## The Power of Languages for the Manipulation of Complex Values (1995)

### Cached

### Download Links

- [www.sigmod.org]
- [www.vldb.org]
- [www.acm.org]
- [ftp.inria.fr]
- DBLP

### Other Repositories/Bibliography

Venue: | VLDB Journal |

Citations: | 48 - 0 self |

### BibTeX

@ARTICLE{Abiteboul95thepower,

author = {Serge Abiteboul and Catriel Beeri},

title = {The Power of Languages for the Manipulation of Complex Values},

journal = {VLDB Journal},

year = {1995},

volume = {4},

pages = {727--794}

}

### OpenURL

### Abstract

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.

### Citations

1651 |
Foundations of Databases
- Abiteboul, Hull, et al.
- 1995
(Show Context)
Citation Context ...at-Ram, Jerusalem 91904, Israel, beeri@huji.ac.il.s728 (Makinouchi, 1977; Kobayashi, 1980; Macleod, 1981). Many models that incorporate more semantics into databases have been introduced and studied (=-=Abiteboul et al., 1994-=-; Hull, 1986). In the mid-1980's, a variety of models generalized the relational model by allowing hierarchically structured data; these are the nested relation and complex value models (Schek and Sch... |

633 |
Towards a theory of declarative knowledge
- Apt, Blair, et al.
- 1988
(Show Context)
Citation Context ...troducing recursion, we now present a simple language, based on recursive rules. We handle negation using the concept of "layers" (e.g., Naqvi, 1986; Beeri et al., 1987; Abiteboul and Grumbach, 1988; =-=Apt et al., 1988-=-; Van Gelder, 1988).s780 Given a database scheme, the relation names in it, R1, • .., Rr~, are called base relations. The language uses names of additional relations, called derived relations. The lan... |

571 |
The Implementation of Functional Programming Languages
- Jones
- 1987
(Show Context)
Citation Context ...use in mathematics for a long time. The idea of using set terms in a calculus for complex values seems to have first appeared in [39]. A similar notation for functional languages has been proposed in =-=[55]. Comprehe-=-nsions as a query notation have been shown to be closely related to monad-based bulk types; for a recent survey, see [20]. The expression fx j 'g can be replaced by a new variable y "anded" ... |

468 | Comprehending monads
- Wadler
- 1992
(Show Context)
Citation Context ... our approach and the language are related to recent research on query languages for bulk types that uses category-theoretic and type-theoretic frameworks and, in particular, to the notion of monads (=-=Wadler, 1990-=-; Trinder, 1991). It has been shown that a monadic algebra, if restricted to the set and tuple constructors, is equivalent to our algebra without the powerset (Breazu-Tannen, 1992). Conservativeness r... |

340 |
A relational model for large shared data banks
- Codd
- 1970
(Show Context)
Citation Context ...Words. Database, query language, complex value, complex object, database model. 1. Introduction The first normal form restriction forces the components of tuples in relational databases to be atomic (=-=Codd, 1970-=-). It is widely recognized that this restriction imposes unacceptable constraints on the use of database technology in a variety of application domains such as engineering, computer aided design, or o... |

210 |
J.D.: Universality of data retrieval languages
- Aho, Ullman
- 1979
(Show Context)
Citation Context ...hereby characterizing the power of many algebras found in the literature. It is well-known that even simple recursive queries (e.g., transitive closure) cannot be expressed using relational calculus (=-=Aho and Ullman, 1979-=-). This does not hold for our languages: the algebra, the safe (or domain-independent) calculus, and a language for complex values based on recursive rules are equivalent. This is similar to the use o... |

197 | Database description with SDM: A semantic database model
- Hammer, McLeod
- 1981
(Show Context)
Citation Context ... 1988) is much more restrictive. (This is illustrated by a simple cardinality argument given in Section 2.) The values we deal with can also be seen as values resulting in semantic database modeling (=-=Hammer and McLeod, 1981-=-; Hull and Yap, 1984; Abiteboul and Hull, 1988) from the use of aggregation (tuple constructors) and classification (set constructors), only sets of homogeneous values are considered. In that respect,... |

