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Publication Detail
Bunched polymorphism
  • Publication Type:
    Journal article
  • Publication Sub Type:
    Journal Article
  • Authors:
    Collinson M, Pym D, Robinson E
  • Publication date:
    01/12/2008
  • Pagination:
    1091, 1132
  • Journal:
    Mathematical Structures in Computer Science
  • Volume:
    18
  • Issue:
    6
  • Status:
    Published
  • Print ISSN:
    0960-1295
Abstract
We describe a polymorphic, typed lambda calculus with substructural features. This calculus extends the first-order substructural lambda calculus α associated with bunched logic. A particular novelty of our new calculus is the substructural treatment of second-order variables. This is accomplished through the use of bunches of type variables in typing contexts. Both additive and multiplicative forms of polymorphic abstraction are then supported. The calculus has sensible proof-theoretic properties and a straightforward categorical semantics using indexed categories. We produce a model for additive polymorphism with first-order bunching based on partial equivalence relations. We consider additive and multiplicative existential quantifiers separately from the universal quantifiers. © 2008 Copyright Cambridge University Press.
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