T. Grust, M.H. Scholl, Translating OQL into Monoid Comprehensions----Stuck with Nested Loops? Technical Report 3a/  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a major advantage for two reasons. First it enables pattern matching; secondly, it reduces the number of transformation rules needed to deal with the repertoire of OQL operators. In spite of that, normalisation should be treated carefully, because it can sometimes hide optimization opportunities [GS96] Grust and Scholl map monoid comprehensions to a combinator algebra (including map, filter, cross, join, semijoin, antijoin and aggregation operators) The hybrid representation of monoid comprehensions and algebraic combinators is treated as pure syntactic sugar for a single basic recursion ....

T. Grust and M.H. Scholl. Translating OQL into monoid comprehensions --- stuck with nested loops? Technical report, University of Konstanz, Dept. of Mathematics and Computer Science, 1996.

.... (H; true if 9 0 2 dom(states H ) 0 ) otherwise ContainsTimestamp (H; false. For example, if the state sets of two histories H 1 and H 2 both with V = int, TimeIntervals and identical , are 1 = fh[1 6] 12i; h[9 11] 14ig and 2 = fh[5 10] 13i; h[13 20]; 15ig then ContainsTimestamp before(H 1 ; 9 10] true and ContainsTimestamp after(H 2 ; 21 22] false. In contrast to ContainsTimestamp which queries a history for a true false reply, FilterBySnapshot exemplifies operations that query histories for a reply that is itself a history. Given ....

....same timestamp but different snapshot. This is to satisfy the invariants that characterize histories. For example, using infix notation, if the state sets of two histories H 1 and H 2 are as exemplified above, then the state set of H = H 1 d H 2 is = fh[1 5] 12i; h[5 10] 13i; h[10 11] 14i; h[13 20]; 15ig. DeleteTimestamp takes a history H = hV; i and a timestamp of type and yields a new history H 0 = hV; 0 i. The operation maps into a state set 0 in which all states in whose timestamp 0 is such that common points( 0 ) is true, have been recomputed so ....

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T. Grust and M. H. Scholl. Translating OQL into Monoid Comprehensions---Stuck with Nested Loops? Technical Report 3a/1996 (Revised), Department of Mathematics and Computer Science, Konstanz, Germany, September 1996.

.... are popular among systems that adopt the functional data model, such as [30,33] The algebra underlying comprehensions has been the starting point for the theoretical studies of query languages [7,17] Its role as an internal representation language for the ODMG 93 OQL [9] is investigated in [19]. Object comprehensions differ from other dialects of comprehensions in that they are designed to be a user query language for object oriented databases [14] as opposed to just a vehicle for optimisation as in [30,19] or a notation for studying the theoretical foundation of query languages as in ....

.... as an internal representation language for the ODMG 93 OQL [9] is investigated in [19] Object comprehensions differ from other dialects of comprehensions in that they are designed to be a user query language for object oriented databases [14] as opposed to just a vehicle for optimisation as in [30,19] or a notation for studying the theoretical foundation of query languages as in [7,17] The design criteria adopted are thoroughly discussed in [15] A comparison of object comprehensions with ONTOS SQL [29] OSQL [24] O 2 SQL [3] ORION [21] EXCESS [8] OQL[C ] 6] CQL [16] and XSQL [20] ....

T. Grust and M.H. Scholl. Translating OQL into Monoid Comprehensions - Stuck with Nested Loops? Technical Report 03/1996, Department of Mathematics and Computer Science, University of Konstanz, Germany, March 1996.

....can) with user views, but may just result from analyzing the access statistics given in the transaction load. In CROQUE, the transformations between the logical and the physical database schemas are defined in a (formal) query language, a mixture of an object algebra and object calculus (see [GS96] for details of that language and the translation of ODMG OQL into it) The advantages of such a query language based mapping approach are that (i) there is no need for a specific storage structure description language, and more importantly, that (ii) user queries against the logical database ....