177 |
The relational model with relation-valued attributes
- Schek, Scholl
- 1986
(Show Context)
Citation Context ... et al., 1994; Hull, 1986). In the mid-1980's, a variety of models generalized the relational model by allowing hierarchically structured data; these are the nested relation and complex value models (=-=Schek and Scholl, 1986-=-; Korth et al., 1988; Abiteboul and Bidoit, 1986; Abiteboul and Beeri, 1988). 1 Towards the end of the decade, the emphasis shifted to semantic and, particularly, to object-oriented models that incorp... |

131 |
Negation as failure using tight derivations for general logic programs
- Gelder
- 1988
(Show Context)
Citation Context ...xpressive than (complex value) calculus. In the same spirit of introducing recursion, we now present a simple language based on recursive rules. We handle negation using the concept of "layers&qu=-=ot; as in [10, 3, 15, 51, 61]-=- and others. Given a database scheme, the relation names in it, b R 1 ; : : : ; b R n , are called base relations. The language will use names of additional relations, called derived relations. The la... |

129 | Naturally Embedded Query Languages
- Breazu-Tannen, Buneman, et al.
- 1992
(Show Context)
Citation Context ...ated to recent research on query languages for bulk types that uses category-theoretic and type-theoretic frameworks, and in particular to the notion 7 of monads, see [58, 63]. Indeed, it is shown in =-=[19]-=- that a monadic algebra, if restricted to the set and tuple constructors, is equivalent to our algebra without the powerset . Conservativeness results for the monadic languages are presented in [64]. ... |

124 | Beeri: On the Power of Languages for the Manipulation of Complex Objects INRIA Rapports de Recherche No. 846
- Abiteboul, C
- 1988
(Show Context)
Citation Context ...alized the relational model by allowing hierarchically structured data; these are the nested relation and complex value models (Schek and Scholl, 1986; Korth et al., 1988; Abiteboul and Bidoit, 1986; =-=Abiteboul and Beeri, 1988-=-). 1 Towards the end of the decade, the emphasis shifted to semantic and, particularly, to object-oriented models that incorporate some of the features of the complex value models. (An extension of ou... |

119 | The implementation of functional programming languages - Peyton-Jones - 1987 |

112 |
Remarks on the algebra of non-first-normalform relations
- Jaeschke, Schek
- 1982
(Show Context)
Citation Context ...al 4 (3) Abiteboul: Languages for Manipulation of Complex Values 731 1.2 Comparison with Previous and Related Work Our model generalizes the non-first-normal-form relational models (Makinouchi, 1977; =-=Jaeschke and Schek, 1982-=-; Fischer and Thomas, 1983; Schek and Scholl, 1986; Abiteboul and Bidoit, 1986; Korth et al., 1988). The original proposal to generalize the relational model to allow entries in relations to be sets i... |

82 | A calculus for complex objects - Bancilhon, Khoshafian - 1986 |

77 | clauses and database dependencies
- Fagin
(Show Context)
Citation Context ...r any database structure, changing the domains (but keeping them large enough to contain all atomic entries appearing in the database relations, or the query) does not change the result of the query (=-=Fagin, 1982-=-). It is well known that the expressions of relational algebra (assuming complement is not used) define domain-independent queries. The same holds for our algebra. Calculus formulas do not necessarily... |

75 |
Extending relational algebra and relational calculus with set-valued attributes and aggregate functions
- Ozsoyoglu, Ozsoyoglu, et al.
- 1987
(Show Context)
Citation Context ...om an object form a (virtual) tree. Thus, our languages can be applied to such models as well. Equivalence results of algebraic and calculus-based languages have been reported (Kuper and Vardi, 1984; =-=Ozsoyoglu et al., 1987-=-; Ozsoyoglu and Ozsoyoglu, 1983). The equivalence of relational algebra and calculus with aggregates was considered by Klug (1982), and extended by Ozsoyoglu and Ozsoyoglu (1983) to relations with set... |

