observation and behaviour have played an important r ole in computer science, from Nerode equivalence and minimal realisations of automata, to bisimulations in process algebras [21] and in coalgebras, particularly with respect to the object paradigm [1, 13, 25, 20], while notions of observational or behavioural equivalence have formed a continuous thread through the area of algebraic speci cation [24, 26, 23, 3, 10] In this paper we present a categorical logic in which the notion of behavioural satisfaction (or truth up to observability) can be abstracted ....

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Acad. Publ., 1996.

....on the category of sets. A T coalgebra is a pair (A, a) with A being a set and a a function of the form A TA. This notion has proven useful in modelling data structures such as lists, streams and trees; transition systems such as automata; and classes in object oriented programming languages [32, 23]. Generically A is viewed as a set of states, and a as a transition structure. The usefulness of the notion has fueled the development of a theory of universal coalgebra [34, 36, 13] by analogy with, and categorically dual to, the study of abstract algebras. The present paper is a continuation ....

....[ The notation Mod will used for the class of all models of a set l of formulas, and Mod in the case that l consists of a single formula . An Example: Streams of Characters There are many examples of coa]gebraic presentations of data structures to be found in the literature, in such sources as [32, 23, 22, 36, 26, 25]. We now develop an example of this kind, motivated by ideas from [23, 26] to illustrate features of the syntax and semantics just defined. Imagine a simple game machine with a display screen and two buttons labeled play and next. The game starts with a blank screen. Pushing play causes a ....

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Bart Jacobs. Objects and classes, coalgebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Academic Publishers, 1996.

....the category of sets, then a T coalgebra is a pair (A, c) with A being a set and c a function of the form A TA. This notion has proven useful in modelling data structures such as lists, streams and trees; transition systems such as automata; and classes in object oriented programming languages [29, 16, 31, 32]. Generically A is viewed as a set of states, and c as a transition stcture. In many of the examples just mentioned, the functor T is polynomial, i.e. is constructed from constant valued functors and the identity functor by forming products, exponential functors with constant exponent (which ....

Bart Jacobs. Objects and classes, coalgebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Academic Publishers, 1996.

....For example, a deterministic automata hQ; A; Q A Q; Q Bi consisting of a state set Q, an input alphabet A, a next state function and an output function can be represented as a coalgebra (Q; Q Q B) where the transition structure can be defined obviously from and . See [Bar00, Jac96b, Jac98, Jac00, Jac02, Rei95, Wol02] for related work. The coalgebraic approach focuses on the observable behavior of system states, together with the concept of bisimulation being used to formalize observational indistinguishability. The concept of bisimulation is of great importance because it forms the basis of the coinductive ....

....generally infinite behavior and checking the reusability of components. Although coalgebras capture the observational aspect of systems, there is no way to construct a new system state from scratch by coalgebraic operations. Initial states are occasionally used to describe such basic constructors [Jac96a, Jac96b, JT01]. An alternative approach to overcome the lack of constructors is the integration of the complementary algebraic techniques into coalgebraic specification [Cr00] The motivation of our work comes from the observation that the coalgebraic specification languages being currently developed, like ....

[Article contains additional citation context not shown here]

Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. Lengauer C.B. Jones, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-- 103. Kluwer, 1996. References 27

....[23] CCSL allows the coalgebraic specification of classes of object oriented programs. A question in this context is to determine the largest fragment of CCSL that ensures that specified classes of objects have a final semantics (final semantics for objects was proposed by Reichel [19] and Jacobs [9]) The value of our result in such a concrete setting needs further exploration. On the other hand we have pointed out possibilities to extend weaker logics in a way that they still admit final semantics. Possible strengthenings may allow formulas with (1) prefixes of universally quantified ....

Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Acad. Publ., 1996.

....principle. 1 Introduction In recent years the theory of coalgebras gained attention in theoretical computer science, see [Rut00,Gum99] for well written and extensive introductions. Among other applications, coalgebras provide semantics for classes in object oriented programming and speci cation [Rei95,Jac96]. This idea is exploited for coalgebraic speci cation, e.g. in ccsl [RTJ01] but also in the work of C. C rstea [C r02] Coalgebras are usually seen as generalisations of transition systems and one of the greatest advantages of this generalisation is that it delivers standard notions like ....

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. Jones, C. Lenauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Academic Publishers, 1996.

