Container types categorically

  • Authors:
  • Paul Hoogendijk;Oege De Moor

  • Affiliations:
  • Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands;Programming Research Group, Oxford University, Wolfson Building, Parks Road, Oxford OX1 3QD, UK

  • Venue:
  • Journal of Functional Programming
  • Year:
  • 2000

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Abstract

A program derivation is said to be polytypic if some of its parameters are data types. Often these data types are container types, whose elements store data. Polytypic program derivations necessitate a general, non-inductive definition of ‘container (data) type’. Here we propose such a definition: a container type is a relator that has membership. It is shown how this definition implies various other properties that are shared by all container types. In particular, all container types have a unique strength, and all natural transformations between container types are strong.