D. A. Watt, P. Trinder, "Towards a theory of bulk types," Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[52] Wadler [75] showed that they are also useful in organizing syntax, in particular they explain the list comprehension 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 ....

David A. Watt and Phil Trinder. Towards a theory of bulk types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

....for a list instead of a set. Recently, list comprehensions have been generalised to collection comprehensions, which provides a uniform and extensible notation for expressing and optimising queries over many collection classes including sets, bags, lists, trees, ordered sets, and so forth [WT91] The most significant benefit is that, although each primitive operation will require a separate definition for each collection class, only one query notation is needed for all these collection classes; besides, a single definition is all that is required for higher level operations defined in ....

....designing algebras for data models is to use them as vehicles for query optimisation in systems supporting high level interfaces such as query languages. A large number of algebras have been proposed for data models richer than the relational model [Osb88, Day89, CDLR89, SZ89, SO90, VD90, DD91, WT91, Van92, Alh92, Nor92, AB93, Mit93, GM93, LW93] Many of these algebras extend the relational algebra to manipulate richer modelling constructs and object identifiers as well as to provide more expressive and computational powers. Others take a fundamentally different approach and draw on the ....

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D. Watt and P.W. Trinder. Towards a Theory of Bulk Types. Technical Report FIDE/91/26, University of Glasgow, U.K., July 1991. Bibliography 164

....[Obj91] supply all three as primitive types. The study of the commonality between these various collection types is a fruitful extension to the ideas provided here. It may provide us with better ways of structuring syntax [Wad90] with an understanding of the commonality between collection types [WT91] and a more general approach to query languages and optimization for these types [BTBW91] 7 Acknowledgements Val Breazu Tannen deserves our special thanks. He has contributed to many of the ideas in this paper and has greatly helped us in our understanding of type systems. We thank the ....

David A. Watt and Phil Trinder. Towards a Theory of Bulk Types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

....lists. Furthermore, this uniformity is achieved without any loss in type information. 1 Introduction Sets, bags, and lists are among the most commonly used bulk types. The comprehension syntax [21, 22] has recently been proposed as a syntax for the uniform manipulation of these bulk data types [23, 3, 6, 25]. Using this syntax, it is possible to turn a query on sets into a query on bags or on list by simply switching the set brackets into bag brackets or list brackets. For example, set select = p: S: f x j x 2 S; p(x) g bag select = p: S: fj x j x 2 S; p(x) jg list select = p: S: x j x 2 S; ....

D. A. Watt and P. Trinder. Towards a theory of bulk types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

....f 2 y j y 2 X; w 2 ( 1 y eq 1 x)g) j x 2 Xg. 2.2 The nested bag language We now define an ambient bag query language NBL consisting of three corresponding components: the bag algebra NBA, the bag calculus NBC , and the relative bag abstraction RBA. Following Wadler [36] and Watt and Trinder [37], the bag languages are obtained by replacing the set monad constructs in the nested relational languages by the corresponding bag monad constructs. This yields a uniform method for manipulating collection types such as sets and bags. We list only the parts that are changed. Types. NBL has the ....

D. A. Watt and P. Trinder. Towards a theory of bulk types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

.... and Information Science University of Pennsylvania Philadelphia, Pa 19104, USA The study of the common properties of programs that operate over lists, multisets, and sets, generically called collection types, has recently received some attention in database and programming language research [8, 2]. It has been especially important in extending the standard query language for relational databases essentially first order logic to deal with the wider range of data types that are to be found, for example, in object oriented databases. While the commonality between lists, multisets and ....

D.A. Watt and P. Trinder. Towards a Theory of Bulk Types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

....[46] Wadler [61] showed that they are also useful in organizing syntax, in particular they explain the list comprehension syntax of functional programming. Moreover Trinder and Wadler [59] showed that an extension of comprehensions can implement the (flat) relational calculus. Trinder and Watt [58, 62], have also sought after a uniform algebra for several different bulk types; in particular they have proved a number of optimizations using categorical identities. The technical development in the paper does not require familiarity with category theory; however readers interested in understanding ....

.... language CPL The observation that the monad operations we have used in this paper can be used to interpret the syntax of comprehensions used in functional programming languages was first made by Wadler [61] and the connection with database query languages was shown by Trinder, Wadler and Watt [58, 59, 62]. Comprehension syntax, as it is realized in CPL, superficially resembles Zermelo Fraenkel set notation, but there are important differences. For example the composition of binary relations R and S is expressed in CPL as f(x; z) j (nx; ny 1 ) Gamma R; ny 2 ; nz) Gamma S; y 1 = y 2 g The ....

D. A. Watt, P. W. Trinder, Towards a Theory of Bulk Types, Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

....always well defined s.r. suffices to express the relational algebra. Limited forms of s.r. in particular those connected to the categorical notion of monad were studied in [BBW92] Through the connection between monads and comprehension syntax [Wad92] this work ties in with [TW88, TW89, Tri91, WT91] The need for array languages and the possibility of using comprehension syntax for arrays are examined in [Bun93, MV93] An early form of divide and conquer recursion on sets (different from structural recursion) appears under the name pump in FAD [BBKV88] from which it is borrowed, under the ....

David A. Watt and Phil Trinder. Towards a theory of bulk types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

....used to show our main result that our query language is conservative with respect to set height of input output. The two improvements mentioned above are presented in the section 4. 2 Relative set abstraction Wadler and Trinder argued that list set bag comprehension is a natural query notation [20, 19, 26]. They also demonstrated that this notation does not hamper query optimization. In this section we present a query language based on comprehension that is equivalent to our nested relational algebra and nested relational calculus. We call this query language Relative Set Abstraction (or RSA for ....

D. A. Watt and P. Trinder. Towards a Theory of Bulk Types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

.... Theta t 0 g and denotes the cartesian product of the sets denoted by X and Y ; while S f S ff( 1 x; y)g j y 2 2 xg j x 2 Xg has type fs Theta tg and denotes the unnesting of the set denoted by X. Wadler and Trinder argued that list set bag comprehensions is a natural query notation [29, 28, 35]. They also demonstrated that this notation does not hamper query optimization. In the remainder of this section we present a query language based on the comprehension syntax that is equivalent to NRC. We call this query language Relative Set Abstraction (or RSA for short) Types. The types in ....

D. A. Watt, P. Trinder, "Towards a theory of bulk types," Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, 1991.

....of this paper. For further reading on this subject, the idea of using structural recursion for database languages was suggested in [4, 24, 7] and the properties of well defined programs using structural recursion were examined in [8] Comprehension syntax and its associated algebra was studied in [32, 33, 9] and its connection with structural recursion and complex object algebras was studied in [9] That comprehension syntax at relational types gives us a language equivalent to the relational algebra was shown in [25, 35] even if nesting is used in intermediate results. Another result of this kind ....

D.A. Watt and P. Trinder. Towards a Theory of Bulk Types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.

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D. A. Watt, P. Trinder, "Towards a theory of bulk types," Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, 1991.

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D. Watt, P. Trinder, Towards a Theory of Bulk Types, Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, 1991

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