74 | A consideration on normal form of not-necessarily-normalized relation in the relational data model
- Makinouchi
- 1977
(Show Context)
Citation Context ...Cedex, France, abitebou@db.stanford.edu; Catriel Beeri, Prof. Dr., is Full Professor, Department of Computer Science, The Hebrew University, Givat-Ram, Jerusalem 91904, Israel, beeri@huji.ac.il.s728 (=-=Makinouchi, 1977-=-; Kobayashi, 1980; Macleod, 1981). Many models that incorporate more semantics into databases have been introduced and studied (Abiteboul et al., 1994; Hull, 1986). In the mid-1980's, a variety of mod... |

73 | Logic Programming with Sets
- Kuper
- 1987
(Show Context)
Citation Context ... and worthy of study. We consider a calculus-based language (cf., Jacobs, 1982; Hull, 1986; Korth, 1988), an algebra, and a logic-programming language (cf., Kuper and Vardi, 1984; Beeri et al., 1987; =-=Kuper, 1987-=-; Abiteboul and Grumbach, 1988). Our main results concerning these languages are: • The classical equivalence between the domain-independent calculus and the algebra is valid in our model as well. • D... |

67 |
Non first normal form relations: An algebra allowing data restructuring
- Abiteboul, Bidoit
- 1985
(Show Context)
Citation Context ...s, a variety of models generalized the relational model by allowing hierarchically structured data; these are the nested relation and complex value models (Schek and Scholl, 1986; Korth et al., 1988; =-=Abiteboul and Bidoit, 1986-=-; Abiteboul and Beeri, 1988). 1 Towards the end of the decade, the emphasis shifted to semantic and, particularly, to object-oriented models that incorporate some of the features of the complex value ... |

59 | Comprehensions, a query notation for DBPLs
- TRINDER
- 1991
(Show Context)
Citation Context ...and the language are related to recent research on query languages for bulk types that uses category-theoretic and type-theoretic frameworks and, in particular, to the notion of monads (Wadler, 1990; =-=Trinder, 1991-=-). It has been shown that a monadic algebra, if restricted to the set and tuple constructors, is equivalent to our algebra without the powerset (Breazu-Tannen, 1992). Conservativeness results for the ... |

58 | Normal forms and conservative properties for query languages over collection types
- Wong
- 1993
(Show Context)
Citation Context ...n [19] that a monadic algebra, if restricted to the set and tuple constructors, is equivalent to our algebra without the powerset . Conservativeness results for the monadic languages are presented in =-=[64]-=-. It is shown there (in the spirit of [54]) that for relational input and output, the monadic languages have precisely the expressive power of the classical relational languages. The powerset operatio... |

54 |
A new approach to database logic
- Kuper, Vardi
- 1984
(Show Context)
Citation Context ...one to access such structures are important and worthy of study. We consider a calculus-based language (cf., Jacobs, 1982; Hull, 1986; Korth, 1988), an algebra, and a logic-programming language (cf., =-=Kuper and Vardi, 1984-=-; Beeri et al., 1987; Kuper, 1987; Abiteboul and Grumbach, 1988). Our main results concerning these languages are: • The classical equivalence between the domain-independent calculus and the algebra i... |

53 |
The format model: a theory of database organization
- Hull, Yap
- 1984
(Show Context)
Citation Context ...ictive. (This is illustrated by a simple cardinality argument given in Section 2.) The values we deal with can also be seen as values resulting in semantic database modeling (Hammer and McLeod, 1981; =-=Hull and Yap, 1984-=-; Abiteboul and Hull, 1988) from the use of aggregation (tuple constructors) and classification (set constructors), only sets of homogeneous values are considered. In that respect, the data structure ... |

45 | On the Expressive Power of Database Queries with Intermediate Types
- Hull, Su
- 1991
(Show Context)
Citation Context ...res. In particular, one can exhibit a hierarchy of languages, based on restrictions on the types of intermediate results and show that the calculus can express all elementary time (or space) queries (=-=Hull and Su, 1991-=-; Kuper and Vardi, 1993). Exact complexity characterizations are obtained with fixpoint, which is no longer redundant when the level of set nesting is bounded (Grumbach and Vianu, 1991). The algebra p... |

