L. Wong. Normal Forms and Conservative Properties for Query Languages over Collection Types. In PODS, Washington, D.C., May 1993.  Home/Search   Document Details and Download   Summary   Related Articles   Check

...., 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]. ....

L. Wong. Normal Forms and Conservative Properties for Query Languages over Collection Types. In Proceedings 12th ACM PODS (1993), pp. 26--36. 11

....The algebra considered here was introduced in [GM93] Various calculi for bags based on some of the operations of [GM93] were presented in [GMK93] and links with various weak arithmetics were established. The expressive power of languages for bags has been investigated in another setting in [Won93, LW93b, LW93a, LW94]. The paper is organized as follows. In the next section, we briefly present the main definitions. Section 3 is devoted to the algebra. In the following sections, we study the expressive power and the complexity of the algebra, when restricted to bags with one level of nesting (Section 4) two ....

....operator, nest. It was shown in [PG88, PG92] that, in the nested relation algebra with no powerset but a nest operation, the set nesting of intermediate types doesn t increase the expressive power of the algebra for relational queries. Conservative extension properties were shown to carry over [Won93] in a more general setting with sets, bags and lists for queries over nested inputs and outputs. In particular, it was shown that the use of intermediate types higher than the bag nesting of both the input and the output, doesn t increase the expressive power of the bag algebra without the ....

L. Wong. Normal form and conservative properties for query languages. In Proc. 12th ACM Symp. on Principles of Database Systems, 1993. 34

....the append representation is superior to the insertrepresentation when it comes to adding extra properties to the append constructor, such as commutativity and idempotence, to de ne bags and sets. Our normalization algorithm is in uenced by Wong s work on normalization of monad comprehensions [Wong 1993; Wong 1994] He presented some very powerful rules for attening nested comprehensions into canonical comprehension forms whose generators are over simple paths. These canonical forms are equivalent to our canonical forms for monoid comprehensions. His work, though, does not address query ....

Wong, L. 1993. Normal Forms and Conservative Properties for Query Languages over Collection Types. In Proceedings of the 12th ACM Symposium on Principles of Database Systems, Washington, DC (May 1993), pp. 26-36.

....the append representation is superior to the insert representation when it comes to adding extra properties to the append constructor, such as commutativity and idempotence, to de ne bags and sets. Our normalization algorithm is in uenced by Wong s work on normalization of monad comprehensions [Won93, Won94] He presented some very powerful rules for attening nested comprehensions into canonical comprehension forms whose generators are over simple paths. These canonical forms are equivalent to our canonical forms for monoid comprehensions. His work though does not address query unnesting for ....

L. Wong. Normal Forms and Conservative Properties for Query Languages over Collection Types. Proceedings of the 12th ACM Symposium on Principles of Database Systems, Washington, DC, pages 26-36, May 1993.

....Finally, if f is a function into Q, its values on a set X can be added up; that is, one can compute P x2X f(x) Note that if f is identically 1, then the above is the cardinality of X. It was proved in [34] that these features model the main features of SQL. Furthermore, extending a result from [47], a conservativity property was shown in [34] It says that nesting of sets is in a sense superfluous: every query from relational databases to relational databases in AGGRQ can be written in a way that does not use sets of sets. Nesting is essential for modeling grouping, and thus the ....

L. Wong. Normal forms and conservative properties for query languages over collection types. Journal of Computer and System Sciences 52 (1996), 495--505. Extended abstract in PODS 93. 32

....and the fixpoint semantics of our paper are very similar to those of [18, 19, 17] In [28, 29] it is shown how to integrate (flat) finite sets in logic programming with the idea of database applications. Sets and other collection types were also considered in the database related papers [6, 5, 34, 20, 44, 38]. Those papers study the expressive power and practical applications of languages with collection types. Bounded quantification over hereditarily finite sets is introduced in [14] In that paper sets are added to logic programming using a special set unification algorithm. In [4, 3] a limited ....

L. Wong. Normal forms and conservative properties for query languages over collection types. In ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 26--36, 1993. 30

....NRA(powerset) can obviously express exponential queries. More interestingly, NRA(powerset) can express PTIME queries, which are not expressible in NRA: Abiteboul and Beeri prove in [AB88] that transitive closure can be expressed in NRA(powerset) In contrast, we know from Paredaens [PG92] and Wong [Won93], that transitive closure is not expressible in NRA. But the obvious way of expressing transitive closure in NRA(powerset) is through an exponential space query. We prove in the following that exponential space is indeed needed. 3 The Complexity of Evaluation in NRA(powerset) In order to define ....

Limsoon Wong. Normal forms and conservative properties for query languages over collection types. In Proceedings of 12th ACM Symposium on Principles of Database Systems, pages 26--36, Washington, D. C., May 1993. See also UPenn Technical Report MS-CIS-92-59. 9

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L. Wong. Normal forms and conservative properties for query languages over collection types. In Proceedings of 12th ACM Symposium on Principles of Database Systems, pages 26--36, Washington, D. C., May 1993.

