Logical Foundations of Database Transformations for Complex-Value Databases

Database transformations consist of queries and updates which are two fundamental types of computations in any databases the first provides the capability to retrieve data and the second is used to maintain databases in light of ever-changing application domains. In the theoretical studies of database transformations, considerable effort has been directed towards exploiting the close ties between database queries and mathematical logics. It is widely acknowledged that a logic-based perspective for database queries can provide a yardstick for measuring the expressiveness and complexity of query languages. Furthermore, mathematical logics encourage the expedited development of declarative query languages that have the advantage of separating the logical concerns of a query from its implementation details. However, in sharp contrast to elegant theories of database queries resulting from extensive studies over the years, the understanding of logical foundations of database updates is paltry. With the rising popularity of web-based applications and service-oriented architectures, the development of database theories in these new contexts must address new challenges, which frequently call for establishing a theoretical framework that unifies both queries and updates over complex-value databases. More specifically, in rich Web application architectures, queries themselves are not sufficient to support data processing; interactive integration among Web-accessible services requires the compositionality of queries and updates; the increasing complexity of application domains demands more flexible data structures than ubiquitous relations, which leads to complex-values represented by arbitrary nesting of various type constructors (e.g., set, list, multiset and tuple). Therefore, a theoretical framework of database transformations plays an important role in investigating a broad range of problems arising from extensions of query languages with update facilities, such as, database compilers and optimisers. To date, there has been only limited research into a unifying formalisation of database queries and updates. The previous findings reveal that it is very difficult to characterise common features of database queries and updates in a way which is meaningful for further theoretical investigations. However, the advent of the sequential Abstract State Machine (ASM) thesis capturing sequential algorithms sheds light on the study of database transformations. Observing that the class of computations described by database transformations may be formalised as algorithms respecting database principles, I am inspired by using abstract state machines to characterise database transformations. In doing so, this dissertation aims to lay down the foundations for establishing a theoretical framework of database transformations in the context of complex-value databases. My first major contribution in this dissertation is to propose a complete characterisation of database transformations over complex-value databases from an algorithmic point of view. Five intuitive postulates are defined for highlighting the essence of database transformations. Furthermore, a formal computation model for database transformations, called database Abstract State Machines (DB-ASMs), is developed. It turns out that every database transformation characterised by the postulates can be behaviourally simulated by a DB-ASM with the same signature and background, and vice versa. My second major