....(more precisely, a monoid comprehension) formal query language. WT91, Feg94, FM95a] discuss the monoid comprehension calculus, showing transformation properties and normalization algorithms, and [FM95b] presents a non orthogonal physical data model mapped to the monoid comprehension calculus. In [GS96] we give a complete formal translation from OQL 1.2 to the monoid comprehension calculus. We use both notations in the rest of this paper, OQL and monoid comprehensions, to describe storage layouts. GMS93] shows how to maintain views incrementally on base relations. Only flat relations are ....

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Torsten Grust and Marc H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report 3/1996, Department of Mathematics and Computer Science, Database Research Group, University of Konstanz, March 1996.

....some intuitions behind semantics; there are many possible ways of formalization. In [11] the intuitions were formalized through the so called monoid calculus. It is claimed that monoid comprehension calculus is an adequate framework to capture the semantics of OQL and other object query languages [12]. Our doubts concern features of ODMG 93 that seem to be outside the scope of this framework. They are the following. Comprehensions are still value oriented , not object oriented, because they do not deal with object identities. It is unclear how they can address relationships from the ....

T. Grust, M. Scholl. Translating OQL into Monoid Comprehensions - Stuck with Nested Loops? via www.informatik.uni-konstanz.de/Schriften, March 1996

....physical level leads to logical data independence and a very clear formal design of the evaluation process, which has not yet been realized in most object oriented database systems. In this way, extending the system for other logical constructs (e.g. different joins as proposed in [SAB94] and [GS96b] and more flexible storage structures (as developed in [GS96a] is possible independently. In a loop, the first dimension of the search space is spanned: the logical algebra expression is modified by algebraic rewriting. The results of this step have to be factorized and optimized again ....

....in a complete query evaluation process, will investigate the possibility to use the advantages of both the algebraic and calculus style in providing transformations of CROQUE OQL queries into mixed algebra calculus representations. The comprehension part of the hybrid approach is presented in [GS96b] Our project partner (University of Constance) currently implements different storage structures for object sets which will provide full data independence even in object oriented database systems. Acknowledgements: We would like to thank the anonymous referees of the DEXA 96 Conference for ....

T. Grust and Marc H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report 3/1996, Department of Mathematics and Computer Science, Database Research Group, University of Constance, March 1996.

....is more likely an interface language, where the evaluation problems are described on a different level. In fact, the EREQ project pursues quite similar goals as CROQUE. We, however, try to avoid the explosion of algebraic operators due to different collection types by using monoid comprehensions (Grust and Scholl 1996). ffl Among different SQL based extensions, XSQL (Kifer et al. 1992) uses Flogic (Kifer et al. 1993) to get a formal semantics. Therefore, the data model is more restricted than the ODMG approach, because the underlying data model only supports one level set values. On the other side, queries can ....

....on operations of different types. In contrast to the approach of this paper, the typing of the queries has to be done explicitly in the query expressions. Nevertheless, monoid comprehensions are rather useful to get a basis for OO query optimization and are also exploited in the CROQUE project (Grust and Scholl 1996, Grust, Kroger, Gluche, Heuer and Scholl 1997) Figure 1 An ODMG schema 3 THE DATA MODEL AND ODL This section presents the CROQUE approach to define a formal semantics of an OQL. We show the flavor of CROQUE and the differences to ODMG by the running example of the paper. The example database ....

Grust, T. and Scholl, M.: 1996, Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops?, Technical Report 3a/96, Dept. of Mathematics and Computer Science, University of Konstanz.

....makes OQL a suitable candidate for a language to define materialized views that may be incrementally updated in our model: for a view definition v oe f(v) we may code f using OQL. We shed some light on this now. How can one see that a reasonable subset of OQL indeed defines linear mappings [11,10] gave a translation of OQL into an algebra whose core is fold, a common iterator abstraction in functional programming languages. We borrow from this field and look at fold s definition in the monoid context. Let M = M ; Phi; zero[M] unit[M] and N = N ; Omega ; zero[N ] unit[N ] be ....

