When is a type refinement an inductive type

Robert Atkey, Patricia Johann, Neil Ghani

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

8 Citations (Scopus)

Abstract

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.
Original languageEnglish
Title of host publicationFoundations of Software Science and Computational Structures
Subtitle of host publication14th International Conference, FOSSACS 2011
EditorsMartin Hofmann
PublisherSpringer
Pages72-87
Number of pages16
ISBN (Print)978-3-642-19804-5
DOIs
Publication statusPublished - 2011

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume6604
ISSN (Print)0302-9743

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Keywords

  • programming language
  • typed programming
  • data types

Cite this

Atkey, R., Johann, P., & Ghani, N. (2011). When is a type refinement an inductive type. In M. Hofmann (Ed.), Foundations of Software Science and Computational Structures: 14th International Conference, FOSSACS 2011 (pp. 72-87). (Lecture Notes in Computer Science ; Vol. 6604). Springer. https://doi.org/10.1007/978-3-642-19805-2_6