Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science. 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Our calculus is centered on objects; procedures and classes can be defined from them. Despite these differences, we all share the goal of modeling imperative object oriented languages by precise semantic structures and sound type systems. This paper is self contained, but continues our work of [2, 3, 4, 5]. The most apparent novelties are the imperative features, the variance annotations, the treatment of Self types, and the representation of classes and inheritance. The new typing features led us to prefer syntactic proof techniques over denotational methods. In section 2 we give the untyped term ....

Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science, 332-341. 1994.

....of our rules using a subject reduction approach (section 4) Our technique is an extension of Harper s [16] using closures and stacks instead of formal substitutions. This approach yields a manageable proof for a realistic implementation strategy. Elsewhere we have considered functional calculi [2 4]. The main novelty here is the treatment of imperative features, with corresponding proof techniques. In further work [5] we treat second order type structures (with Self types) for an imperative calculus. A few other object formalisms have been defined and studied. Many of these rely on purely ....

Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science. 1994.

....and repackaging of self is no longer necessary. In summary, it seems hard to find simple, general, and correct encodings by syntactic means. Semantically, however, we can resort to the richer vocabulary of type constructions available in models. Specifically, the denotational semantics we give in [2] is a self application semantics where, for example, we interpret the type Point as the union of all the solutions to the equations of the form X = x,y:XInt, including for example X = x,y:XInt and X = x,y:XInt, c:XColor. With this definition, ColorPoint is forced to be a subtype of Point. ....

....can be defined by extending our first order theories with standard second order constructs. Further work describes the second order theories, where some deficiencies of first order systems are remedied with an account of Self types , and shows their soundness using a denotational semantics [2, 3]. Acknowledgments John Mitchell was helpful during initial discussions about the subject of this paper. John Lamping suggested using sums to type the natural numbers. Page 32 June 5, 1995 11:11 AM Appendix A: Objects Fragments These are the typing and equality rules for first order objects. ....

Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science, 332-341. 1994.

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Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science, 332-341. 1994.

....representation types. For example, we might expect that the terms (pack X :Int=Nat, 0,succ Nat ) and (pack X :Int=Int, 0,succ Int ) be equal at type (X :A)X(XX) because they have the same behavior, but this does not seem to be derivable. This can be proved using parametricity in the theory of [21]. For simplicity we restrict attention to our conservative rules, although more ambitious rules may have advantages in combination with objects. Universals are contravariant and existentials are covariant in their bounds, as reflected by the rules (Sub All) and (Sub Exists) Moreover, if B is ....

Plotkin, G.D., M. Abadi, and L. Cardelli, Subtyping and parametricity. Proc. IEEE Symposium on Logic in Computer Science, 310-319. To appear. 1994.

....next section; however, the reader may want to consult the full report on that work [Abadi, Cardelli 1994c] A tutorial by Fisher and Mitchell [13] may also be helpful as background material. As we mentioned above, this paper is part of a larger effort. Elsewhere, we consider denotational models [1]; we study imperative semantics [3] we give direct rules for Self, building on the present work [3] and we compare subtyping with the related notion of matching [4] Palsberg has studied type inference for our first order systems [20] the problems of type inference remain open for second order ....

....in the same ways; for example, if o has type [l:Int] then it is legal to set o. l: 3, but there is no corresponding operation on values of type (X :Int) l:X] In the next section we show that Ob : can encode F : and that Ob : can encode F : ignoring the first order h rule) Conversely, in [1] we show that Ob : can be translated into a typed l calculus without objects and without subtyping. In collaboration with Ramesh Viswanathan, we have since obtained a translation of Ob : and Ob : into F : this latest translation has the property of preserving subtypings. These translations ....

Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science, 332-341. 1994.

....of our rules using a subject reduction approach (section 4) Our technique is an extension of Harper s [16] using closures and stacks instead of formal substitutions. This approach yields a manageable proof for a realistic implementation strategy. Elsewhere we have considered functional calculi [2 4]. The main novelty here is the treatment of imperative features, with corresponding proof techniques. In further work [5] we treat second order type structures (with Self types) for an imperative calculus. A few other object formalisms have been defined and studied. Many of these rely on purely ....

Abadi, M. and L. Cardelli, A semantics of object types. Proc. IEEE Symposium on Logic in Computer Science. 1994.

....because it separates fields from methods, and methods cannot be overridden in objects. A translation of objects is possible but non trivial (is type driven) because of the splitting of self into fields and methods. Fits well with class based objectoriented languages. Sum of Extensions Semantics [Abadi, Cardelli 1994b] l i :B i i1. n ] X: l i i1. n ) Y) Yl i :B i i1. n ,X Derived from a denotational semantics of object types. Satisfies the primitive semantics (is based on the self application semantics at the term level) Satisfies object subtyping only in a specialized theory of . The ....

M. Abadi and L. Cardelli. A semantics of object types . Proc. IEEE Symposium on Logic in Computer Science (to appear).

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Abadi, M., Cardelli, L. (1994a). A semantics of Object Types. Proc. of the IEEE Symposium on Logic in Computer Science, LICS'94.

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