.... in [15, 25] However, since # calculus uses the function as a primitive construct, object calculi based on # calculus quickly tend towards high levels of complexity [4] Generally, the reuse in an OO context of existing formalisms, such as # calculus, first order logic [24] and co algebras [38], does result in e#ciency of concept, but can quickly become prohibitively complex. The # calculus of Abadi and Cardelli makes use of objects as a primitive construct and is arguably able to express more fully the features of object systems as a consequence. The existence of a fundamental theory ....

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer, Massachusetts, 1996.

....1 Introduction In recent years the theory of coalgebras gained attention in theoretical computer science, see [Rut00, Gum99] for well written and extensive introductions. Among other applications, coalgebras provide semantics for classes in object oriented programming and specification [Rei95, Jac96]. This idea is exploited for coalgebraic specification, e.g. in ccsl [RTJ01] but also in the work of Corina Crstea [Cr02] Coalgebras are usually seen as generalisations of transition systems and one of the greatest advantages of this generalisation is that it delivers standard notions like ....

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. Jones, C. Lenauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Academic Publishers, 1996.

....science, due to their role in representing various data structures, as well as structures used in operational semantics. These include automata, labelled transition systems and other types of state based system; lists, streams and trees; and classes in object oriented programming languages [28, 21, 22]. In many of these cases the forgetful functor U : T Coalg Set on the category of T coalgebras has a right adjoint : Set T Coalg, providing a cofree coalgebra G X over each set X. This situation has spurred the development of a general theory of Set based coalgebras [30, 31, 16, 18] by ....

Bart Jacobs. Objects and classes, coalgebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83{ 103. Kluwer Academic Publishers, 1996. 17

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B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Acad. Publ., 1996.

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B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Acad. Publ., 1996.

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B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Acad. Publ., 1996.

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B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.- J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Acad. Publ., 1996.

....for removing an element may fail or succeed, depending on whether the stack is empty or not. In the latter case, the pop operation produces an element (in D) together with a (modi ed) state. More information on the coalgebraic description of classes in object oriented languages may be found in [20, 9, 7, 14, 11, 24]. 3) Deterministic and non deterministic automata. Let A be an arbitrary set, often called an alphabet of symbols in this context. A deterministic automaton consists of a set of states X with a transition function : X A X and a subset F X of nal (or halting) states. This function and ....

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Acad. Publ., 1996.

....invariant, bisimulation, refinement. Classification: 68Q60, 68Q65, 03B70 (AMS 91) F.3.1, F.3.2, D.1. 5 (CR 91) 1 Introduction This paper is part of a recent research line of applying coalgebraic and coinductive notions and techniques in the formalisation of object oriented concepts, see [25, 13, 10, 12, 14, 5, 6], building on earlier work [29, 2, 15] Coalgebras consist of a state space together with a transition function and can be used to describe various kinds of dynamical systems, including automata, transition systems and hybrid systems, see e.g. 27, 20, 11] A coalgebraic specification (as ....

.... on earlier work [29, 2, 15] Coalgebras consist of a state space together with a transition function and can be used to describe various kinds of dynamical systems, including automata, transition systems and hybrid systems, see e.g. 27, 20, 11] A coalgebraic specification (as developed in [13]) formally captures several crucial aspects of classes in object oriented languages: it consists of a (hidden) state space (typically written as X) to which a client has only limited access, together with several operations (or methods) which act on X. These operations may be attributes X A ....

[Article contains additional citation context not shown here]

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C.B. Jones, C. Lengauer, and H.- J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Acad. Publ., 1996.

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Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. Lengauer C.B. Jones, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer, 1996.

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B. Jacobs. Objects and classes, co-algebraically. In Object orientation with parallelism and persistence, Kluwer Acad. Publ., 1996.

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Bart Jacobs. Objects and classes, coalgebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Academic Publishers, 1996.

No context found.

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. L. C.B. Jones, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer, 1996.

No context found.

B. Jacobs. Objects and classes, co-algebraically. In C. Lengauer B. Freitag, C.B. Jones and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83103. Kluwer Academic Publishers, 1996.

No context found.

B. Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. L. C.B. Jones, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer, 1996.

No context found.

B. Jacobs. Objects and classes, co-algebraically. In C. L. B. Freitag, C.B. Jones and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83-103. Kluwer Academic Publishers, 1996.

No context found.

Bart Jacobs. Objects and classes, co-algebraically. In B. Freitag, C. B. Jones, C. Lengauer, and H.-J. Schek, editors, Object-Orientation with Parallelism and Persistence, pages 83--103. Kluwer Academic Publications, 1996.

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