## An Equational Chase for Path-Conjunctive Queries, Constraints, and Views (1999)

Venue: | In ICDT |

Citations: | 44 - 12 self |

### BibTeX

@INPROCEEDINGS{Popa99anequational,

author = {Lucian Popa and Val Tannen},

title = {An Equational Chase for Path-Conjunctive Queries, Constraints, and Views},

booktitle = {In ICDT},

year = {1999},

pages = {39--57}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider the class of path-conjunctive queries and constraints (dependencies) defined over complex values with dictionaries.

### Citations

1571 |
Foundations of Databases
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(Show Context)
Citation Context ...[YP82,Abi83], although in a different equational theory. Proposition 1 which in our framework is almost "for free" immediately implies an extension and generalization of the corresponding SP=-=C algebra [AHV95]-=- result of [KP82] (but not the SPCU algebra result). Due to the space restrictions, the proofs of the theorems stated here and some technical definitions are in the companion technical report [PT98]. ... |

997 | Mec[~a[~rs in the Architecture of Future Information Systems
- Wiederhold
- 1992
(Show Context)
Citation Context ...ow that some important classical results on containment, dependency implication, and chasing extend and generalize to this class. 1 Motivation We are interested in distributed, mediator-based systems =-=[Wie92]-=- with multiple layers of nodes implementing mediated views (unmaterialized or only partially materialized) that integrate heterogenous data sources. Most of the queries that flow between the nodes of ... |

466 |
Optimal implementation of conjunctive queries in relational data bases
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- 1977
(Show Context)
Citation Context ...s (EPCDs)) for which the methods illustrated in earlier sections are complete, and in certain cases decidable. Theorem 1 in section 4 extends and generalizes the containment decidability/NP result of =-=[CM77]-=-. Theorem 3 and corollary 1 in section 5 extend and generalize the corresponding results on the chase in [BV84]. Theorem 1 and theorem 3 also state that CoDi's equational axiomatization is complete fo... |

444 | The Theory of Relational Databases - Maier - 1983 |

336 | The Object Database Standard – ODMG-93 - Cattell - 1996 |

247 | On the decidability of query containment under constraints
- Calvanese, Lenzerini
- 1998
(Show Context)
Citation Context ...e queries [CGM88], containment under Datalog-expressible constraints and views [DS96], and containment of non-recursive Datalog queries with regular expression atoms under a rich class of constraints =-=[CGL98]-=-. We are not aware of any extension of the chase to complex values and oodb models. Hara and Davidson [HD98] provide a complete intrinsic axiomatization of generalized functional dependencies for comp... |

212 | Data Model and Query Evaluation in Global Information Systems - Levy, Srivastava, et al. - 1995 |

132 | Naturally Embedded Query Languages - Breazu-Tannen, Buneman, et al. - 1992 |

119 |
A proof procedure for data dependencies
- Beeri, Vardi
- 1984
(Show Context)
Citation Context ...th the constraint itself put in an equational form and with the (idemloop) law (see section 3). We shall also see that when restricted to the relational model, the method amounts exactly to the chase =-=[BV84]. Anyway, -=-chasing ABC DP with (INV1) gives select distinct struct(PN: s, DN: d.DName) from depts d, d.DProjs s, Proj p where s = p.PName and p.PDept = d.DName and p.CustName = "ABC" while chasing ABC ... |

115 | Testing Implications of Data Dependencies - Maier, Mendelzon, et al. - 1979 |

112 | Testing containment of conjunctive queries under functional and inclusion dependencies - Johnson, Klug - 1984 |

98 | Conjunctive query containment revisited - Chekuri, Rajaraman - 2000 |

80 | Equivalences among relational expressions - Aho, Sagiv, et al. - 1979 |

73 | Virtual schemas and bases
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- 1994
(Show Context)
Citation Context ...somewhat more general since there exist monads (trees for example) whose monad algebras are not monoids. The maps of [ALPR91], the treatment of object types in [BK93] and in [DHP97], that of views in =-=[dSDA94]-=-, and that of arrays in [LMW96] are related to our use of dictionaries. An important difference is made by the operations on dictionaries used here. The idea of representing constraints as equivalence... |

68 | J.D.: The theory of joins in relational databases - Aho, Beeri, et al. - 1979 |

66 | Towards an effective calculus for object query languages
- Fegaras, Maier
- 1995
(Show Context)
Citation Context ...s well as unnesting of the corresponding structures. 7 Related Work and Further Investigations Related work. The monad algebra approach to aggregates [LT95] is related to the monoid comprehensions of =-=[FM95b]-=- but it is somewhat more general since there exist monads (trees for example) whose monad algebras are not monoids. The maps of [ALPR91], the treatment of object types in [BK93] and in [DHP97], that o... |

