## Questions and Answers About Categorical Data Types (1994)

Venue: | in Proceedings on the BCS Workshop on Bulk Data Types for Architecture Independence, London (20 |

Citations: | 7 - 0 self |

### BibTeX

@INPROCEEDINGS{Skillicorn94questionsand,

author = {D. B. Skillicorn},

title = {Questions and Answers About Categorical Data Types},

booktitle = {in Proceedings on the BCS Workshop on Bulk Data Types for Architecture Independence, London (20},

year = {1994}

}

### OpenURL

### Abstract

this document without fee provided it is copied in its entirety and this notice remains attached. the computation and communication of an operation on the data type are arranged. That's a job for the implementer and compiler writer. So there's a separation of concerns at just the right level --- programmers think about monolithic operations on data types, while implementers worry about how to make them happen. This provides architecture independence. If the target machine is replaced during the night by some new machine, even a completely different architecture, there is no need to alter the software. The differences between machines can be hidden by the compiler.

### Citations

740 |
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- Chandy, Misra
- 1988
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Citation Context ... yet been built or even thought of. This suggests that a good model should be low-level enough that efficient implementations can be found. Models like higher order functional programming [20], UNITY =-=[9]-=-, and Maude [19] have the right kind of properties for programmers, but it has proven hard to build efficient implementations. Models like the Message Passing Interface [11], and Occam make it easy to... |

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An introduction to the theory of lists
- Bird
- 1987
(Show Context)
Citation Context ...n= log n processors. What other categorical data types have been built? The first type to be investigated was the type of join or concatenation lists, and more is known about them than any other type =-=[2, 5, 6]-=-. Such lists have three constructors: [ ] : 1 ! As[\Delta] : A ! As++ : A \Theta A ! A The first constructor makes an empty list, the second a singleton list, and the third concatenates two lists to m... |

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Citation Context ...ms [22, 23]. Other types that have been built include bags or multisets, graphs [21], and arrays [4]. Thus categorical data types generalises languages such as Gamma [3], Parallel SETL [16], and NESL =-=[7]-=-, as well as more general object-oriented approaches such as Mentat [15] and C** [17].. When I'm deriving programs, how can I decide whether to use one algorithm or another? Don't I need to know the c... |

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- 1987
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87 |
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- 1987
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58 |
Algebraic identities for program calculation
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Citation Context ...n= log n processors. What other categorical data types have been built? The first type to be investigated was the type of join or concatenation lists, and more is known about them than any other type =-=[2, 5, 6]-=-. Such lists have three constructors: [ ] : 1 ! As[\Delta] : A ! As++ : A \Theta A ! A The first constructor makes an empty list, the second a singleton list, and the third concatenates two lists to m... |

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- 1992
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Citation Context ...n= log n processors. What other categorical data types have been built? The first type to be investigated was the type of join or concatenation lists, and more is known about them than any other type =-=[2, 5, 6]-=-. Such lists have three constructors: [ ] : 1 ! As[\Delta] : A ! As++ : A \Theta A ! A The first constructor makes an empty list, the second a singleton list, and the third concatenates two lists to m... |

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Algebras for Tree Algorithms. D
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Citation Context ...chemas for maps and reductions. Many derivations involving lists have been done. Some small-scale implementations have been built [8], and quite a lot is known about code generation for list programs =-=[22, 23]-=-. Other types that have been built include bags or multisets, graphs [21], and arrays [4]. Thus categorical data types generalises languages such as Gamma [3], Parallel SETL [16], and NESL [7], as wel... |

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