44 |
A survey of theoretical research on typed complex database objects
- Hull
- 1988
(Show Context)
Citation Context ... Israel, beeri@huji.ac.il.s728 (Makinouchi, 1977; Kobayashi, 1980; Macleod, 1981). Many models that incorporate more semantics into databases have been introduced and studied (Abiteboul et al., 1994; =-=Hull, 1986-=-). In the mid-1980's, a variety of models generalized the relational model by allowing hierarchically structured data; these are the nested relation and complex value models (Schek and Scholl, 1986; K... |

41 | New techniques for studying set languages, bag languages, and aggregate functions - Libkin, Wong - 1994 |

39 | Some properties of query languages for bags
- Libkin, Wong
- 1993
(Show Context)
Citation Context ...s. 29. Note, however, that aggregates may require the use of bags rather than sets for producing correct results. The problem can be addressed either by including bag as a type constructor (see e.g., =-=Libkin and Wong, 1993-=-a, 1993b, 1994) or using, for example, Klug's approach (1982). We do not consider the issue further in this article.s776 {x I 3y( 0,) A x.A =yA Ax.B = co=t (y.B))}, {x I S (x) A x.a _> 5 A even (x.B)}... |

29 |
Query languages for object-oriented database systems: the 02 proposal
- Bancilhon, Cluet, et al.
- 1989
(Show Context)
Citation Context ...can use set-collapse to transform it into a set of T-values. In the special case that each of the sets is a singleton, this has the same effect as the operation the, used in the query language of 02 (=-=Bancilhon et al., 1989-=-). Similarly, given a tuple, we can select one of its components, drop the others, and leave this component without the tuple constructor. For example, if we have R: { [A: T, ... ]}, then p (A) (R) ha... |

29 | Aggregate functions, conservative extension, and linear orders. This volume
- Libkin, Wong
(Show Context)
Citation Context ...s. 29. Note, however, that aggregates may require the use of bags rather than sets for producing correct results. The problem can be addressed either by including bag as a type constructor (see e.g., =-=Libkin and Wong, 1993-=-a, 1993b, 1994) or using, for example, Klug's approach (1982). We do not consider the issue further in this article.s776 {x I 3y( 0,) A x.A =yA Ax.B = co=t (y.B))}, {x I S (x) A x.a _> 5 A even (x.B)}... |

27 |
RELOOP: An Algebra Based Query Language For Object-Oriented Database System
- Cluet, Delobel, et al.
- 1990
(Show Context)
Citation Context ...r practical use. In this context, it is important to note that we have not considered SQL extensions in this article. Most implemented systems actually use languages based on this paradigm (see e.g., =-=Cluet et al., 1990-=-). Comprehensions (considered insVLDB Journal 4 (3) Abiteboul: Languages for Manipulation of Complex Values 785 Wadler, 1990; Trinder, 1991) can be viewed as a pure form of generalized SQL. We conject... |

26 |
The Recursive Unsolvability of the Decision Problem for the Class of Definite Formulas
- Paola
- 1969
(Show Context)
Citation Context ...not necessarily define domain-independent queries. Domain independence is a semantic property, defined in terms of structures, and known to be undecidable, even for the classical relational calculus (=-=DiPaola, 1969-=-; Vardi, 1981). The same holds for our calculus, since it contains the relational calculus. For relational calculus, there are syntactic restrictions that guarantee domain independence, yet do not lim... |

26 | Database Query Languages Embedded in the Typed Lambda Calculus
- Hillebrand, Kanellakis, et al.
- 1993
(Show Context)
Citation Context ...ong, 1993). These include the monadic algebra mentioned above, and comprehensions that can be viewed as a pure form of generalized SQL (the only paradigm not considered here). Finally, a recent work (=-=Hillebrand et al., 1993-=-) also consider the .R-calculus as a query language, but with an emphasis on the complexity of query evaluation. 1.3 Organization The article is organized as follows. In Section 2, we present the data... |

