Abstract. Various models and languages for describing and manipulating hierar-chically structured data have been proposed. Algebraic, calculus-based, and logic-programming oriented languages have all been considered. This article presents a general model for complex values (i.e., values with hierarchical structures), and languages for it based on the three paradigms. The algebraic language generalizes those presented in the literature; it is shown to be related to the functional style of programming advocated by Backus (1978). The notion of domain independence (from relational databases) is defined, and syntactic restrictions (referred to as safety conditions) on calculus queries are formulated to guarantee domain inde-pendence. The main results are: The domain-independent calculus, the safe cal-culus, the algebra, and the logic-programming oriented language have equivalent expressive power. In particular, recursive queries, such as the transitive closure, can be expressed in each of the languages. For this result, the algebra needs the powerset operation. A more restricted version of safety is presented, such that the restricted safe calculus is equivalent to the algebra without the powerset. The results are extended to the case where arbitrary functions and predicates are used in the languages. Key Words. Database, query language, complex value, complex object, database model.

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The expressiveness and complexity of several calculus-based query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objects. For instance, it is shown that the way the database makes use of its higher-order types has direct impact on query complexity. The use of fixpoint operators is shown to yield languages well-behaved with respect to complexity and expressiveness. In particular, an extension of the fixpoint queries to complex objects is shown to express precisely the PTIME queries, under the assumption that the database makes "full" use of all its types. Similar results involve range-restricted queries. 1 Introduction Complex objects are increasingly part of advanced database systems. They provide the structural core of object-oriented databases. Several query languages for complex objects have been propo...

We discuss the declarative and computational issues in combining equational, subset, and relational assertions in a logic programming language. The novel feature in this work is the subset assertion, whose interactions with equational and relational assertions are discussed in this paper. The semantics of subset assertions incorporate a collect all capability, which is expressed formally by the completion of the program. When used in conjunction with equational assertions, subset assertions serve to define set-valued functions, and the resulting paradigm is called subset-equational programming. We also present the class of stratified subset-equational programs for formalizing the class of closure functions, which are useful in defining various transitive-closure sets. The declarative and operational semantics of simple and stratified subset-equational programs are the main focus of this paper. The operational semantics of closures is based on memo-tables (or extension tables). When sub...

Set-based languages have emerged as a powerful means for expressing not only programs but also requirements, test cases and so on. However, a uniform compilation schema for sets has not yet been completely developed. The present paper tries to overcome this lack using a set-based logic language, SL (set language), as target. The approach is based on an imperative abstract machine, the SAM (set abstract machine). The translation from SL to SAL (SAM assembly language) is described and all the possible optimizations, both at source code level and at assembly code level, are detailed. The potentials for identifying parallel flows of computations are analysed. Several examples of compilations are presented and discussed.

A * * * * * a b c d e f C A C A E A E B A B (a) A sort and a value of that sort A B C a b A E c d e f A E (b) Another representation of the same value Figure 20.1: Complex Value 3 Director Movies Hitchcock Title Actors The Trouble with Harry John Forsythe Edmund Gwenn Shirley MacLaine Alfred Hitchcock The Birds Tippi Hedren Rod Taylor Suzanne Pleshette Alfred Hitchock Psycho Anthony Perkins Janet Leigh Alfred Hitchcock Bergman Title Actors Cries and Whispers Harriet Andersson Kari Sylwan Ingrid Thulin Liv Ullman The Seventh Seal Max von Sydow Gunnar Bjornstrand Bengt Ekerot Mils Poppe Figure 20.2: The CINEMA database revisited (with additional data shown) 4 CHAPTER 20. COMPLEX VALUES these sorts are provided. For example, we have: Sort Complex V alue dom a fdomg fa; b