V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally Embedded Query Languages. In Proceedings 4th ICDT, pp. 140--154. LNCS 646, Springer Verlag, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a variety of semantics to express various fixpoint logics. In addition, extensions have been proposed to this framework to manipulate complex object databases, based on high order formulas over finite structures, e.g. 1, 2] The study of functional database query languages is more recent, see [6, 8, 7, 28], and is also part of the research on complex object databases. In [23] we showed that TLC (without additions, but with different I O conventions) can express exactly the ELEMENTARY database queries. The basic idea was to use the framework of finite model theory instead of Church numerals. In ....

....languages, see [31, 26, 33] Some progress on this is reported in [25] involving functional characterizations of other complexity classes, in particular PSPACE and EXPTIME. 2) Study optimal reduction strategies [36] in TLC. 3) Study languages that combine list iterators and set iterators ala [6, 8, 7, 28]. One consequence of the limitations of computing on Church numerals was a focus on the expressive power of typed calculi with more primitives and more complex type disciplines. Examples are the Girard Reynolds second order typed calculus or System F [18, 42] adding type polymorphism via type ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally Embedded Query Languages. In Proceedings 4th ICDT, pp. 140--154. LNCS 646, Springer Verlag, 1992.

...., with its emphasis on abstraction and on data types, might provide more insight into object oriented database problems. There is a growing body of work on functional query languages, from the early FQL language of [11] to the more recent work on structural recursion as a query language [8, 10, 9, 25, 39]. In this context, it is natural to ask: Is there a functional analog of the logical framework of first order and fixpoint formulas over finite structures In [21] we partly answered this question by computing on finite structures with the typed calculus. In this paper, we continue our ....

....as for higher orders, see [28, 22, 30] 3) Determine functional 9 characterizations of other complexity classes, in particular NP, PHIER and PSPACE, see [18, 23, 38, 5] 4) Study optimal reduction strategies [32] in the TLC. 5) Study languages that combine list iterators and set iterators ala [8, 10, 9, 25, 39]. ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally Embedded Query Languages. In Proceedings 4th ICDT, pp. 140--154. Lecture Notes in Computer Science 646, Springer Verlag, 1992.

.... concrete data model (e.g. relational, complex object) as it can be used with a variety of models, see [6, 19] Then we explain a data oriented paradigm for the query language design [7] This approach is based on incorporating operations naturally associated with datatypes into a query language [3]. To find such operations, it is necessary to describe the semantic domains of those datatype via universality properties. In section 3 we use the ordered semantics to give formal models of approximations and classify them. The main part of the paper is section 4 in which we show that most of the ....

....objects of a given type whereas the elimination operations are used for doing computations over them. For example, record formation is the introduction operation for records, and projections are the elimination operations. Databases work with various kinds of collections. One approach (cf. [3, 4]) to find the introduction and elimination operations for those collections is to look for operations naturally associated with them. To do so, one often characterizes the semantic domains of collection types via universality properties, which tell us what the introduction and the elimination ....

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V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In LNCS 646: Proc. ICDT, Berlin, Germany, October, 1992, pages 140--154. Springer-Verlag, October 92.

....and Monoid Comprehensions In this section we describe the syntax, semantics and implementation of C 3 monoids and monoid comprehension. The formal counterpart of C 3 monoid comprehensions is monoid comprehensions of [FM] which is a restricted version of monoid homomorphizms [BTBN, BTS, BTBW] written using the syntax of monad comprehensions [Wad] as is done by [BLS 94] We first review the formal definition of monoids and monoid comprehensions borrowing heavily from [FM] and [BW95] 3.1 Review of Monoid Comprehensions BAG f fc fc all file cabinets, fc color = ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In 4th International Conference on Database Theory.

....0 x Figure 1. The function bd. A complex value algebra, denoted ALG cv , is a functional language based on a small set of operations. An important subset of ALG cv , denoted N R A , is formed from the core operators of ALG cv by removing the powerset operator and adding the nest operator [6]. Let S = f f 1 ; f l g be a signature. N R A(S) is the nested relation algebra over S. In [17] Suciu proposed that all queries in N R A(S) are ef domain independent and continuous. We expect all em allowed queries expressed in CALC cv to be also ef domain independent and ....

V. Breazu-Tannen, P. Buneman and L. Wong. Naturally embedded query languages. In Proceedings of 4th International Conference on Database Theory, (LNCS 646), 1992, pages 140 - 154.