66 | A query language for multidimensional arrays: design, implementation, and optimization techniques
- Libkin, Machlin, et al.
- 1996
(Show Context)
Citation Context ...e exist monads (trees for example) whose monad algebras are not monoids. The maps of [ALPR91], the treatment of object types in [BK93] and in [DHP97], that of views in [dSDA94], and that of arrays in =-=[LMW96]-=- are related to our use of dictionaries. An important difference is made by the operations on dictionaries used here. The idea of representing constraints as equivalences between boolean-valued (OQL a... |

50 | Polynomial-time implication problems for unary inclusion dependencies - Cosmadakis, Kanellakis, et al. - 1990 |

46 | An object-oriented query algebra - Shaw, Zdonik - 1989 |

45 | A methodology for query reformulation in CIS using semantic knowledge
- Florescu, Raschid, et al.
- 1996
(Show Context)
Citation Context ...ies. An important difference is made by the operations on dictionaries used here. The idea of representing constraints as equivalences between boolean-valued (OQL actually) queries already appears in =-=[FRV96]-=-. The equational theory of CoDi proves almost the entire variety of proposed algebraic query equivalences beginning with the standard relational algebraic ones, and including [SZ89a,SZ89b], [CD92,Clu9... |

41 | Deciding containment for queries with complex objects
- Levy, Suciu
(Show Context)
Citation Context ... within first-order logic using appropriate translations of queries and views. Since we deal with complex values (nested sets and records) and with oo classes, some kind of "flattening" enco=-=ding (eg. [LS97]-=-) would be necessary. Here we take the opposite approach, by translating constraints into a functional algebra, CoDi where queries and views are comfortably represented. We shall see that the fragment... |

35 | Interaction between path and type constraints
- Buneman, Fan, et al.
(Show Context)
Citation Context ...lex values and oodb models. Hara and Davidson [HD98] provide a complete intrinsic axiomatization of generalized functional dependencies for complex value schemas without empty sets. Fan and Weinstein =-=[FW98]-=- examine the un/decidability of logical implication for path constraints in various classes of oo-typed semistructured models. Further investigations. We conjecture that the simple type restriction ca... |

35 | Object-oriented queries: equivalence and optimization - Shaw, Zdonik - 1989 |

34 |
clauses and database dependencies
- Horn
- 1982
(Show Context)
Citation Context ...ry equivalence (and therefore containment via intersection). This generalizes the relational chase of [ABU79,MMS79,BV84] for conjunctive queries (with equality) [CM77,ASU79] and embedded dependencies =-=[Fag82]. In the same sectio-=-n we discuss composing dependencies with views. 3 From "Collections and Dictionaries" 4 "An OQL interface to the K2 system", by J. Crabtree, S. Harker, and V. Tannen, forthcoming.s... |

32 | Rule languages and internal algebras for rule-based optimizers
- Cherniak, Zdonik
- 1996
(Show Context)
Citation Context ... relational theory and a significant class of non-relational queries, constraints and views. A novel property of our approach, one that we hope to exploit in relation to rule-based optimization as in =-=[CZ96]-=-, is that optimizing under constraints or deriving other constraints can be done within the equational theory of our internal framework by rewriting with the constraints themselves. 1 In this paper, w... |

31 |
Embedded implicational dependencies and their inference problem
- CHANDRA, LEWIS, et al.
- 1981
(Show Context)
Citation Context ...the maximum height of a type in the schema. Therefore, the complexity of the chase decision procedure for full EPCDs is not worse than in the relational subcase [BV84] (recall also the lower bound of =-=[CLM81]-=-). For EGDs, which are always full, it is easy to see that the problem is actually in PTIME, as in the relational case. The chase with full EPCDs also enjoys the following nice properties: Theorem 5 (... |

20 |
Determining view dependencies using tableaux
- Klug, Price
- 1982
(Show Context)
Citation Context ...ough in a different equational theory. Proposition 1 which in our framework is almost "for free" immediately implies an extension and generalization of the corresponding SPC algebra [AHV95] =-=result of [KP82]-=- (but not the SPCU algebra result). Due to the space restrictions, the proofs of the theorems stated here and some technical definitions are in the companion technical report [PT98]. This report also ... |

20 | Subtree elimination algorithms in deductive databases - Saraiya - 1991 |

17 |
Conjunctive query containment with respect o views and constraints
- Dong, Su
- 1996
(Show Context)
Citation Context ...d algebra is reducible to the relational case. Other studies include semantic query optimization for unions of conjunctive queries [CGM88], containment under Datalog-expressible constraints and views =-=[DS96]-=-, and containment of non-recursive Datalog queries with regular expression atoms under a rich class of constraints [CGL98]. We are not aware of any extension of the chase to complex values and oodb mo... |

17 |
A calculus for collections and aggregates
- Lellahi, Tannen
- 1997
(Show Context)
Citation Context ...ates in CoDi as the equation All (p 2 Proj) All (d 2 domDept) if eq(p:PDept; d ! Dept:DName) then Some (s 2 d ! Dept:DProjs) eq(p:PName; s) = true 5 These generic notations are not ad-hoc. We show in =-=[LT97] that they-=- correspond to monad algebras which here are structures associated with the set monad and are "enriched" with a nullary operation.sLucian Popa, Val Tannen Expressing constraints this way wil... |

