Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 149:3--48, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and modifications of containment algorithms to consider semantics of class hierarchies were considered in [Cha92, LR96] However, containment and equivalence for query languages for complex objects have not been considered previously. Complex Objects Several query formalisms have been proposed [TF86, OOM87, Col93, BNTW95, AB95]. We consider the containment and equivalence problems for a certain subset of the Object Query Language, OQL [Cat94] which we call conjunctive idealized OQL, COQL. It is a generalization of conjunctive queries [Ull89] and also corresponds to natural fragments of other query languages for complex ....

....in the presence of empty sets is still open. 3 Complex Objects We start by briefly reviewing complex object values and query languages for complex objects. We consider a fragment of such languages, which we call conjunctive queries for complex objects. 3. 1 How we query them Following [AB95, BNTW95] we define complex objects recursively to be: 1) an atomic value d from an infinite domain D, or, 2) a record [A 1 : x 1 ; A k : x k ] where x 1 ; x k are complex objects, or, 3) a set fx 1 ; xn g where x 1 ; xn are complex objects. Complex objects are typed, ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 1995. To appear.

....data whose structure is not fully known. For example in the query above Ullman can be either the value of Y.author or of Y.author.lastname. UnQL The language UnQL (Unstructured Query Language) BDS95, BDHS96a] was derived from structural recursion, a construct introduced in [BBW92, BLS 94, BNTW95] for programming with sets, bags, and lists. For semistructured data structural recursion is particularly attractive because it can express both queries and transformations in the same formalisms. Here queries just return a subset of nodes from the input data, while transformations may a ....

Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 149:3--48, 1995.

....and prove that its range restricted fragment is equivalent to NRA with bounded fixpoints. Keywords: nested relational algebra, conservative extension, complex objects, fixpoints, indexes. 1 Introduction Several query languages for databases with complex objects have been studied in recent years [AGVW89, AK89, AB88, BNTW95, dB92, GV91, GF88, GG91, GG92, HS89, HS91, PG92]. A natural way of designing such a language is to extend first order logic to a logic for hereditary finite sets, and consider only domainindependent queries, like in the case of first order logic. Abiteboul and Beeri follow this path in [AB88] define safe queries, and show that the resulting ....

.... calculus (the resulting language is called the strictly safe calculus) This work was done while the author was at the University of Pennsylvania, and was partially supported by NSF Grant CCR 90 57570 Another way of designing query languages for complex objects is followed by Buneman et al. [BNTW95]. Based on an investigation of the primitives associated with the types occurring in complex objects, they develop a hierarchy of languages, one of which has the same expressive power as the algebra without powerset of [AB88] Following established tradition, they call this language the nested ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 1995. To appear.

....input and a scalar as an output, or (4) relations both as inputs and outputs. Instead of considering several cases we adopt a uniform approach by working in the context of complex objects, and replacing first order structures with higher order structures. The definitions below are consistent with [HS89, GV91, PG92, BBW92, BNTW95]. Definition 2.3 We define complex object types by the grammar t : d j t Theta : Theta t j ftg. Here d is a special symbol. For any set D and type t we define dom(t; D) to be: dom(d; D) def = D dom(t 1 Theta : Theta t n ; D) def = dom(t 1 ; D) Theta : Theta dom(t n ; ....

....u j ; v j are types. To emphasize the domains and codomains, we will write the signature as Sigma = fp 1 : u 1 v 1 ; p l : u l v l g, and call p 1 ; p l external function symbols. We define the Nested Relational Algebra over Sigma, NRA( Sigma) following the formalism in [BNTW95], as an algebra of functions. The constructs are given in Figure 1. For any database D = D; P 1 ; P l ; i.e. which has only external functions, no relations) every expression f : s t in the language NRA( Sigma) denotes a function f D : dom(s; D) dom(t; D) as described shortly. We ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 149:3--48, 1995.

....[15] and modifications of containment algorithms to consider semantics of class hierarchies were considered in [10, 30] However, containment and equivalence for query languages for complex objects have not been considered previously. Complex Objects Several query formalisms have been proposed [40, 33, 16, 7, 1]. We consider the containment and equivalence problems for a certain subset of the Object Query Language, OQL [9] which we call conjunctive idealized OQL, COQL. It is a generalization of conjunctive queries [41] and also corresponds to natural fragments of other query languages for complex ....