....level query. The language should support both. Now let us describe our approach to the language design. Our language is based on the functional paradigm. Design of functional database query languages has been studied extensively in the past few years and proved very useful. See, for example [2, 3, 18, 22, 26, 27]. Moreover, there are theoretical foundations for studying such languages [4, 11] Functional languages have certain advantages over logical languages for complex objects. They have clear syntax (there is no need, for example, to give complicated syntactic rules for range restriction, cf. 1] ....

....we have to deal with nested relations, or complex objects. The language we describe contains the nested relational algebra as a sublanguage. The standard presentations of the nested relational algebra [7, 24, 25] have a cumbersome syntax. Therefore, we have decided to follow the approach of [3], which gives a very clean and simple language that has precisely the expressive power of the nested relational algebra. The relational language introduced in [3] was based on earlier languages for lists [27, 28] and it was later generalized to other collection types [17, 18] The language ....

[Article contains additional citation context not shown here]

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In LNCS 646: Proc. ICDT-92, pages 140--154. Springer, October 92.

....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 ....

Val Breazu-Tannen, Peter Buneman, and Limsoon Wong. Naturally embedded query languages. In J. Biskup and R. Hull, editors, LNCS 646: Proceedings of 4th International Conference on Database Theory, Berlin, Germany, October, 1992, pages 140--154. Springer-Verlag, October 1992. Available as UPenn Technical Report MS-CIS-92-47.

....and on a few selected higher order operations. Both 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 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] It is shown there (in the spirit of [54] that for relational input and output, the monadic ....

.... of classical paradigms, such as the relational calculus and algebra, the monad based approach considers another important computational paradigm, namely the calculus, and shows that interesting and well designed query languages can be obtained from it by adding a few bulk type specific operations [19, 64]. These include the monadic algebra mentioned above, and also comprehensions, that can be viewed as a pure form of generalized SQL (the only paradigm not considered here) Finally, some nice recent works [33] also consider the calculus as a query language, but with an emphasis on the complexity ....

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Breazu-Tannen,V.,Buneman,P.and Wong, L. Naturally embedded query languages. to appear, ICDT 92.

.... hand, there has been a wide interest in languages for hierarchical data structures [KV84, TF86] The complexity and the expressive power of languages for nested relations have been extensively studied [KV88, HS91, PG92, GG92, AFS89, HS89, GV90, GV95] Collection types have been investigated in [BBN91, BTBW92], in connection with structural recursion. Nested bags, on the other hand had never been addressed. In this paper, we consider algebraic languages for manipulating nested bags, i.e. complex objects constructed by tuple and bag constructs) The algebra we present is a simple extension of the ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In Proc. of Intl. Conf. on Database Theory, pages 140--154. LNCS, Springer Verlag, 1992.

....but also as contractions. More precisely, we will apply it to prove: confluence and strong normalization for simple typed lambda calculus with expansive # and SP , also in the presence of terminal object and iteration confluence and strong normalization for the monadic calculus from [26] confluence for the polymorphic lambda calculus with expansive # and SP , also in the presence of algebraic term rewriting systems confluence for Girard s F # with expansive #, even with algebraic term rewriting systems confluence and strong normalization of the polymorphic ....

....quite easy to show that the previous systems stays confluent if we add a recursion operator. 5 The monadic calculus for database query languages This calculus, that arises from category theoretic considerations and forms the basis for an elegant database query language, was first introduced in [26]. An equivalent calculus NRC (see table 3)without these two last features has been proven confluent and strongly normalizing by Woong in his PhD thesis [28] It contains a subset of the simple typed lambda calculus we have seen above, as it provides a limited form of # reduction (arguments of ....

V. Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In 4th Int. Conf. on Database Theory, n. 646 in LNCS, 1992. Available as ftp://www.cis.upenn.edu/pub/papers/db-research/icdt92.dvi.Z.

....query. The language should support both. Now let us describe our approach to the language design. First, our language is based on the functional paradigm. Design of functional database query languages has been studied extensively in the past few years and proved very useful. See, for example [2, 3, 19, 23, 27, 28]. Moreover, there are theoretical foundations for studying such languages [4, 12] Functional languages have certain advantages over logical languages for complex objects. They have clear syntax (there is no need, for example, to give complicated syntactic rules for range restriction like in COL ....

