Refining inductive types

Robert Atkey, Patricia Johann, Neil Ghani

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
69 Downloads (Pure)


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 characterisations of refinements of inductive types, and argue that these characterisations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. Our 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.
Original languageEnglish
Article number9
Number of pages30
JournalLogical Methods in Computer Science
Issue number2
Publication statusPublished - 4 Jun 2012


  • programming language
  • programme developers
  • data


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