5 Concluding Remarks 4 a Semantics for Oodb 4.1 Schemas and Databases 4.2 Inheritance State $ Term $ Proposition Transition $ Rewriting $ Deduction 3.4 Initial Model Semantics

platform for database languages (or why predicate calculus is not enough). 10 the level of classes (more generally sorts) and the level of modules was already clearly made in the FOOPS language (besides the original paper 17], see also 21] for a very good discussion of inheritance issues and of the class-module distinction in the context of FOOPS), and indeed goes back to the distinction between sorts and modules in OBJ 20]. In MaudeLog, code in modules can be modiied or adapted for new purposes by means of a variety of module operations|and combinations of several such operations in module expressions|whose overall eeect is to provide a very exible style of software reuse that can be summarized under the name of module inheritance. Module operations of this kind include: 1. importing a module in a protecting, extending, or using mode 2. adding new equations or rules to an imported module 3. renaming some of the sorts or operations of a module 4. instantiating a parameterized module 5. adding modules to form their union 6. redeening a function so that its sort and syntax requirements are kept intact, but its semantics can be changed by discarding previously given equations or rules involving the function so that new equations or rules can then be given in their place 7. removing a sort or function altogether along with the equations or rules that depend on it so that it can be either discarded or replaced by another sort or function with diierent syntax and semantics. Operations 1{5 are exactly as in OBJ3 20]. Operations 6{7 are new and give a simple solution to the thorny problem of message specialization without complicating the class inheritance relation, which remains based on the order-sorted semantics. The need for message specialization, that is, for providing a diierent behavior for a message, arises frequently in practice. For example, a bank may at some point want to introduce a new kind of checking account in which there is a charge of 50 cents for each cashed check. The updating of an account's balance upon receipt of a message of type (chk A # K amt M) has to be modiied by the extra 50 cents charge. The problem is that if the new class of checking accounts with checking charges is deened as a subclass of the old, then the nice property supported by class inheritance of inheriting the …