....to deal with nested relations, or complex objects. The language we describe in this paper contains the nested relational algebra as a sublanguage. The standard presentations of the nested relational algebra [8, 25, 26] have a cumbersome syntax. Therefore, we have decided to follow the approach of [3], which gives a very clean and simple language that has 1 precisely the expressive power of the nested relational algebra. The relational language introduced in [3] was based on earlier languages for lists [28, 29] and it was later generalized to other collection types [18, 19] The language ....

[Article contains additional citation context not shown here]

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In LNCS 646: Proc. ICDT, Berlin, Germany, October, 1992, pages 140--154. Springer-Verlag, October 92.

....(i.e. fixed) set of operators. ffl query optimization can tolerate query representations that are larger (within reason) than the queries themselves because queries tend to be small (compared with functional programs for example) Still to write about: ffl Naturally Embedded Query Languages [BTBW92] ffl Complexity of Translations [JRSB85] 7.2 Comparing COKO with Query Rewrites of Rule Based Optimizers Many rule based systems (e.g. Loh88] FMS93] use rules to map algebraic operators to plan level implementations. This was the intended purpose of rules when first proposed ( Fre87] and ....

Val Breazu-Tannen, Peter Buneman, and Limsoon Wong. Naturally embedded query languages. In J. Biskup and R. Hull, editors, Database Theory - ICDT'92, 4th International Conference, volume 646 of LNCS. Springer Verlag, 1992.

....lists, but not sets. A similar language for sets is not known to us. We present a technique to relate sets and lists, and use it to transfer parametricity from lists to sets, for a restricted set of types, that is, however, sufficiently expressive to cover the languages for complex values in [1, 4, 5], powerset included. We give some examples to illustrate the potential relationship between genericity paramtericity and query optimization. We conclude with a discussion in Section 5. 2 Definitions, Notions of Genericity We assume that a database instance may be defined over a signature ....

....for optimizing queries defined in general declarative languages, and over user defined data types. This is a promising direction for future research. We point out that the L to S types are rich enough to capture the entire nested relational algebra. The core constructs of the monadic algebra of [5] can be expressed using only regular universal quantification and are thus fully generic. The addition of = to their algebra gives the full nested relational algebra, and now we have relgeneric queries w.r.t. injective mappings. Indeed their naturality theorem states that their language is ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In ICDT 1992. Springer-Verlag. LNCS 646.

.... these functions, namely the monoid homomorphisms from sets to sets, captures the nested relational algebra (since these homomorphisms are equivalent to the extension operator ext(f) for sets, which has been shown to be at least as expressive as the nested relational algebra [Buneman et al. 1995; Breazu Tannen et al. 1992]) But monoid homomorphisms go beyond that algebra to capture operations over multiple collection types, such as the join of a list with a bag returning a set, as well as predicates and aggregates. For example, an existential predicate over a set is a monoid homomorphism from the set monoid to the ....

Breazu-Tannen, V., Buneman, P., and Wong, L. 1992. Naturally Embedded Query Languages. In 4th International Conference on Database Theory, Berlin, Germany (Oct. 1992), Optimizing Object Queries Using an Eective Calculus
49 pp. 140-154. Springer-Verlag. LNCS 646.

....general. The fully generic queries can be viewed as the pure restructuring queries, which do not use any domain specific information whatsoever. Our candidate for a complete fully generic language presented in Section 2 is closely related to the elegant core nested relational algebra presented in [BBW92]. As shown in [BBW92] adding equality to this core language gives precisely the nested relational algebra. We feel that, in [BBW92] a key behind the elegant language design is the separation of the fully generic restructuring queries from the domain specific operations (such as equality, ....

....queries can be viewed as the pure restructuring queries, which do not use any domain specific information whatsoever. Our candidate for a complete fully generic language presented in Section 2 is closely related to the elegant core nested relational algebra presented in [BBW92] As shown in [BBW92], adding equality to this core language gives precisely the nested relational algebra. We feel that, in [BBW92] a key behind the elegant language design is the separation of the fully generic restructuring queries from the domain specific operations (such as equality, orderings etc. which are ....

[Article contains additional citation context not shown here]

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In Biskup and Hull, editors, International Conference on Database Theory, Berlin, Germany, October 1992. Springer-Verlag. LNCS 646.

....and whose main idea is that partiality is represented via orderings on objects. 2. We are not interested in semantics per se; the semantics that we define will help us find the right programming constructs for query languages for partial information. Our approach is based on [Car88, BBN91, BBW92, BLS 94] and its gist is that operations naturally associated with datatypes should be used as the basis for the language design. The word naturally has a precise mathematical meaning, and it has to do with the properties of semantic domains of the datatypes used. Thus, we can formulate ....

