Specification and verification of abstract database types

Abstract

A database system, comprising a schema, integrity constraints, transactions, and queries, constitutes a single abstract data type. This type, which we call an abstract database type, has as its object the database itself. Thus, the value set of such a type is the set of all legal database states, legal in the sense of obeying all the structural specifications of the schema and the semantic prescriptions of the integrity constraints. The database transactions are the operations of the abstract database type and must be functions on the value set of the type. A transaction specification is safe if it defines a function which is closed on the database state set, i. e., any execution of the transaction on a legal database yields a legal database.We propose an approach to the definition of abstract database types which is both usable by typical database designers and which facilitates the mechanical verification of transaction safety. The Boyer and Moore theorem proving technique is used to prove transaction safety theorems using abstract data type axioms and recursive functions generated from the database schema and transaction programs.