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L. Wong, Normal forms and conservative properties for query languages over collection types, JCSS 52 (1996), 495--505. This article was processed using the L A T E X macro package with LLNCS style

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L. Wong, Normal forms and conservative properties for query languages over collection types, Journal of Computer and System Sciences, 52(3):495--505, 1996. 32

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L. Wong, Normal forms and conservative properties for query languages over collection types, in "Proceedings of 12th ACM Symposium on Principles of Database Systems," Washington D. C., May 1993.

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L. Wong. Normal forms and conservative properties for query languages over collection types. In Proc. of the 12th Symposium on Principles of Database Systems, Washington, DC, May 1993, pages 26--36. 8

....of [5] coded Boolean values as elements of type funitg, where unit is a type having one value. We code Booleans as 0 and 1, but it does not affect expressiveness, see [34] The flat fragment of the language, without aggregation, has the power of the relational algebra, that is, first order logic [44]. When the standard arithmetic and the aggregate are added, the language becomes powerful enough to code standard SQL aggregation features such as the GROUPBY and HAVING clauses, and aggregate functions such as TOTAL, COUNT, AVG, MIN, MAX, present in all commercial versions of SQL [41] This ....

L. Wong. Normal forms and conservative properties for query languages over collection types. Journal of Computer and System Sciences 52(1):495--505, June 1996.

....eq, geq, fit) where lt(i) m I m M, m) i L leq(i) m IraM, geq(i) m I m M,I(m) i , and gt(i) m I m M,I(m) i . See also CO, COBag, and COList. See [3] for the theory of structural recursion. See [2] for some clever examples of programming with structural recursion. See [4, 19, 18] for the monad view of sets. 66 15 COUnit structure COU nit Routines for manipulating the unique object of CPL type unit. val Mk : unit val Km : unit unit Mk The unique object of CPL type unit. Return the ML value ( Assume M is the unique object of CPL type unit. See also ....

Limsoon Wong. Normal forms and conservative properties for query languages over collection types. Journal of Computer and System Sciences, ???(???):???-???, ??? To appear. 227

....of [5] coded Boolean values as elements of type funitg, where unit is a type having one value. We code Booleans as 0 and 1, but it does not affect expressiveness, see [34] The flat fragment of the language, without aggregation, has the power of the relational algebra, that is, first order logic [44]. When the standard arithmetic and the P aggregate are added, the language becomes powerful enough to code standard SQL aggregation features such as the GROUPBY and HAVING clauses, and aggregate functions such as TOTAL, COUNT, AVG, MIN, MAX, present in all commercial versions of SQL [41] This ....

L. Wong. Normal forms and conservative properties for query languages over collection types. Journal of Computer and System Sciences 52(1):495--505, June 1996.

....we need to describe the representation of CPL queries in SML, the host programming language of Kleisli. While CPL uses the comprehension syntax [6] as its surface syntax, its internal representation is based on the nested relational calculus derived from the categorical notion of a monad [7, 27]. 3.1 Query Representation The actual implementation of the representation of CPL queries in SML is given below. We omit bags, lists, variants, and a few other constructs as they are not needed for the purpose of this report. Consult the Kleisli Query System Reference Manual [30] for full ....

....llExtSet, and lllExtSet constructors indirectly represent the comprehension construct in CPL. The actual meaning of ExtSet(N; x; M) is the set f(o 1 ) Delta Delta Delta [ f(o n ) where f(x) N and fo 1 ; o n g = M . This representation is based on viewing sets as a monad; see [27, 7]. We discuss its virtue in Subsection 3.2. lExtSet, llExtSet, and lllExtSet have exactly the same denotational meaning as ExtSet, but with slightly different operational behaviours. Note that the UnionSet constructor also comes in the same four flavours as ExtSet. We omit them in this report. We ....

[Article contains additional citation context not shown here]

Limsoon Wong. Normal forms and conservative properties for query languages over collection types. Journal of Computer and System Sciences, ???(???):???--???, ??? To appear.

....of [3] coded Boolean values as elements of type funitg, where unit is a type having one value. We code Booleans as 0 and 1, but it does not affect expressiveness, see [25] The flat fragment of the language, without aggregation, has the power of the relational algebra, that is, first order logic [34]. When the standard arithmetic and the P aggregate are added, the language becomes powerful enough to code standard SQL aggregation features such as the GROUPBY and HAVING clauses, and aggregate functions such as TOTAL, COUNT, AVG, MIN, MAX, present in all commercial versions of SQL [32] This ....

