Refining Inductive Types

Refining Inductive Types
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DOI:
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发表时间:
2012
期刊:
Log. Methods Comput. Sci.
影响因子:
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通讯作者:
Neil Ghani
Neil Ghani
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文献类型:
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作者:
R. Atkey;Patricia Johann;Neil Ghani

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依赖性键入的编程语言允许在类型系统中表达数据的复杂属性。在依赖类型的编程中特别使用的是索引类型,可通过计算有用的信息来完善数据。例如,n索引的向量类型通过其长度来完善列表。其他数据类型可以以相似的方式进行完善,但是程序员必须在临时基础上产生特定特定的改进,开发人员必须预料到包含哪些改进,并且实施方式通常必须存储有关数据及其改进的冗余信息。在本文中,我们展示了如何普遍得出归纳类型改进的归纳特征,并认为这些特征可以减轻与临时改进有关的上述一些困难。我们的特征还确保了用于编程的标准技术以及有关归纳类型的推理,适用于改进,并且可以进一步完善改进。
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce purpose-specific refinements on an ad hoc basis, developers must anticipate which refinements to include in libraries, and implementations must often store redundant information about data and their refinements. In this paper we show how to generically derive inductive characterizations of refinements of inductive types, and argue that these characterizations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. Our characterizations also ensure that standard techniques for programming with and reasoning about inductive types are applicable to refinements, and that refinements can themselves be further refined.
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