....and list some of the properties of semantic domains of collections which will be used for the language design. In Section 3 we develop the second idea which says that semantics suggests programming constructs. We start by explaining the approach to the language design based on [Car88, BBN91, BBW92, BLS 94] that suggests building lan7 guages for data around datatypes involved. Specifically, for each datatype constructor one needs introduction and elimination operations, and those can be obtained if one looks at the operations naturally in the categorical sense associated with the ....

[Article contains additional citation context not shown here]

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In J. Biskup and R. Hull, editors, LNCS 646: Proceedings of 4th International Conference on Database Theory, Berlin, Germany, October, 1992, pages 140--154. Springer-Verlag, October 1992.

.... subset of these functions, namely the monoid homomorphisms from sets to sets, captures the nested relational algebra (since these homomorphisms are equivalent to the extension operator ext(f) for sets, which has been shown to be at least as expressive as the nested relational algebra [BNTW95, BTBW92] But monoid homomorphisms go beyond that algebra to capture operations over multiple collection types, such as the join of a list with a bag returning a set, as well as predicates and aggregates. For example, an existential predicate over a set is a monoid homomorphism from the set monoid to ....

....more bulk operations an algebra supports, the more transformation rules it needs and, therefore, the harder the optimization task becomes. Our framework is based on monoid homomorphisms, which were rst introduced as an e ective way to capture database queries by Tannen, et al. BTBN91, BTS91, BTBW92] Their form of monoid homomorphism (also called structural recursion over the union presentation SRU) is more expressive than ours. Operations of the SRU form, though, require the validation of the associativity, commutativity, and idempotence properties of the monoid associated with the ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally Embedded Query Languages. In 4th International Conference on Database Theory, Berlin, Germany, pages 140-154. Springer-Verlag, October 1992. LNCS 646.

....OR SML supports both views of or sets and therefore can answer conceptual queries. The language design. Our language is based on the functional paradigm. Design of functional database query languages has been studied extensively in the past few years and proved very useful. See, for example [1, 2, 10, 11, 13, 16]. Functional languages have certain advantages over logical languages for complex objects. They have clear syntax, they can be typechecked, their semantics is generally easy to define and they allow a limited form of polymorphism. Since entries in databases are allowed to be or sets possibly ....

....we have to deal with nested relations, or complex objects. The language we describe contains the nested relational algebra as a sublanguage. The standard presentations of the nested relational algebra (cf. 15] have a cumbersome syntax. Therefore, we have decided to follow the approach of [2], which gives a very clean and simple language that has precisely the expressive power of the nested relational algebra. The language obtained from the nested relational algebra by adding appropriate primitives dealing with or sets was called or NRA in [10] One of the problems that should be ....

[Article contains additional citation context not shown here]

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In LNCS 646: Proc. ICDT-92, pages 140--154. Springer, October 92.

....result finds such a representation at type s where s is between t and hsk(t)i. To guarantee uniqueness, some restrictions on types must be imposed. We need a language to express the operations used for normalizing objects. We adopt the framework of [LW93a] which in turn is based on [BBW92] and finds its origins in [AB88, BBN91] The operators together with their most general types are given in figure 2. Recall briefly the semantics of the general and set operators. f ffi g is composition of functions; f; g) is pair formation. 1 and 2 are the first and the second projections. ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In LNCS 646: Proc. ICDT-92, pages 140--154.

....if the or object X is of type t. Ambient language and normalization theorems. Normalization theorems provide us with a list of operations that can be applied to an object until the normal form is produced. We need a language that contains these operations. We adopt the framework of [12] based on [2, 3]. The operators and their most general types are given in figure 4. Semantics. For general operations: f ffi g is function composition; f; g) is pair formation; 1 and 2 are the first and the second projections; always returns the unique element of type unit ; eq is equality test; id is the ....

....Extending the language In this section we show how a number of desirable normalization primitives mentioned in the Introduction can be obtained if apnorm cont is present in the language. We divide these primitives into four groups. It is known that there exists a calculus version of NBOA, see [3, 12], in which expressions denote objects and not functions. This equally expressive version of the language allows the standard if then else construct, as well as using abstraction to specify the function argument of b map and or map. In this section, we shall use both if then else construct and ....

