A. Ohori. Semantics of types for database objects. Theoretical Computer Science, Vol. 76, pp. 53--91, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of the two method definitions in the formal system. BCC 96] gives some of the problems and solutions to multi methods. Our notion of giving only the difference was partly inspired by the notion of Mixin based inheritance [BC90] There are many works on the merge (join) operation on records ( Oho90] OB88] Wan89] HP91] which also inspired this work. ....

A. Ohori. Semantics of types for database objects. Theoretical Computer Science, Vol. 76, pp. 53--91, 1990.

....the special treatment of sets in Hilog so that direct access to deeply nested data and grouping using several rules recursively are allowed as well. However, these languages are all value based. They are lacking in its data modeling power compared to deductive object oriented database languages [2, 27, 28, 33, 34, 37, 39, 43, 59]. Besides, none of them are computationally complete so that all programming tasks can be performed in a single framework. They do not allow unknown values which are common in database applications. Finally, they require stratification with regard to sets and negation. Indeed, it is still an open ....

....Proceedings of the International Conference on Data Engineering, pages 264 271, Kobe, Japan, 1990. IEEE Computer Society. 26] W. Kiebling, H. Schmidt, W. Straub, and G. Dunzinger. DECLARE and SDS: Early efforts to commercialize deductive database technology. VLDB Journal, 3(2) 211 243, 1994. [27] M. Kifer, G. Lausen, and J. Wu. Logical foundations of object oriented and frame based languages. Journal of ACM, 42(4) 741 843, 1995. 28] M. Kifer and J. Wu. A logic for programming with complex objects. J. Computer and System Sciences, 47(1) 77 120, 1993. 29] Robert Kowalski. The early ....

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A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76(1):53--91, 1990.

....spread in several sources to obtain a comprehensive description of the object. In the past several years, a sub problem, that is, integrating data with partial and complete tuples and or partial sets, has been investigated in depth in the context of relational and complex object databases [5, 7, 11, 14, 20, 21, 22, 28, 29, 30, 31, 39, 40]. Specific operators such as union [5] and join [7] are introduced to integrate partial information. However, these works focus on typed data and support homogeneous sets and tuples. Thus, it is difficult to apply them directly on semistructured data, where although the data may have some ....

....data which have been represented in our framework. We propose a new operator integration for this purpose and discuss its semantic properties. 1. 1 Related Work There has been a lot of work on the integration of heterogeneous data sources, such as multiple databases or data sources on the web [5, 7, 14, 20, 21, 22, 23, 28, 29, 30, 31, 37, 39, 40, 10]. In particular, there are two questions closely related to our study. One is how to decide that two objects mentioned in two different sources refer to the same entity in the world. Another is how to reconcile partial or inconsistent data values from sources referring to the same entity. Most ....

A. Ohori. Semantics of Types for Database Objects. Theoretical Computer Science, 76(1):53--91, 1990.

.... ( Gun92, Smy78, Plo76] Hoare) X v [ B , 8x 2 X9y 2 Y : x y (Smyth) X v ] Y , 8y 2 Y 9x 2 Y : x y (Plotkin) X v Y , X v [ Y and X v ] Y All of them have been used for databases with partial information: the Hoare ordering in [Bis81, IL84, Lib91] the Smyth ordering in [BJO91, Oho90] the 10 Plotkin ordering in [PS93] However, none of these papers addressed the question whether the chosen ordering is appropriate for the intended semantics of collections. Choosing the right orderings is the main purpose of this subsection. Our main claims are summarized in the table below. ....

A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76(1):53--91, 1990.

.... would complicate the application mechanism (though desirable in some cases [AH87] we feel that simplicity of the overall conception dominates) Since type constructors may be nested we achieve type completeness [AB87, ABC 2 M84] For a detailed description of types and constructors, see [oho90] In the following we show how all the previous ideas can be turned into a concrete DBPL. Therefore, the different concepts of the applicative database programming language ADAPLAN are presented by giving several examples. The language provides schema, update, and query operations and furthermore ....

OHORI, A.: Semantics of Types for Database Objects, Theoretical Computer Science, Vol. 76, No.1, 1990, pp. 53-93.

