By Martín Abadi, Luca Cardelli
Procedural languages are in general good understood and their formal foundations solid within the kinds of quite a few lambda-calculi. For object-oriented languages but the scenario isn't really as uncomplicated. during this booklet the authors suggest and increase a unique technique by means of constructing item calculi during which gadgets are taken care of as primitives. utilizing item calculi, the authors may be able to clarify either the semantics of gadgets and their typing principles and show find out how to boost all the most vital thoughts of object-oriented programming languages: self, dynamic dispatch, periods, inheritance, secure and personal equipment, prototyping, subtyping, covariance and contravariance, and process specialization. Many researchers and graduate scholars will locate this a massive improvement of the underpinnings of object-oriented programming.
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Additional resources for A theory of Objects
20 REVIEW. OBJECT-ORIENTED FEATURES Previously inaccessible attributes can now be used in the rc branch. 13 The typecase mechanism is useful, but it is considered impure for several methodological reasons (and also for theoretical ones). First, it violates the object abstraction, revealing information that may be regarded as private. Second, it renders programs more fragile by introducing a form of dynamic failure when none of the branches apply. Third, and probably most important, it makes code less extensible: when adding another subclass of cell one may have to revisit and extend the type case statements in existing code.
MO has type InstanceTypeOj(c) and not, for example, InstanceTypeOj(c'). In general, adopting InstanceTypeOj(c') as the result type for the inherited method m in c' is unsound, because m may construct and return an instance of c that is not an instance of c'. Suppose, though, that m returns self, perhaps after modifying the field x. Then it would be sound to give the inherited method the result type InstanceTypeOj(c'), since self is always bound to the receiver of invocations. With this more precise typing, we would avoid subsequent uses of typecase: limiting the result type to InstanceTypeOj(c) constitutes an unwarranted loss of information.
Although minMaxClass is a subclass of maxClass, MinMax cannot be a subtype of Max. min(self) = other then return self else return other end; end; end; For any instance mm' of minMaxClass' we have mm' : MinMax. max(m) would be allowed for any m of type Max. Since m may not have a min attribute, the overridden max method of mm' may break. Therefore: MinMax <: Max does not hold Thus subclasses with contravariant occurrences of Self do not always induce subtypes. 32 REVIEW . 5 Object Protocols Even when subclasses do not induce subtypes, we can find a relation between the type induced by a class and the type induced by one of its subclasses.