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In Proceedings International Conference on Database Theory, 1992, Springer LNCS 646, pages 140--154.

....databases with incomplete and disjunctive information, and its application to querying HOL90 theories. Our language is based on the functional paradigm. Design of functional database query languages has been studied extensively in the past few years and proved very useful. See, for example [1, 2, 11, 14, 9]. Functional query languages have clear syntax, they can be typechecked, their semantics is generally easy to define and they allow a limited form of polymorphism. We believe that such a powerful and general query language will greatly facilitate the user in interactively finding useful theorems ....

....the nested relational algebra as a sublanguage. The nested relational algebra is a standard query language for database objects that freely combine values of base types, records and sets. Its standard presentations [4, 12, 13] have cumbersome syntax, so we have decided to follow the approach of [2] which gives a clean and simple language that has precisely the same expressive power. In order to represent disjunctive information in our query language, we added a new type constructor for or sets to the nested relational algebra. One of the problems addressed in the language is the difference ....

[Article contains additional citation context not shown here]

V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In LNCS 646: Proc. ICDT, Berlin, Germany, October, 1992, pages 140--

....a type B 6= A is needed, e.g. when collecting labels in a set; in that case we have: B = 2 A . Since the definition of aggregate does not have to take the adjacency structure of the map into account, we can use the well known aggregations of sets (Breazu Tannen et al. 1991; Erwig et al. 1991; Breazu Tannen et al. 1992; Fegaras et al. 1995) agg( f ; u;S) to denote the aggregation of a finite, non empty set by a binary function: agg( f ; u; u agg( f ; u;fag[S) f (a;agg( f ; u;S) Now we can define map aggregation as follows (recall that for p : A] we have s rng[p] fa 2A j fag2 rng(p)g) aggregate ....

Breazu-Tannen, V., Bunemann, P. and Wong, L. (1992). Naturally Embedded Query Languages. 4th Int. Conf. on Database Theory. LNCS 646. 140--154.

....B 6= A is needed, for example, when collecting labels in a set; in that case we have: B = 2 A . Since the definition of aggregate does not have to take the adjacency structure of the map into account, we can use the well known aggregations of sets (Breazu Tannen et al. 1991; Erwig et al. 1991; Breazu Tannen et al. 1992; Fegaras et al. 1995) agg( f ; u;S) to denote the aggregation of a finite, non empty set by a binary function: agg( f ; u; u agg( f ; u;fag [S) f (a;agg( f ; u;S) Now we can define map aggregation as follows (recall that for p : A] we have s rng[p] fa 2 A j fag 2 rng(p)g) ....

Breazu-Tannen, V., Bunemann, P. and Wong, L. (1992). Naturally Embedded Query Languages. 4th Int. Conf. on Database Theory. LNCS 646. 140--154.

....has the same expressive power as the algebra. NRA has essentially the same expressive power as Schek and Scholl s NF 2 relational algebra [SS86] as Thomas and Fischer s algebra [TF86] and as Paredaens and Van Gucht s nested algebra [PG88, PG92] In defining NRA, we follow the formalism in [BBW92]. The nested relational algebra NRA is a typed language. Its types are build from the following base types: B (the booleans) unit (the single valued type, unit = f( g) and N (the natural numbers) and are given then by the grammar: t : unit j B j N j t Theta t j ftg The values of the type ....

....algebra without powerset of [AB88] Proposition 2.1 The following operations are definable in NRA: the database projections, cartesian product, equality at all types, set difference, set intersection, set membership, set inclusion, selection over any predicate definable in NRA, nest, unnest. See [BBW92]. Now we consider a new primitive operation, the powerset: powerset : fsg ffsgg 2 and denote with NRA(powerset) the language NRA extended with powerset. While all queries expressible in NRA are in PTIME, NRA(powerset) can obviously express exponential queries. More interestingly, ....

Val Breazu-Tannen, Peter Buneman, and Limsoon Wong. Naturally embedded query languages. In J. Biskup and R. Hull, editors, LNCS 646: Proceedings of 4th International Conference on Database Theory, Berlin, Germany, October, 1992, pages 140--154. Springer-Verlag, October 1992. Available as UPenn Technical Report MSCIS -92-47.

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V. Breazu-Tannen, P. Buneman, and L. Wong. Naturally embedded query languages. In Proceedings of the International Conference on Database Theory (ICDT), pages 140-154, Berlin, Germany, October 1992.

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