15 | Query interoperation among object-oriented and relational databases - Qian, Raschid - 1995 |

14 |
Design issues in a map language
- Atkinson, Lecluse, et al.
- 1991
(Show Context)
Citation Context ... to aggregates [LT95] is related to the monoid comprehensions of [FM95b] but it is somewhat more general since there exist monads (trees for example) whose monad algebras are not monoids. The maps of =-=[ALPR91]-=-, the treatment of object types in [BK93] and in [DHP97], that of views in [dSDA94], and that of arrays in [LMW96] are related to our use of dictionaries. An important difference is made by the operat... |

14 | An algebraic framework for physical oodb design - Fegaras, Maier - 1995 |

13 | Langages et Optimisation de requetes pour Systemes de Gestion de Base de donnees orienteobjet - Cluet - 1991 |

9 |
The verso algebra or how to answer queries with fewer joins
- Bidoit
- 1987
(Show Context)
Citation Context ...ral in other ways, by incorporating dictionaries and considering constraints. Containment of PC queries is in NP while a double exponential upper bound is provided for containment of COQL queries. In =-=[Bid87]-=- it is shown that containment of conjunctive queries for the Verso complex value model and algebra is reducible to the relational case. Other studies include semantic query optimization for unions of ... |

7 |
Principles of Programming with Collection Types
- Buneman, Naqvi, et al.
- 1995
(Show Context)
Citation Context ...n set. The syntax for tuples (records) is standard. We also use an equality test: eq(E 1 ; E 2 ) and boolean conjunction. 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 algeb... |

7 |
Foundations of semantic query optimization for deductive databases
- Charkravarthy, Grant, et al.
- 1988
(Show Context)
Citation Context ...ntainment of conjunctive queries for the Verso complex value model and algebra is reducible to the relational case. Other studies include semantic query optimization for unions of conjunctive queries =-=[CGM88]-=-, containment under Datalog-expressible constraints and views [DS96], and containment of non-recursive Datalog queries with regular expression atoms under a rich class of constraints [CGL98]. We are n... |

7 | Querying an object-oriented databases using cpl
- Davidson, Hara, et al.
- 1997
(Show Context)
Citation Context ...ions of [FM95b] but it is somewhat more general since there exist monads (trees for example) whose monad algebras are not monoids. The maps of [ALPR91], the treatment of object types in [BK93] and in =-=[DHP97]-=-, that of views in [dSDA94], and that of arrays in [LMW96] are related to our use of dictionaries. An important difference is made by the operations on dictionaries used here. The idea of representing... |

5 |
A general framework for the optimization of object oriented queries
- Cluet, Delobel
- 1992
(Show Context)
Citation Context ...nores intra- and inter-data source integrity constraints 1 . It has been recognized for some time that exploiting integrity constraints (so-called semantic optimization) plays a crucial role in oodbs =-=[CD92]-=- and in integrating heterogenous data sources [QR95,LSK95]. Relational database theory has studied extensively such issues [Mai83,Ull89,AHV95] but in the recent literature the use of constraints in op... |

3 |
Algebraic analogues to fundamental notions of query and dependency theory
- Abiteboul
- 1983
(Show Context)
Citation Context ...other important direction of work is allowing alternations of conditionals and BigU and trying to extend the result of [LS97] from weak equivalence to equivalence. The axiomatization of inclusions in =-=[Abi83]-=- can be soundly translated into CoDi's equational theory. We conjecture that CoDi is a conservative extension of this axiomatization. An interesting observation is that the equational chase does not r... |

3 | Chase and axioms for PC queries and dependencies
- Popa, Tannen
- 1998
(Show Context)
Citation Context ...ts like the ones we used in the examples in section 1 as equalities between boolean-valued queries. We also give the basic equational laws of CoDi while the rest of the axiomatization can be found in =-=[PT98]-=-. In section 3 we also show how that the transformations shown in section 1 correspond to precise rewrites in CoDi. This suggests the definition of a general notion of chase by rewriting, which connec... |

2 |
Inference rules for nested functional dependencies
- Davidson
- 1998
(Show Context)
Citation Context ...-recursive Datalog queries with regular expression atoms under a rich class of constraints [CGL98]. We are not aware of any extension of the chase to complex values and oodb models. Hara and Davidson =-=[HD98]-=- provide a complete intrinsic axiomatization of generalized functional dependencies for complex value schemas without empty sets. Fan and Weinstein [FW98] examine the un/decidability of logical implic... |

1 |
Enriched monads
- Lellahi, Tannen
- 1995
(Show Context)
Citation Context ...g of relations into nested sets or dictionaries, as well as unnesting of the corresponding structures. 7 Related Work and Further Investigations Related work. The monad algebra approach to aggregates =-=[LT95]-=- is related to the monoid comprehensions of [FM95b] but it is somewhat more general since there exist monads (trees for example) whose monad algebras are not monoids. The maps of [ALPR91], the treatme... |