25 |
Operators for non-first-normal-form relations
- Fischer, Thomas
- 1983
(Show Context)
Citation Context ...ges for Manipulation of Complex Values 731 1.2 Comparison with Previous and Related Work Our model generalizes the non-first-normal-form relational models (Makinouchi, 1977; Jaeschke and Schek, 1982; =-=Fischer and Thomas, 1983-=-; Schek and Scholl, 1986; Abiteboul and Bidoit, 1986; Korth et al., 1988). The original proposal to generalize the relational model to allow entries in relations to be sets is often attributed to Maki... |

24 |
Computable queries for relational database systems
- Chandra, Harel
- 1980
(Show Context)
Citation Context .... • Finally, the transitive closure of R is obtained by intersecting the elements of R4: q ~ {x'[Vx(~b4(x) ~x' Cx)}. We could extend the calculus with a fixpoint operator as in the language fixpoint (=-=Chandra and Harel, 1980-=-). However, the technique used in the previous example can be generalized to demonstrate that this would result in no gain of expressivity; that is, complex-value-fixpoint is no more expressive than (... |

23 | Tractable Query Languages for Complex Object Databases
- Grumbach, Vianu
- 1991
(Show Context)
Citation Context ...me (or space) queries (Hull and Su, 1991; Kuper and Vardi, 1993). Exact complexity characterizations are obtained with fixpoint, which is no longer redundant when the level of set nesting is bounded (=-=Grumbach and Vianu, 1991-=-). The algebra proposed in the earlier models did not incorporate powerset and could not express this operation. When considering mappings from relations to relations, the algebra without powerset doe... |

20 | The representation and deductive retrieval of complex objects », 11th Int Conf. on Very Large Data Bases, août 1985. Une extension de l’algèbre relationnelle au support de fonctions. Cet article présente une extension de l’algèbre relationnelle permettant - Zaniolo |

18 |
Learning logic
- Jacobs, jordan
- 1985
(Show Context)
Citation Context ...es are an important component of object-oriented and semantic models, languages that allow one to access such structures are important and worthy of study. We consider a calculus-based language (cf., =-=Jacobs, 1982-=-; Hull, 1986; Korth, 1988), an algebra, and a logic-programming language (cf., Kuper and Vardi, 1984; Beeri et al., 1987; Kuper, 1987; Abiteboul and Grumbach, 1988). Our main results concerning these ... |

18 | On the Complexity of Queries in the Logical Data Model
- Kuper, Vardi
- 1993
(Show Context)
Citation Context ...ures. In particular, one can exhibit a hierarchy of languages, based on restrictions on the types of intermediate results and show that the calculus can express all elementary time (or space) queries =-=[35, 45]-=-. Exact complexity characterizations are obtained with fixpoint, which is no longer redundant when the level of set nesting is bounded [30]. The algebra proposed in the earlier models did not incorpor... |

17 | Safety and correct translation of relational calculus formulas - Gelder, Topor - 1987 |

16 | The powerset algebra as a result of adding programming constructs to the nested relational algebra - Gyssens, Gucht - 1988 |

15 |
Can programming be liberated from the von Neuman style
- Backus
- 1978
(Show Context)
Citation Context ...nal algebra uses a different paradigm--it is based on a small set of operations (i.e., given functions) that encapsulate useful iterations over relations, and that can be composed to express queries (=-=Backus, 1978-=-, presented a seminal paper on this paradigm of functional programming). Our algebra generalizes this approach. It uses several of the relational algebra operations, such as union, intersection, and d... |

13 | Space Usage in Functional Query Languages
- Abiteboul, Hillebrand
- 1995
(Show Context)
Citation Context ...iu and Paredaens, 1994). This seems to indicate that adding powerset is not the right way to obtain additional expressive power. However, recent optimization techniques for the algebra with powerset (=-=Abiteboul and Hillebrand, 1994-=-) indicate that this issue is not yet settled. Another direction is the study of alternative mechanisms that increase the expressive power, yet are more amenable to efficient programming, such as vari... |