....investigating the problem of schema merging for this model we can understand how to merge schemas in these other models. However, as it stands, the model is not sophisticated enough to represent the variants and set valued attributes occurring in certain models such as those proposed in [10] and [11], and would Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Qs XXXXXXXXXX Xz H H H H H H H H H Hj S S S S S S S S S S S Sw Q Q Q Q Q Qs Q Q Q Q Q Qs Z Z Z Z Z Z Z Z Z Z Z B B B B B B B BN Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z ....

A. Ohori, "Semantics of Types for Database Objects, " Theoretical Computer Science, vol. 76, pp. 53--91, 1990.

....according to the definition given in Section 2, then this upper bound is the least one. Theorem 8. Given a set of instances I = fI 1 ; I n g of type oe, I is rich for oe iff oe = lub(I) 3 Similar orderings for database types have been used also in other frameworks; see, for example, Oho90] This result shows that solving the schema finding problem amounts to computing the least upper bound of a set of instances according to the template subsumption relation. However, we are not dealing with abstract objects, but with strings that encode them. We next show how to solve the ....

A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76(1):53--91, 1990.

....iterated rewriting of type symbols became possible [3] A.Ohori continued investigation of structural type systems (including labeled records, labeled disjoint unions, finite sets and recursion) as a proper generalization of the relational data model. Tractable type inference has been emphasized [15]. R.J.Peters introduced an object model with meet, join and product operations for type signatures intended for query type signature inference in course of object database access [16] R.Mili, A.Mili, R.Mittermeier considered structure of component repository as an information retrieval system. ....

Ohori A. Semantics of types for database objects. Theoretical Computer Science, 76, 1990, p. 53 - 91

....does not present the full syntax of TM, but instead presents significant examples to illustrate the main features of the model. The language TM is not unique in that it is based on a formal theory; other notable examples are IQL [AbKa89] Iris [LyVi87] LIFE [Ait K86] Logres [CCCT90] Machiavelli [OhBB89,Ohor90], and F logic [KiLa89] However, we know of no other language that is formally capable of dealing with arbitrary set expressions and (their) powertypes (or set types) in the context of subtyping and multiple inheritance. In fact, TM is a syntactically sugared version of its underlying Formal ....

....issues are, of course, important, but (solely due to reasons of lack of space) we refer the interested reader to the last two articles mentioned above for a full treatment of the semantical part of our theory. For readers interested in other issues regarding subtyping in type theory we refer to [CaWe85,FuMi88,KiLa89,Ohor90,Stan88,Wand87]. 3.1 Cardelli type theory In this section we give a brief summary of the system described in [Card84,Card88] Full details of syntactical and proof theoretical aspects can be found in the technical report. 3.1.1 Expressions and Types Types in our version of the Cardelli system are either 1. ....

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A. Ohori, "Semantics of types for database objects," Theoretical Computer Science 76 (October, 1990), 53--92.

....complex attribute values. The attribute values can be changed but such changes have no effect on the object s identity. Classes can have subclasses and attributes defined on superclasses are inherited by subclasses. Subclasses of a class must be declared explicitly. In complex object data models [7, 9, 22], objects are represented by structured values such as nested tuples and sets. There isn t a notion of object identity. Instances and subclasses of classes are inferred rather than asserted. On the other hand, deductive query languages such as Datalog [10] extend the expressive power of ....

A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76:53--91, 1990.

....6 . As we stated before, we will often omit the word generalized . For example, r 1 ; r 2 ; r 3 defined above are generalized records and R = fr 1 ; r 2 ; r 3 g is a (generalized) relation. It is not hard to describe a type system using the given definition of database domains as it was done in [14, 15]. Suppose we have basic types 0 i whose domains of values D 0 i are exactly domains from B. Let L be a set of labels. Denote the domain of values of type by [ Then if 1 ; n 6 Therefore a generalized relation consists of objects of the same type as it is in the case of ....

