C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....because they resemble notions familiar from (finite) lists. Similar operations for more sophisticated coalgebraic datatypes such as possibly infinitely branching trees with possible infinite depth [HJ97] might be more difficult. In these cases the general notions of shape and position [Jay96] will occur. Here the shape 14 (length) of a sequence is either a natural number if it is finite or bot for infinity and a position is a natural number. Another useful basic operation is composition or concatenation of two sequences explained in Section 3. compstruct : Seq[A] Seq[A] ....

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

....carrier X:T ( Gamma; X) C n C , for a datafunctor T : C n 1 C . The completeness and cocompleteness which is assumed in this definition refers to the existence of the initial algebras and terminal coalgebras mentioned in point 3. The class of datafunctors we use is akin to the one in [19], but does not involve shape . Also, at this stage, we do not consider the concept of strength (see [5, 23, 16] although it forms an essential part of the complete story of these functors. Explicitly, the functor X:T ( Gamma; X) C n C in the third clause maps a sequence of objects Y 2 C ....

B. Jay. Data categories. In M.E. Houle and P.Eades, editors, Computing: The Australasian Theory Symposium Proceedings, number 18 in Australian Comp. Sci. Comm., pages 21--28, 1996.

....because they resemble notions familiar from (finite) lists. Similar operations for more sophisticated coalgebraic datatypes such as possibly infinitely branching trees with possible infinite depth [HJ97] might be more difficult. In these cases the general notions of shape and position [Jay96] will occur. Here the shape 13 (length) of a sequence is either a natural number if it is finite or bot for infinity and a position is a natural number. Another useful basic operation is composition or concatenation of two sequences explained in Section 3. compstruct : Seq[A] Seq[A] ....

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

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C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

No context found.

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

No context found.

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

No context found.

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

....Nielsen [24] which pre computes the shape of the result Proceedings of CATS 97 (Computing: The Australasian Theory Symposium) Sydney, Australia, February 5 7 1997. and also the shapes of all the intermediate data structures used in computation. The solid semantics underlying shape theory (Jay [15]) should yield novel forms of abstract domains (e.g. Abramsky and Hankin [1] Cousot and Cousot [9] Schmidt [26] in which a type is interpreted by the standard interpretation of its type of shapes. Shape can also be viewed as type information, and shape analysis as a form of dependent type ....

C.B. Jay. Data categories. In M.E. Houle and P. Eades (editors), Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, Volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157-- 3055.

....of different computational paradigms [Jay96b] Shape analysis can be considered a form of partial evaluation (e.g. JGP93] which pre computes the shape of the result and also the shapes of all the intermediate data structures used in computation. The solid semantics underlying shape theory [Jay96a] should yield novel forms of abstract domains (e.g. Ae87, CC92, Sch95] in which a type is interpreted by the standard interpretation of its type of shapes. Shape can also be viewed as type information, and shape analysis as a form of dependent type analysis [ML73] However, dependent types ....

C.B. Jay. Data categories. In Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, pages 21--28, 1996.

....types of interest can be separated into their shape and their data. This separation can be modelled formally, has strong properties, and can be exploited in the design of programs and programming languages. The original presentation [Jay95b] used finite lists to represent the data: recent work [Jay96a] generalises these to position functors. These use an object of positions as a means of indexing data locations. Shape information is used to determine which positions store a datum. The result is a data functor. Under some mild assumptions, used to define data categories, the data functors are ....

....common operations, such as composition, products and sums, initial algebras and final co algebras. They are also closed under the formation of objects of transformations, used to model transformation types. This is because every natural transformation between data functors has a uniform algorithm [Jay96a]. It follows that the covariant types can be modelled by data functors in any data category, such as Sets. Thus, despite the general understanding of the past decade, there is an impredicative polymorphic type system with a set theoretic model. Further, the model is full (there is no restriction ....

[Article contains additional citation context not shown here]

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

....types and functions represent data processes, rather than data storage. The simplicity of the description above suggests that a rather weak categorical setting, let us say a data category, may suffice for expressing the key properties of data types. Though some preliminary results are presented in [Jay96], many open problems remain. The shape data separation supports novel approaches to computation. One application is shape polymorphism, first proposed in [JC94] in which programs can be applied to arguments of different (types and) shapes, e.g. to a list, tree or matrix. The latest work in this ....

C.B. Jay. Data categories. In M.E. Houle and P. Eades, editors, Computing: The Australasian Theory Symposium Proceedings, Melbourne, Australia, 29--30 January, 1996, volume 18, pages 21--28. Australian Computer Science Communications, 1996. ISSN 0157--3055.

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