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... and history constraints are static, unless marked with the instance modifier. Static invariants may only refer to static fields, while instance invariants can refer to both instance and static fields. The first invariant in the figure says that in every publicly visible state, every reachable object that is a BoundedThing must have a positive MAX_SIZE field. The second invariant says that, in each publicly visible state, every reachable object that is a BoundedThing must have a size field that is nonnegative and less than or equal to MAX_SIZE. Following the invariants is a history constraint [LW94]. Like the invariants, it uses the modifier instance, because it refers to instance fields. A history constraint is used to say how values can change between earlier and later publiclyvisible states, such as a method’s pre-state and its post-state. This prohibits subtype objects from making certain state changes, even if they implement more methods than are specified in a given class. The history constraint in the specification of BoundedThing says that the value of MAX_SIZE cannot change, since in every pre-state and post-state, its value in the post-state, written MAX_SIZE, must equal its va...

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...ubtyping). In order to relate subtyping to signature and specification matching, we must first convert object types to our context. We base our definition of an object type on that of Liskov and Wing =-=[LW94]-=- but differ from their definition in that we do not include invariants or constraints. We restrict our focus here to relating methods, which is only one aspect of their subtyping relation. We model an...

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...ons of rich possibilities for interface specifications and composition. Reflecting behavioral properties in interfaces, of course, has also proved useful in general-purpose computing (see for example =-=[22]-=-). But where we are concerned with properties that have not traditionally been expressed at all in computing, the ability to develop and compose specialized “interface theories” [11] is extremely prom...

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...(this, x) def = this.cntss→ x and scope it to the Cell class. This stops the Cell’s client using the field directly as it is hidden in the abstract predicate. (b) Using standard behavioural subtyping =-=[17]-=-, to allow dynamic dispatch, the Recell’s specification needs to be compatible with the Cell’s, i.e. we require the following two implications to hold pre(Cell, set)⇒ pre(Recell,set) (1) post(Recell, ...

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...ignatures. Monotone subclassing requires that the subclass relationship be declared and that the subclass preserve the interface of the superclass, while possibly extending it. Behavioral conformance =-=[2, 5, 15, 40]-=- allows any class to be a subtype of another if it preserves the interface and behavior of all methods available in the supertype. Finally, strictly monotone subclassing additionally demands that the ...

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...ticated interface technologies havesbeen developed for object-oriented and other languages.sThese include higher-order value typing like generic types,s[5] state typing [10], behavioral specification =-=[6, 27, 30]-=-sand others. One area of research is to explore the aspectaware equivalent of these other kinds of interfaces.sOursbelief is that the basic idea of aspect-aware interfacessshould carry-over to these i...

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... of arbitrarily aliased objects are difficult to capture across program abstractions. The interaction of typestates and subclasses generally follows the notion of behavioral subtypes of Liskov et.al. =-=[14]. -=-Our formalism however does not support history constraints. On the other hand, unlike in Liskov’s approach, our pre- and post-conditions are abstract predicates that allow subclasses to rely on stro...