L. Wong. Normal forms and conservative properties for query languages over collection types. JCSS 52(1):495-- 505, June 1996. 10

.... N, where f : t N, with semantics P [f ] fx 1 ; x n g) f(x 1 ) f(x n ) The language NRL obtained from NRL nat by removing the arithmetic operations is equivalent to the nested relational algebra, which is a generalization of 6 relational algebra to complex objects (cf. [13, 16]) According to [11] for any boolean query q of type fb Theta bg bool in NRL nat , there exists a number k such that for any l 1 , l 2 k and any two cycles C 1 and C 2 of length l 1 and l 2 respectively, q(C 1 ) q(C 2 ) Thus, NRL nat cannot define a query that is equivalent to ....

....to the first order case. So far, all inexpressibility results for the nested relational languages were proved in the following way. First, a conservativity result is established that shows that expressive power of the language is independent of the depth of set nesting in intermediate results (see [10, 13, 16] for examples of such results) Then the desired results are proved by reduction to the first order case, when no nested relations are allowed. For example, the flat fragment of the nested relational algebra is equivalent to the relational algebra [13, 16] Hence, recursive queries such as ....

[Article contains additional citation context not shown here]

L. Wong. Normal forms and conservative properties for query languages over collection types. In Proc. of the 12th Symposium on Principles of Database Systems, Washington, DC, May 1993, pages 26--36. 8

....of [3] coded Boolean values as elements of type funitg, where unit is a type having one value. We code Booleans as 0 and 1, but it does not a ect expressiveness, see [25] The at fragment of the language, without aggregation, has the power of the relational algebra, that is, rst order logic [34]. When the standard arithmetic and the P aggregate are added, the language becomes powerful enough to code standard SQL aggregation features such as the GROUPBY and HAVING clauses, and aggregate functions such as TOTAL, COUNT, AVG, MIN, MAX, present in all commercial versions of SQL [32] This ....

L. Wong. Normal forms and conservative properties for query languages over collection types. JCSS 52(1):495{ 505, June 1996. 10

....to the constraint model, other extensions of Codd s relational model have received much attention in the past few years. Among them are extensions to complex objects and bags. It is interesting to compare the addition of constraints with those extensions. Several conservativity results proved in [33, 20, 21] show that the addition of nested relations (as in complex objects) does not add relational expressive power. On the other hand, the addition of bags does add relational expressive power [9, 19, 22] In particular, parity test is definable using bags on ordered domains [19] Organization. Section ....

L. Wong. Normal form and conservative properties for query languages. In Proc. 12th ACM Symp. on Principles of Database Systems, 1993. 24

....to the graphical specification is then generated automatically by QUICK. The CPL engine comes with an optimizer which will automatically avoid materializing intermediate views Figure 5: All conditions added. as well as migrating joins, selections and projections on GDB to the remote server (see [15, 10, 2]) Therefore, QUICK only needs to generate queries that are clear and easy to understand. These queries will be automatically optimized when they are passed to the CPL engine. Step 4. Getting the result. The generated query can be executed with the click of a button. The result is returned in a ....

L. Wong. Normal Forms and Conservative Properties of Query Languages over Collection Types. PODS'93, 26--36.

....of tuples of base types) have height 1. Given an expression e, the height of e is defined as the maximal height of all types that appear in the typing derivation of e. For example, S f S ff(x; y)g j x 2 Rg j y 2 Sg is an expression of height 1 if both R and S are flat relations. It is known [26, 28] that when restricted to expressions of height 1, NRC( is equivalent to the usual relational algebra. We also write NRC( b ) when the equality test is restricted to base types b, B , and Q. We sometimes list the free variables in an expression in brackets like: e(R; x) As was mentioned, the ....

....b. Let e( R) be a relational query in NRC aggr . By Lemma 19, we can assume that e( R) has the form if P 1 ( R) then e 1 ( R) else if P d ( R) then e d ( R) else e d 1 ( R) where each e i ( R) is in NRC( b ) Since NRC( enjoys the conservative extension property [28], each e i can be defined in relational calculus. By Fact 1, every e i has some finite locality index r i . From this we immediately conclude that e has locality index max i r i . 2 From here, applying verbatim the proof of Theorem 9, we conclude Corollary20. Relational queries in NRC aggr ....

L. Wong, Normal forms and conservative properties for query languages over collection types, JCSS 52 (1996), 495--505. This article was processed using the L A T E X macro package with LLNCS style

No context found.

L. Wong. Normal Forms and Conservative Properties for Query Languages over Collection Types. In PODS, Washington, D.C., May 1993.

No context found.

L. Wong. Normal Forms and Conservative Properties for Query Languages over Collection Types. In PODS,Washington, D.C., May 1993.

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L. Wong. Normal forms and conservative properties for query languages over collection types. In Proc. ACM Symp. on Principles of Database Systems, pages 26--36, 1993.

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