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....or rede ne methods supplied by the prototype, and any message sent to the object is handled directly by that object, if it contains a corresponding method, or it is passed back , i.e. delegated, to the prototype. Delegation based languages have gained renewed popularity in the last years. In [1], an object calculus is presented that supports (destructive) method override and inheritance by object subsumption. In [5] a functional model of a delegationbased calculus is presented that extends previous foundational work from [8] The Lambda Calculus of Objects of [5] is an untyped lambda ....

M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of LNCS, pages 296-320. SpringerVerlag, 1994.

....attributi, o variabili di istanza, possono essere considerati come metodi costanti) ed i metodi sono funzioni con un parametro, usualmente chiamato self, che denota l oggetto ricevente del messaggio. Tra le proposte pi u interessanti di linguaggi ad oggetti ricordiamo quelle di Abadi e Cardelli [AC94] e Fisher, Honsell e Mitchell [FHM94] i) Abadi e Cardelli [AC94] hanno presentato un calcolo ad oggetti che supporta riscrittura di metodi ed eredit a via sussunzione di oggetti (ovvero un oggetto con una interfaccia estesa pu o essere utilizzato in ogni contesto che attende un oggetto con ....

....metodi costanti) ed i metodi sono funzioni con un parametro, usualmente chiamato self, che denota l oggetto ricevente del messaggio. Tra le proposte pi u interessanti di linguaggi ad oggetti ricordiamo quelle di Abadi e Cardelli [AC94] e Fisher, Honsell e Mitchell [FHM94] i) Abadi e Cardelli [AC94] hanno presentato un calcolo ad oggetti che supporta riscrittura di metodi ed eredit a via sussunzione di oggetti (ovvero un oggetto con una interfaccia estesa pu o essere utilizzato in ogni contesto che attende un oggetto con una interfaccia pi u limitata) La sussunzione tra oggetti ha la sua ....

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M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 296--320. Springer-Verlag, 1994.

....methods, or pass them back , i.e. delegate them, to the prototype. Originated with the seminal work on Self [9] the object based model has subsequently been studied in several papers, among which the record calculus of [3] and then in recent papers on functional object oriented languages [1, 5]. These latter proposals are centered around two main design choices: i) objects are first class values consisting of the set of their methods (attributes are viewed as constant methods) and (ii) methods are functions with a distinguished parameter denoting the host object. The resulting ....

....from left to right, p: send [ move 2 ] 7 q yields the binding: q = hx : s: x 7 3 2: move : D move ; col : D col :i and, finally, the last message yields c = blue as expected. Object numerals. As a further example, we show how natural numbers can be represented in O Gammaffi . Following [1], we define object numerals as objects that respond to the methods is zero (test for zero) pred (predecessor) and succ (successor) and behave like natural numbers. In fact, we need only to define the numeral zero as the prototypical number, and let al..l other numerals be generated by repeated ....

M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of LNCS, pages 296--320. Springer-Verlag, 1994.

....or rede ne methods supplied by the prototype, and any message sent to the object is handled directly by that object, if it contains a corresponding method, or it is passed back , i.e. delegated, to the prototype. Delegation based languages have gained renewed popularity in the last years. In [1], an object calculus is presented that supports (destructive) method override and inheritance by object subsumption. In [5] a functional model of a delegationbased calculus is presented that extends previous foundational work from [8] The Lambda Calculus of Objects of [5] is an untyped lambda ....

M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of LNCS, pages 296-320. SpringerVerlag, 1994.

....rpoly Ray infinity Perim. In such a hierarchy, however, nothing prevents the method set of the superclass rpoly from being selected after opening a circle object. This might lead to run time errors, e.g. multiplication of Ray by infinity which, however, is just a dummy constant. As outlined in (Abadi and Cardelli 1994; Fisher et al. 1994) a better understanding of the basic concepts of object orientation can be achieved by focusing on object based Mathematical Structures in Computer Science 17 Objects and Messages object: Identifier o o o. frozen: Identifier o o o. send: Identifier Msg ....

M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 296--320. Springer-Verlag, 1994.

