Object-oriented semantics in the UTP Sample Clauses

Object-oriented semantics in the UTP. ‌ Object-orientation was first given a UTP semantics in the work of Xxxxxx [37, 10]. This work provides a general theory for the definition of class structures containing attributes and methods. Classes can be inherited to add further attributes and methods, and method implementations in parent classes can be overridden as is usual in OO languages. Unlike VDM-RT, Xxxxxx’ theory considers only classes which have one parent, that is single-inheritance, where VDM-RT has multiple-inheritance. The class theory uses the UTP theory of designs to define these commands in a purely relational setting. Objects in this setting are simply described by records that enumerate the attributes of the corresponding class. Methods are represented as UTP procedures that are defined with the context of Higher Order UTP (see [21] chapter 9 and also [46]) that enables predicates to contain variables that themselves have predicate types. Thus a method definition corresponds to a UTP variable with such a predicate type defining the method’s implementation. This work was later extended by Xxxxx [47] who added a modular approach to method defini- tions in the presence of recursion. The original work [10] requires that a collection of (mutually) recursive methods be declared simultaneously so that a common fixed-point can be declared that encompasses them all. Xxxxx [47] overcomes this problem by introducing higher-order method variables that can be invoked in the body of a method and only later bound to an actual implementation. This means the fixed point need only be created at the point of method call, not the point of definition. We will not explicitly consider recursion in our theory, although we note that Xxxxx’s work is fully compatible.