5.2 an Object-type System for O ?

that does not break the type structure we have devised, provided that uniication be instrumented to deal with the new types. This, and the other related problems relative to the extension with object-types represent subject of our future work. Acknowledgements. The authors wish to thank the anonymous referees for their comments and suggestions. {disjunctions of atomic formulas playing the role of attributes, while methods are speciied as linear clauses that are used to rewrite (possibly modifying them) the attributes of objects. In O ? , instead, objects are encoded as terms that encapsulate their methods as subterms. With this encoding, while retaining the form of method inheritance peculiar to 2], we also obtain a natural modeling of dynamic method redeenition, a functionality that could hardly be accounted for in 2]. The encoding of objects in O ? is inspired to the language F&O of 4], from which, however, our approach diiers for the choice of both the computational model and the object model. F&O subscribes to the proofs-as-computations principle of Linear Logic which interprets sequents as en-codings of the state of the computation and proofs as descriptions of the state evolution. Furthermore, F&O takes, essentially, a class-based approach where objects are created by instantiating a class and referenced to by means of the identiiers they are associated with at creation time. A similar approach is taken in the HACL language of 7]. HACL is a concurrent linear logic calculus which also adheres to the proofs-as-computations and formulas-as-processes principles of Linear Logic. Again, the object model is, essentially, a class-based model where objects are encoded as (abstraction of) records that result as the xed points of their associated class deenitions. On the other hand, O ? is a standard logic programming language, that uses uniication to compute values returned as results in answer substitutions , and shared variables to capture the semantics of cascaded method invocations peculiar to the companion functional calculi. Furthermore, the underlying data model is an object-based model, where the recursive nature of objects is captured relying on the self-application semantics of method invocation rather than on the on the explicit use of xed-point operators. Using this encoding, objects in O ? could be construed as elements of recur-sive types in a way similar to that described in 5]. The rest of this section brieey describes how this can be done. In the type system of 5], the …