....for higher order languages [CM89, HP90] and for ML [JM88, OB88, Oho90, R em93b] Object encoding, based on record calculi, has revealed severe difficulties, mainly due to over reliance on recursive values. Consequently, the tendency has been to design languages with objects as primitive operations [Bru93, AC94, Hen91a, MHF93], rather than encodings, to achieve important simplification of type theoretical models. Pierce and Turner produced convincing evidence that object oriented programming can be treated as a matter of programming style, at least from a theoretical point of view [PT93] However, the use of F : ....

Martin Abadi and Luca Cardelli. A theory of primitive objects. In International Symposium on Theoretical Aspects of Computer Software, April 1994.

....due to the self application mechanism used to solve a method call. Many approaches are focused on capturing this aspect in very simple representation of classes and object. Among the foundational works in this field, it is interesting to briefly introduce the extensions of calculus with objects, [1, 27, 28, 55]. For instance, in [1] objects are represented by a term having form self:e, where e is a record consisting of a list of method definitions. The body of methods may contain occurrences of self , as, for instance, in the case of the identity method e = id = self ] An object is now obtained as ....

....used to solve a method call. Many approaches are focused on capturing this aspect in very simple representation of classes and object. Among the foundational works in this field, it is interesting to briefly introduce the extensions of calculus with objects, 1, 27, 28, 55] For instance, in [1] objects are represented by a term having form self:e, where e is a record consisting of a list of method definitions. The body of methods may contain occurrences of self , as, for instance, in the case of the identity method e = id = self ] An object is now obtained as fix point of such a ....

M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of LNCS, pages 296--320. Springer-Verlag, 1994.

....framework based on Linear Logic [6] suitable to describe operational aspects of programming languages. Differently from the authors previous proposal [5] inheritance is reconsidered by defining, in logical terms, a delegation based mechanism with characteristics similar to the ones presented in [1, 7]. Furthermore, the representation of an object is modified in order to preserve encapsulation of methods in the newly defined setting where objects can be dynamically extended. Keywords. Linear Logic Programming, Higher Order, Object Oriented Programming. Introduction to the logical aspects. The ....

....i.e. the query becomes hhid : get(X)ii returning the binding X ; 0. Extending objects by adding special messages. As shown in [5] the model of objects presented in the previous section allows to use a programming style typical of other object calculi based uniquely on methods invocations [1, 7]. In particular, since methods can access and modify 2 ff ffi Gamma fi Gammaffi fl should de read as ff ffi Gamma (fi Gammaffi fl) 3 Since, a method execution turns into one application of the resolution step, it is enough to set the flag everytime the methods are fired, i.e, in rule (a) and ....

M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of LNCS, pages 296--320. Springer-Verlag, 1994.

....Abstract. This paper presents a linear logic programming language, called O Gammaffi , that gives a complete and logically sound account of an object calculus with inheritance and override. This language can be seen as the logic programming counterpart of recent proposals of calculi of objects [1, 6]. Our main interest in this study is in investigating the logical foundations of these calculi, the goal being to show that equally elegant accounts of objectoriented concepts like self, overriding, and inheritance by delegation can be given in logic. This study is also interesting, in ....

....to messages, if it contains corresponding methods, or pass them back , i.e. delegate them, to the prototype. Originated with the seminal work of [14] the delegation model has gained renewed interest from recent proposals of functional object oriented languages, such as the Object Calculus [1], the Lambda Calculus of Objects [6] and other related calculi [3, 7] These proposals are centered around two main design choices: i) objects are first order entities that consist of the set of their methods (attributes are viewed as constant methods) and (ii) methods are functions with a ....

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M. Abadi and L. Cardelli. A Theory of Primitive Objects. In Proceedings of Theoretical Aspect of Computer Software, volume 789 of LNCS, pages 296--320. Springer-Verlag, 1994.

....more formally. Sections 3 and 4 describe a denotational semantics for the calculus. Section 5 concerns the translation into a calculus without objects. We conclude in Section 6 with comparisons with related work. An appendix summarizes our formal systems. Examples and proofs can be found in [Abadi, Cardelli 1994a] 2. A Theory of Primitive Objects We now review the typed object calculus, leaving most rules for the appendix. Each rule has a number of antecedent judgments above a horizontal line and a single conclusion judgment below the line. Each judgment has the form E # , for an environment E and an ....

M. Abadi and L. Cardelli, A theory of primitive objects. To appear.

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Abadi, M., Cardelli, L., A Theory of Primitive Objects. Manuscript,

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