When is a type refinement an inductive type
Atkey, Robert and Johann, Patricia and Ghani, Neil; Hofmann, Martin, ed. (2011) When is a type refinement an inductive type. In: Foundations of Software Science and Computational Structures. Lecture Notes in Computer Science . Springer, pp. 72-87. ISBN 978-3-642-19804-5 (https://doi.org/10.1007/978-3-642-19805-2_6)
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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 often store redundant information about data and their refinements. This paper shows how to generically derive inductive characterisations of refinements of inductive types, and argues that these characterisations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. These characterisations 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.
ORCID iDs
Atkey, Robert ORCID: https://orcid.org/0000-0002-4414-5047, Johann, Patricia and Ghani, Neil ORCID: https://orcid.org/0000-0002-3988-2560; Hofmann, Martin-
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Item type: Book Section ID code: 32474 Dates: DateEvent2011PublishedSubjects: Science > Mathematics > Electronic computers. Computer science Department: Faculty of Science > Computer and Information Sciences Depositing user: Pure Administrator Date deposited: 09 Aug 2011 15:46 Last modified: 11 Nov 2024 14:43 URI: https://strathprints.strath.ac.uk/id/eprint/32474