Dan Suciu and Limsoon Wong. On two forms of structural recursion. In LNCS 893: Proceedings of 5th International Conference on Database Theory, pages 111--124, Prague, January 1995. SpringerVerlag.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....object algebra must use the powerset operator, and thus requires exponential time and space in the intended semantics, while everybody knows a simple recursive algorithm which does it in quadratic time and quadratic space. Another example are two kinds of structural recursion of Suciu and Wong [SW], which, if added to the relational algebra for complex objects, represent precisely the same class of queries, but one of them appears to represent much better algorithms than the other does. 1.2 Reflective machines In this paper we want to discuss yet another example of the mismatch class of ....

D. Suciu and L. Wong, On two forms of structural recursion, in: G. Gottlob, M.Y. Vardi (eds.) Proc. ICDT'95, Lecture Notes in Computer Science No. 893, Springer Verlag, pp. 111--124.

....v in CPL are higher order because u and v can contain function types. This is different from the first order function types s t of NRC(bool ; in [3] Higher order function types are allowed in CPL for two reasons. To discuss these two reasons, I need some results obtained by Suciu and myself [20] on the two forms of structural recursion sri and sru. Let HNRC(bool ; sri) and HNRC(bool ; sru) respectively denote the language obtained by generalizing NRC(bool ; sri) and NRC(bool ; sru) to higher order function types. We showed that HNRC(bool ; sri) HNRC(bool ; sru) ....

....is also expressible using the first order languages. This result gives us the first reason for having higher order function types in CPL it makes many things more convenient but without making analysis of first order expressive power of CPL more complicated. Another result in the same paper [20] is that all uniform 8 implementations of sri in NRC(bool ; sru) are bound to be expensive while there are efficient uniform implementations of sri in HNRC(bool ; sru) This gives us the second reason for having higher order function types in CPL it allows the implementation of more ....

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Dan Suciu and Limsoon Wong. On two forms of structural recursion. In LNCS 893: Proceedings of 5th International Conference on Database Theory, pages 111--124, Prague, January 1995. SpringerVerlag.

....taking the big union of e 1 [o=x] over each o in the set e 2 . NRC (suitably extended) is implemented by the NRC Module of Kleisli and is the abstract counterpart of CPL, a la Wadler s equations relating monads and comprehensions[30] The expressive power of NRC and its extensions are studied in [28, 15, 19, 9, 29]. The impact of these and other theoretical results on the design of CPL and Kleisli is that CPL adopts NRC(Q , Delta, Gamma, Xi, P , Q ; as its core, while allowing for full fledged recursion and other operators to be imported easily as needed into the system. NRC(Q , ....

....= NONE 8 2 5 Higher Order Functions and Optimization Another idea that we have exploited in implementing Kleisli is the use of higher order functions. There are many advantages and conveniences of higher order functions, besides allowing the expression of better algorithms as discussed in [29]. We use the implementation of the Kleisli query optimizer module for illustration here. The optimizer consists of an extensible number of phases. Each phase is associated with a rule base and a rule application strategy. A large number of rule application strategies are supported. The more ....

D. Suciu and L. Wong. On two forms of structural recursion. In LNCS 893: Proc. 5th International Conference on Database Theory, pages 111--124, 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 ....

Dan Suciu and Limsoon Wong. On two forms of structural recursion. In Georg Gottlob and Moshe Y. Vardi, editors, Proceedings of the Fifth International Conference on Database Theory, number 893 in Lecture Notes in Computer Science, pages 111--124. Springer Verlag, January 1995.

....in query language theory, it has to enable generalization of existing results in query language theory, it has to facilitate practical implementation, it has to allow for good query optimization, and it has to enable new applications. The expressive power of NRC and its extensions are studied in [29, 15, 18, 8, 30]. These papers presented solutions to several open problems in query language theory. The most important of these results are directed at NRC( and NRC(Q , Delta, Gamma, Xi, P , Q ) The former is NRC augmented with equality test. The latter is NRC( further augmented with rational ....