....resp. idempotent whenever Phi is. Note that fold[N ; f ] 2 hom M N , as one can see from (1) and (3) Fold s recursion scheme is sufficiently general to be able to compute all linear OQL clauses that represent linear functions. Due to space constraints we can merely provide examples here. [11] gives a comprehensive treatment. Suppose it is our task to sum the elements of the list [1; 2; 3] We can do so by applying fold[sum; id] to the list (remember that merge[sum] and zero[sum] 0) fold[sum; id] 1; 2; 3] fold[sum; id] 1] fold[sum; id] 2; 3] id(1) fold[sum; ....

Torsten Grust and Marc H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report 3a/1996, Department of Mathematics and Computer Science, Database Research Group, University of Konstanz, September 1996.

....as a Target for OQL Translation Since ODMG OQL [Cat95] is in fact a calculus based language (as SQL is as well) and due to the fact that the collection types OQL can query are monoids, the mapping turns out to be simple. Let us only give an idea here how such a translation can be accomplished. [GS96b] gives a complete translation of OQL 1.2 to the monoid calculus. OQL s select from where block is equivalently translated into select E from E 1 as x 1 , En as xn where E f 7 ffE j x 1 E 1 ; xn En ; E f gg with E i being collection valued OQL expressions, and E f denoting ....

Torsten Grust and Marc H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report 3/1996, Department of Mathematics and Computer Science, Database Research Group, University of Konstanz, March 1996.

....on operations of different types. In contrast to the approach of this paper, the typing of the queries has to be done explicitly in the query expressions. Nevertheless, monoid comprehensions are rather useful to get a base for OO query optimization and are also exploited in the CROQUE project [GS96] 5 Conclusion and further research We presented a framework how the ODMG model can be treated formally using a well defined type system and the notions of the object lattice. We formalized ODMG OQL in this context. Additionally, our type system allowed us to extend ODMG OQL for cast and set ....

T. Grust and M.H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report, University of Konstanz, 1996.

....often can) with user views, but may just result from analyzing the access statistics given in the transaction load. In CROQUE, the transformations between the logical and the physical database schemas are defined in a (formal) query language, a mixture of an object algebra and object calculus (see [GS96b] for details of that language and the translation of ODMG OQL into it) The advantages of such a query language based mapping approach are that (i) there is no need for a specific storage structure description language, and more importantly, that (ii) user queries against the logical database ....

Torsten Grust and Marc H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report 3/1996, Department of Mathematics and Computer Science, Database Research Group, University of Konstanz, March 1996.

....the corresponding generalization of set comprehensions or ZF expressions. The homomorphisms provide us with a semantically clean way to reason about queries that involve multiple collection and scalar types since the range and destination monoids of these mappings may not be the same [8,10]. In the monoid comprehension Mff j q 1 ; q n g the qualifiers q i are either generators of the form e E or predicates p. A generator q i sequentially binds variable e to the elements of its range E; e is bound in q i 1 ; q n and f . The binding of e is propagated until a ....

....] e 1 ; e 2 ) f(e 1 ) Phi fold[ Phi; f ] e 2 ) These three equations reflect the way of how values are constructed by the calculus, namely by the application of zero[M] unit[M] and merge[M] exclusively. In fact, one can show that fold s expressiveness is sufficient to capture OQL. In [10] we actually gave a complete mapping of OQL to the monoid comprehension calculus. Summing things up, what we gain with the monoid calculus is (1) the necessary expressive power to capture OQL like languages, 2) a uniform and extensible way of manipulating values of diverse collection types, 3) a ....

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Torsten Grust and Marc H. Scholl. Translating OQL into Monoid Comprehensions --- Stuck with Nested Loops? Technical Report 3a/1996, Department of Mathematics and Computer Science, Database Research Group, University of Konstanz, September 1996.

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T. Grust, M.H. Scholl, Translating OQL into Monoid Comprehensions----Stuck with Nested Loops? Technical Report 3a/

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T. Grust and M. H. Scholl. Translating OQL into Monoid Comprehensions---Stuck with Nested Loops? Technical Report 3a/1996.

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