A. Ohori. Semantics of types for database objects. 2nd International Conference on Database Theory, 1988.

....and use them to show that the merging process described in Section 3 respects such restrictions. In an unconstrained form, our schemas are similar to those of the functional data model ( 6, 8] though they are not sophisticated enough to interpret data models such as those proposed in [1] or [9], which incorporate constructors for variants. As we develop our data model, we will incorporate the idea of object identity, thus making it suitable for modeling the object oriented databases described in [10] Extending schemas with cardinality constraints If one of our schemas asserts that a ....

A. Ohori. Semantics of Types for Database Objects. Theoretical Computer Science, 76:53--91, 1990.

....data models. Consequently, despite its apparent simplicity, the generality of the model makes it a good candidate for schema merging. One should note, however, that further adornment of these graphs is needed to describe instances of sophisticated data models such as those proposed in [7] and [8], which contain constructors for sets and variants. A A A A AU Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi Phi oe oe ffl Delta Delta Delta Delta Delta Delta Delta Delta Delta Deltaff ffl S S S S S S S S S S Sw Gamma Gamma Gamma Gamma Gamma Gamma ....

A. Ohori, "Semantics of Types for Database Objects," Theoretical Computer Science, vol. 76, pp. 53--91, 1990.

....result type R when the operator is applied to operands of type O 1 and O 2 . last] first O 2 O 1 [first] salary] name g f f g [name age] R last] first] name age] name salary] c 2 c 1 g f [first Figure 2: The rproduct Greatest lower bound join The glbjoin operator is the join operator of [Ohori88], and can be considered as the complex version of the natural join from the relational model: the glbjoin joins two values if they have a part in common, and the common part is included into the result just once. For relations (sets of tuples of atomic values) the glbjoin is indeed natural join. ....

....of the operand set or list then has to be searched. Projection is realized by an expression like project [ E) If the type of the expression E is a subtype of the type the projection is well typed. The type of the expression E may be arbitrary. This is the project operator as defined in [Ohori88] which also can be defined in terms of application, field selection, and tuple denotations. An example of a projection is (see figure 4 for parameter and operand type) project [f[name: first:string] g] f[name= first= Joe ,last= Doe ] salary=21.000] ....

Ohori, A., "Semantics of Types for Database Objects", Proceedings International Conference on Database Theory, Lecture Notes in Computer Science 326, Bruges, Belgium, August 1988, pages 239-251.

....is how to obtain information as complete as possible from such a database. In other words, what is the intended semantics of such a database. In the past several years, a sub problem, that is, a database which contains partial and complete tuples and or partial sets, has been investigated in depth [4, 6, 9, 13, 14, 15, 19, 20, 21, 22, 27]. Specific operators such as union [4] and join [6] are introduced to integrate partial information. However, complete sets are not supported and all sets are treated simply as partial sets. Another sub problem, that is, a database which contains partial and complete sets and complete tuples, has ....

A. Ohori. Semantics of Types for Database Objects. Theoretical Computer Science, 76(1):53--91, 1990.

....most successful attempt so far is the language Machiavelli [OhBB89] where, for example, projection and join operations can be defined and the result types of operations be inferred. A key idea to achieve this is a generalization of the relational model by a partial order on tuple (or record) types [Oh88, OhB88]. Recently, the notion of kinds has also been used in [BuO91] to model subtyping; a kind describes all record types which have a given set of components (labels) this is related to the POWER[A] kind of [Ca88] There is also some work related to SOS on the algebraic specification side. In ....

Ohori, A., Semantics of Types for Database Objects. Proc. Int. Conf. on Database Theory 1988, 239-251.

....for which row variables may not be a suitable mechanism. It is possible to ACM Transactions on Programming Languages and Systems, 1995. A Polymorphic Record Calculus and Its Compilation 849 generalize the relational natural join operation to general record structures [Buneman et al. 1991; Ohori 1990] and to extend a polymorphic type system with the generalized natural join [Buneman and Ohori 1995; Ohori and Buneman 1988] However, we are not sure that such an operation should be in the polymorphic core of programming languages. The operations considered in this article support a wide range of ....

Ohori, A. 1990. Semantics of types for database objects. Theor. Comput. Sci. 76, 53-91.

