H. Balsters and C. C. de Vreeze. A semantic of object-oriented sets. In Proc. of 3rd Intl. Workshop on Database Programming Languages, pages 187--200, Nafplion, Greece, August 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....sets of pairs, such that equality is decidable. Hence, we do not need to separate types with equality from those without equality, which would be necessary otherwise. 6 3.1. 1 Basic and Constructed Types Except for object types, our semantics of types and subtyping is quite usual and follows [3, 4, 14]: i.e. the denotations of basic types are given by the following equations: Definition Semantic Domain: fi i ] B i , in case that B i is a summand of V [ f g ] fx 2 S j x [ g 2 V [ 1 2 ] ff 2 F j x 2 [ 1 ] f(x) 2 [ 2 ] g 2 V: The subtype relationship ( is based ....

H. Balsters and C. C. de Vreeze. A semantic of object-oriented sets. In Proc. of 3rd Intl. Workshop on Database Programming Languages, pages 187--200, Nafplion, Greece, August 1991.

.... 2 ) Notice, however, that the sets X and F do not depend on the state. Thus, they are constant during the evaluation of expressions and update operations. 3.2. 3 Semantics of Type Expressions, Subtyping Except for object types, our semantics of types and subtyping is quite usual and follows [BdV91, BF91, MCB90] i.e. the denotations of basic types are given by the following equations: i ] B i , in case that B i is a summand of V [ f g ] fx 2 S j x [ g 2 V [ 1 2 ] ff 2 F j x 2 [ 1 ] f(x) 2 [ 2 ] g 2 V: The subtype relationship ( is based on ....

H. Balsters and C. C. de Vreeze. A semantic of object-oriented sets. In Proc. of 3rd Intl. Workshop on Database Programming Languages, pages 187--200, Nafplion, Greece, August 1991.

....as finite sets of pairs, such that equality is decidable. Hence, we do not need to separate types with equality from those without equality, which would be necessary otherwise. Basic and Constructed Types. Except for object types, our semantics of types and subtyping is quite usual and follows (Balsters and de Vreeze 1991, Balsters and Fokkinga 1991, Mannino, Choi and Batory 1990) i.e. the denotations ( of basic types are given by the following equations: Definition Semantic Domain: ffi i ] D i , in case that D i is a summand of V [ 1 2 ] ff 2 F j x 2 [ 1 ] f(x) 2 [ 2 ] g ....

Balsters, H. and de Vreeze, C. C.: 1991, A Semantics of Object-Oriented Sets, Intl. Workshop on Database Programming Languages, Nafplion, Greece, pp. 187--200.

....Our current solution to at least an important subset of the interoperability problems is to combine two existing formal languages, one to describe the database schema, the other to describe the way the database systems interact. TM is an object oriented (and type theoretic) data model [BaBZ91,BaVr91], that is theoretically well founded, and capable of expressing many, if not all, features of data models currently in use. LOTOS is a specification language [BoBr87,ISO87,VSSB91] that was designed for the formal description of distributed, concurrent systems. LOTOS is an ISO standard (ISO 8807) ....

....communicated, and the internal database actions or, in database terminology: transactions that coincide with the basic actions used above. 4 Monolithic Database Functionality For the description of the communicated data structures and of the local database schemata we use the language TM [BaVr91,ByBV92]. TM is a high level, object oriented database specification language. It is formally founded in the language FM, a typed lambda calculus allowing for subtyping and multiple inheritance, based on the ideas of [Card84,Card88] Characteristic features of TM are the distinction between types, classes ....

[Article contains additional citation context not shown here]

H. Balsters & C. C. de Vreeze, "A semantics of object-oriented sets," in The Third International Workshop on Database Programming Languages: Bulk Types & Persistent Data (DBPL--3), August 27--30, 1991, Nafplion, Greece, P. Kanellakis & J. W. Schmidt, eds., Morgan Kaufmann Publishers, San Mateo, CA, 1991, 201--217.

....= 0 is applied. 3 Nested TM Queries 3.1 General Description of TM In this section we describe the features of TM that are important for the purpose of this paper support for complex objects and the SELECT FROM WHERE construct. For a more comprehensive description of TM we refer the reader to [1, 2, 3]. TM is a high level, object oriented database specification language. It is formally founded in the language FM, a typed lambda calculus allowing for subtyping and multiple inheritance. Characteristic features of TM are the distinction between types, classes, and sorts, support for object ....

Balsters, H. and de Vreeze, C.C.: A Semantics of Object-Oriented Sets. Proceedings 3rd International Workshop on Database Programming Languages, Nafplion, Greece (1991)

....] P( where P(S) fX j X Sg. 2.2.2 Semantics of Expressions Correctly typed expressions are interpreted as elements of a set by induction on their types. This set is the interpreted associated type. The following list is not complete; the most interesting expressions are listed. See [BaFo88,BaVr91a,BaVr91b] for more on the semantics of expressions. ffl [ true] tt; f alse] ff ffl [ ha 1 = e 1 ; a n = e n i] is the total function from fa 1 ; a n g mapping each a i into [ e i ] ffl [ e except (a 1 = e 1 ; a n = e n ) is the total function from fa 1 ; a n ....

H. Balsters & C. C. de Vreeze, "A semantics of object-oriented sets," in The Third International Workshop on Database Programming Languages: Bulk Types & Persistent Data (DBPL--3), August 27--30, 1991, Nafplion, Greece, P. Kanellakis & J. W. Schmidt, eds., Morgan Kaufmann Publishers, San Mateo, CA, 1991, 201--217.