....in the presence of empty sets is still open. 3 Complex Objects We start by briefly reviewing complex object values and query languages for complex objects. We consider a fragment of such languages, which we call conjunctive queries for complex objects. 3. 1 How we query them: COQL Following [1, 7] we define complex objects recursively to be: 1) an atomic value d from an infinite domain D, or, 2) a record [A 1 : x 1 ; A k : x k ] where x 1 ; x k are complex objects, or, 3) a set fx 1 ; xn g where x 1 ; xn are complex objects. Complex objects are typed, ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 1995.

....syntax of functional programming. Moreover Trinder and Wadler [71] showed that an extension of comprehension can implement the (flat) relational calculus. Trinder and Watt [70, 76] have also sought after a uniform algebra for several different collection types. This was followed by work at Penn [14, 15, 77, 17, 48, 47, 68, 67] and elsewhere [29] NESL NESL is a powerful, general purpose parallel functional languages designed by Guy Blelloch [8] which comes with a high level definition of the parallel complexity. It is compiled into a Vector Random Access Machine (VRAM) by flattening nested parallelism and using ....

....LogP algorithms for the one to one and one to many monotone communications, and in Sec. 5.4 we report on some LogP simulation experiments. We conclude in Sec. 6 2 The Specification of CoPa We present here our language CoPa. The language is inspired by recent developments in query language [25, 17, 20] and adds a novel kind of recursion, map recursion. It is a monomorphic functional language, with emphasis on operations on collections, their combinations, and user defined external functions. The language is first order in its treatment of functions (functions cannot be arguments or results of ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 149:3--48, 1995.

....queries has emerged from several equivalent formalisms. Some of these formalisms are syntactically restricted higher order logics, others are algebraic languages, often called nested relational algebras, hence our statement above. In fact, we will use the family of query languages introduced in [BBW92, BNTW95] because it is semantically related to dcr (Section 2) dcr and (nested) relational algebra have meaning over any (nested) relational database. But, as with all known characterizations of query complexity classes below NP , we know how to capture the entire NC only over ordered databases. ....

....and Stemple ( IPS91] Theorem 7.8) They also note that dcr is in NC . As part of a larger group of researchers, we became interested in dcr because it fits into a natural hierarchy of query languages that share a common semantic basis, built around forms of structural recursion on collection types [BTS91, BTBN91, BBW92, BNTW95] (see Section 3) Theoretical studies of expressiveness, such as [Won93, LW94a, Suc94, LW94b, SW95] and the present paper help us with the choice and mix of primitives, as well as implementation strategies. In particular, dcr is at the core of a sub language for which we are currently seeking ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 1995. To appear.

....about UnQL. For example: Theorem 6.4 All queries expressible in UnCAL (and, hence, in UnQL) are defined on all cyclic structures and are computable in ptime. Finally, we end this subsection with a proof of Theorem 5.1: Proof: of Theorem 5. 1) Let NRA stand for the nested relational algebra [BNTW95] A quick way to introduce it is to notice that it extends the relational algebra (RA) with the operations nest and unnest. It is easy to show that UnQL can express all RA operators. unnest (T ) where T encodes a nested relation, say of type f[A : String ; B : f[C : String ]g]g can be expressed ....

Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 1995. To appear.

....values and dictionaries (finite functions) the latter allowing the representation of oodb schemas and queries. This is done by representing queries and constraints (dependencies) in CoDi 1 a language and equational theory that combines a treatment of dictionaries with our previous work [BBW92, BNTW95, LT97] on collections and aggregates using the theory of monads. While here we focus on set related queries, we show elsewhere 2 that the (full) CoDi collection, aggregation and dictionary primitives suffices for implementing the quasi totality of ODMG ODL OQL [Cat96] Using boolean aggregates, ....

....num (assume a symbolic completion of numbers with Sigma1) We will also use the abbreviation if [ff] B then E def = if B then E else null [ff] and to improve readability we will omit the ff s in generic contexts. As for expressive power (so far) note that BigU is the operation ext Phi of [BNTW95] shown there to have (with singleton and primitives for tuples and booleans) the expressive power of the relational algebra over flat relations and the expressive power of the nested relational algebra over complex objects. In CoDi membership is expressible with disjunction aggregation: ....

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Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of proramming with collection types. Theoretical Computer Science, 149:3--48, 1995.

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