....Age = 21] and [Name = Joe ; Sal = 30; 000] join to form [Name = Joe ; Age = 21; Sal = 30; 000] This can be regarded as a form of record concatenation [Wan89, HP91, Rem91] but can be generalized to arbitrary complex description terms to form natural join of complex database objects. In [BJO91, Oho90] we have achieved this by exploiting information orderings v and respectively on description terms and description types. d 1 v d 2 represents our intuition that d 2 is a better description than d 2 and 1 2 denotes the fact that the structure represented by 2 is more informative than ....

A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76:53-91, 1990.

....ffi . The intuition underlying their generalization is the idea exploited in [BJO91] that database objects are partial descriptions of real world entities and can be ordered by goodness of description. The polymorphic type system to represent these generalized operations has been developed in [Oho90] In what follows, we describe how equality, join and projection are generalized to acyclic description terms. For the treatment of cyclic structures as well as the precise semantics of the type system for descriptions, the reader is referred to [Oho90] We first consider join and equality. We ....

....generalized operations has been developed in [Oho90] In what follows, we describe how equality, join and projection are generalized to acyclic description terms. For the treatment of cyclic structures as well as the precise semantics of the type system for descriptions, the reader is referred to [Oho90] We first consider join and equality. We claim that join in the relational model is based on the underlying operation that computes a join of tuples. By regarding tuples as partial descriptions of real world entities, we can characterize it as a special case of very general operations on ....

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A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76:53--91, 1990. 48

....ML s severe restriction on functions manipulating records and mandatory requirement of recursive type declarations. Here we give an overview of the language with an emphasis on the features that are relevant to database programming. Formal properties underlying the language are described in [OB88, Oho88] 3.1 Types Let l range over a set of labels. The types of Machiavelli (ranged over by ) are represented by the following syntax: unit j int j bool j string j real j j [l : l : j hl : l : i j f g j ref( j rec v: v) l : l : represent ....

....are given the following polymorphic types. con : ffi 1 Theta ffi 2 ) bool if ffi 1 t ffi 2 exists join : ffi 1 Theta ffi 2 ) ffi 1 t ffi 2 if ffi 1 t ffi 2 exists project ffi : ffi 0 ffi if ffi ffi 0 For their precise typing rules and semantics, readers are referred to [OB88, Oho88] respectively. The following example shows how expressions involving join and projection are typed by using the information ordering on description types. val fun Join3(x,y,z) join(x,join(y,z) val Join3 = fn : a b c) d where d = a lub e, e = b lub c ....

A. Ohori. Semantics of types for database objects. In Proc. International Conference on Database Theory, Lecture Notes in Computer Science 326, pages 239--251, Bruges, Belgium, August 1988. Extended version to appear in a special issue of Theoretical Computer Science dedicated to 2 nd ICDT.

....P [ D) is a lattice, Lemma 14 For a domain D, the schemes in P [ D) are the singleton sets ffdgg where d 2 D 2 which means that functional dependencies in such a domian are rather trivial constraints. Another possibility is to consider sets as values ordered by v ] which is done in [12, 13, 29]. Smyth showed that [45] for any domain D, a domain P ] D) corresponding to the space of of sets of elements in D ordered by v ] called Smyth powerdomain of D, can be constructed. Under this approach, a natural join can be given coherent semantics. Again there are no non trivial schemes in ....

....of relations of different types. Our formalism cannot be directly applied to such a database. One way to overcome this limitation would be to develop a theory of the relationship between various domains and to extend our characterization of the relational databases to a family of domains. [29] proposed one such theory for join and projection and showed that a family of database domains can be integrated in an ML style type system. In [31] we have also shown that ML type inference method can be generalized to such an integrated type system. We further hope that the theory of functional ....

A. Ohori. Semantics of Types for Database Objects. In Proc. Internat. Conf. on Database Theory, Lecture Notes in Computer Science, Vol. 326 (Springer, Berlin, 1988), pages 239--251; Extended version submitted to a special issue of Theoret. Comput. Sci..

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A. Ohori. Semantics of types for database objects. Theoretical Computer Science, 76:53--91, 1990.

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Ohori, A., "Semantics of Types for Database Objects," Proceedings of the International Conference on Database Theory, LNCS 326, 1988.

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