....as finite sets of pairs, such that equality is decidable. Hence, we do not need to separate types with equality from those without equality, which would be necessary otherwise. Basic and Constructed Types. Except for object types, our semantics of types and subtyping is quite usual and follows [BdV91, BF91, MCB90] i.e. the denotations of basic types are given by the following equations: Definition Semantic Domain: ffi i ] D i , in case that D i is a summand of V [ 1 2 ] ff 2 F j x 2 [ 1 ] f(x) 2 [ 2 ] g [ f g ] fx 2 S j x [ g [ ff gg ] ff jf : ....

H. Balsters and C. C. de Vreeze. A semantic of object-oriented sets. In Proc. of 3rd Intl. Workshop on Database Programming Languages, pages 187--200, Nafplion, Greece, August 1991.

....is described in Section 2. The formal theory of FM, which is based on the Cardelli type system [Card84] is described in more detail in Section 3. We refrain from offering denotational semantics for this extended Cardelli type system solely for lack of space; we refer the interested reader to [BaFo88,BaVr91,Vree89]. To define the mathematical meaning of TM in terms of FM we translate the structural concepts of TM into elements of FM where the mathematical meaning is precisely given. This translation is described in Section 4. 2 Motivation with examples We will demonstrate the new features of the TM ....

....boss =x) 2 Class constraints not involving two explicit quantifications are, for instance, those that use aggregate functions like sum, count, etc. 3 Formal language features The formal semantics of the TM language are based on those of FM, a formal model that is extensively described in [BaFo88,BaVr91,Vree89]. The semantics of TM is precisely determined by describing a mapping from TM expressions to FM expressions. This mapping is described in Section 4. Here, we focus on FM. FM is an extension of the theory described in [Card84,Card88] The extension consists of introducing set constructs and logical ....

[Article contains additional citation context not shown here]

H. Balsters & C. C. de Vreeze, "A Semantics of Object-Oriented Sets," 1991, To appear in: Proceedings of The Third International Workshop on Database Programming Languages (DBPL--3), August 27--30, 1991, Nafplion, Greece.

....FM. FM, in turn, is a language that is based on the ideas of Luca Cardelli [Card84,Card88] It can be seen as a strongly typed lambda calculus that allows for subtyping and multiple inheritance. Over the past four years the theory of FM has been developed by Balsters, Fokkinga, and de Vreeze [BaFo91,BaVr91,Vree89] to exploit the ideas of Cardelli and to augment the theory to make it one that is suitable for object oriented database specification. The language TM should be understood as a (rather heavily) syntactically sugared as not to say syruped version of FM, that gives a database modeller the full ....

....Originally, TM was conceived of as a sugared layer on top of its formal counterpart, the language FM. The FM language consists of a typed lambda calculus employing a notion of subtyping and is based on the well known ideas of Cardelli Wegner [CaWe85] type theory. The typing rules as defined in FM [BaFo91,BaVr91] could be used to type check a TM specification [BaBZ91,BaBV92] However, this would be a rather rough test, because apart from the types we also have a user defined ISA hierarchy in TM. In this ISA hierarchy it is for instance defined which methods are defined for a certain class or sort, hence ....

[Article contains additional citation context not shown here]

H. Balsters & C. C. de Vreeze, "A semantics of object-oriented sets," in The Third International Workshop on Database Programming Languages: Bulk Types & Persistent Data (DBPL--3), August 27--30, 1991, Nafplion, Greece, P. Kanellakis & J. W. Schmidt, eds., Morgan Kaufmann Publishers, San Mateo, CA, 1991, 201--217.

....a powerful specification and verification environment for object oriented databases with transactions and integrity constraints. The specification framework uses TM [6,7] a typed formal specification language based on the well known ideas of Cardelli [8] extended with logic formalism and sets [9]. The declarative flavour of this language permits compile time transaction verification using a theorem prover, while retaining ODMG compliancy [10] The verification framework uses higher order logic. Specifications in TM are automatically mapped to expressions in higher order logic (HOL) such ....

Herman Balsters & Chris C. de Vreeze, "A semantics of object-oriented sets," in The Third International Workshop on Database Programming Languages: Bulk Types & Persistent Data (DBPL--3), Aug. 27--30, 1991, Nafplion, Greece, Paris Kanellakis & Joachim W. Schmidt, eds., Morgan Kaufmann Publishers, San Mateo, CA, 1991, 201--217.

....by its support for various type constructors (record, variant, set and list) object identity, object sharing, structural and behavioural (multiple) inheritance, static type checkability, and a weak notion of encapsulation. We have reported on several matters relating to the theory [5] [6] and the use of the language [4] 14] in the past. A class (or sort) definition is constructed from three optional definition sections: a structure section in which, for instance, attributes can be defined, a constraint section in which constraints that restrict the possible structural values are ....

H. Balsters & C.C. de Vreeze, "A semantics of object-oriented sets", in The Third Int. Workshop on Database Programming Languages: Bulk Types & Persistent Data (DBPL-3), August 27-30, 1991, Nafplion, Greece, P. Kanellakis & J.W. Schmidt, eds., Morgan Kaufman Publishers, San Mateo, CA, 1991, pp. 201-217.

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