....3. 3 Higher Order Functions and Optimization There is another very pleasant experience in implementing the optimizer for the Kleisli system that illustrates very well the many advantages and conveniences of higher order functions, besides allowing the expression of better algorithms as discussed in [30]. The optimizer consists of an extensible number of phases. Each phase is associated with a rule base and a rule application strategy. A large number of rule application strategies are supported. The more familiar include BottomUpOnce, which applies rules to rewrite an expression tree from leaves ....

D. Suciu and L. Wong. On two forms of structural recursion. ICDT, 5:111--124, 1995.

....of the form e 1 : T ; e 2 , which says that e 1 : T 1 and e 1 rewrites in one step to e 2 . The set of rules we have implements a deterministic callby name semantics. See [10, 7] for various ways of specifying operational semantics. A call by value operational semantics can also be given; see [18, 19]. We list the rules for evaluating coll set , coll bag , and coll list below and omit the rest. coll set (e 1 j x t 2 2 empty set;t 2 ) coll(set; t 1 ) empty set;t 1 coll bag (e 1 j x t 2 2 empty bag;t2 ) coll(bag; t 1 ) empty bag;t1 coll list (e 1 j x t 2 2 empty ....

D. Suciu and L. Wong. On two forms of structural recursion. In Proceedings of 5th International Conference on Database Theory, pages 111--124, Prague, January 1995.

....in query language theory, it has to facilitate practical implementation, it has to allow for good query optimization, and it has to enable new applications. The expressive power of NRC and its extensions are studied in (Suciu, 1997; Dong et al. 1997; Libkin Wong, 1997; Buneman et al. 1995; Suciu Wong, 1995). These papers presented solutions to several open problems in query language theory. The most important of these results are directed at NRC( and NRC(Q , Delta, Gamma, Xi, P , Q ) The former is NRC augmented with equality test. The latter is NRC( further augmented with ....

.... Higher Order Functions and Optimization There is another very pleasant experience in implementing the optimizer for the Kleisli system that illustrates very well the many advantages and conveniences of higher order functions, besides allowing the expression of better algorithms as discussed in (Suciu Wong, 1995). The optimizer (Wong, 1995c) consists of an extensible number of phases. Each phase is associated with a rule base and a rule application strategy. A large number of rule application strategies are supported. The more familiar include BottomUpOnce, which applies rules to rewrite an expression ....

Suciu, D., & Wong, L. (1995). On two forms of structural recursion. Pages 111--124 of: LNCS 893: Proceedings of 5th International Conference on Database Theory. Prague: Springer-Verlag.

.... we consider only sr comb and what can be from it, then our definitions and results further generalize to binary trees (by dropping the associativity requirement) hence to all the levels of Boom s hierarchy of types [43] 3 Using some higher order programming [8] or some exponential computations [56], one can also define sr add in terms of sr comb. Some identities Because initiality postulates unique homomorphisms and because the composition of two homomorphisms is also a homomorphism it follows immediately that if i is left commutative then sr add list (i; e) sr add bag (i; e) ffi ....

....exponential implementation in complex object algebra [1] 30] show how to encode related database languages in the simply typed lambda calculus. The possibility of treating arrays as collection types is suggested in [12] Connections with parallel complexity classes are studied in [53] [56] shows that, in the presence of suitable external functions, sr add set is strictly more expressive that sr comb set . 55] studies foundational issues concerning complex objects with queries over external functions. Acknowledgements. The authors thank Foto Afrati, Dirk Van Gucht, Leonid Libkin, ....

D. Suciu, L. Wong, On two forms of structural recursion, in "LNCS 893: Proceedings of 5th International Conference on Database Theory," 111--124, Prague, Czech Republic, January 1995.

....Computable Queries In the previous Section we offered examples of query languages L( Sigma) parameterized by some signature Sigma. By adding new language constructs we obtain more powerful query languages: e.g. we have NRA( Sigma) ae NRA( Sigma; dcr ) NRA( Sigma; loop) NRA( Sigma; sri) see [SW95]. For fix , we have, for Sigma = NRA(fix ) NRA(loop) while for certain Sigma, NRA( Sigma; fix ) 6 NRA( Sigma; loop) because, over total database, the former language can express partial queries, while the latter expresses only total queries. The question arises: when do we stop adding ....

Dan Suciu and Limsoon Wong. On two forms of structural recursion, January 1995.

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