12 |
A logic for negation in database systems
- Naqvi
- 1986
(Show Context)
Citation Context ...ressive than (complex value) calculus. In the same spirit of introducing recursion, we now present a simple language, based on recursive rules. We handle negation using the concept of "layers" (e.g., =-=Naqvi, 1986-=-; Beeri et al., 1987; Abiteboul and Grumbach, 1988; Apt et al., 1988; Van Gelder, 1988).s780 Given a database scheme, the relation names in it, R1, • .., Rr~, are called base relations. The language u... |

9 |
The decision problem for database dependencies
- Vardi
- 1981
(Show Context)
Citation Context ...as do not necessarily define domain independent queries. Domain independence is a semantic property, defined in terms of structures, known to be undecidable even for the classical relational calculus =-=[26, 62]-=-. The same holds for our calculus, since it contains the relational calculus. For relational calculus, there exist syntactic restrictions that guarantee domain independence, yet do not limit its expre... |

8 |
Sets and negation in a logic database language
- Beeri, Naqvi, et al.
(Show Context)
Citation Context ...ctures are important and worthy of study. We consider a calculus-based language (cf., Jacobs, 1982; Hull, 1986; Korth, 1988), an algebra, and a logic-programming language (cf., Kuper and Vardi, 1984; =-=Beeri et al., 1987-=-; Kuper, 1987; Abiteboul and Grumbach, 1988). Our main results concerning these languages are: • The classical equivalence between the domain-independent calculus and the algebra is valid in our model... |

7 |
An extension of relational algebra for summary tables
- Ozsoyoglu, Ozsoyoglu
- 1983
(Show Context)
Citation Context ...tual) tree. Thus, our languages can be applied to such models as well. Equivalence results of algebraic and calculus-based languages have been reported (Kuper and Vardi, 1984; Ozsoyoglu et al., 1987; =-=Ozsoyoglu and Ozsoyoglu, 1983-=-). The equivalence of relational algebra and calculus with aggregates was considered by Klug (1982), and extended by Ozsoyoglu and Ozsoyoglu (1983) to relations with set-valued attributes. A compariso... |

7 |
A database management system for document retrieval applications
- Macleod
- 1981
(Show Context)
Citation Context ...y recognized that this restriction imposes unacceptable constraints on the use of database technology in a variety of application domains such as engineering, computer aided design, or office systems =-=[40, 49, 50]-=-. Many models that incorporate more semantics into databases have been introduced and studied (see [7, 34]). In the mid 80's, a variety of models generalized the relational model by allowing hierarchi... |

6 |
Object identity as a query language
- Abiteboul, Kanellakis
- 1989
(Show Context)
Citation Context ...fted to semantic and particularly to object-oriented models that incorporate some of the features of the complex value models. (An extension of our model with object-oriented features can be found in =-=[8]-=-.) A variety of languages were proposed for these models, encompassing all known paradigms of query languages: algebraic, calculus-based, logic-programming oriented, and SQLextensions. The variety of ... |

6 |
On the expressive power of logic programming languages with sets
- Kuper
- 1988
(Show Context)
Citation Context ...between various proposals of logic programming with a set construct is in their approach to nesting: grouping in LDL [15], data functions in COL [3] and a form of universal quantification in [42]. In =-=[43]-=-, equivalence of various rule-based languages is proved. In [31], it is shown that various programming primitives are interchangeable: powerset, fixpoint, various iterators. As already mentioned, the ... |

3 |
An overview of database management technology
- Kobayashi
- 1980
(Show Context)
Citation Context ...tebou@db.stanford.edu; Catriel Beeri, Prof. Dr., is Full Professor, Department of Computer Science, The Hebrew University, Givat-Ram, Jerusalem 91904, Israel, beeri@huji.ac.il.s728 (Makinouchi, 1977; =-=Kobayashi, 1980-=-; Macleod, 1981). Many models that incorporate more semantics into databases have been introduced and studied (Abiteboul et al., 1994; Hull, 1986). In the mid-1980's, a variety of models generalized t... |