On bunched polymorphism

Authors:
Matthew Collinson;David Pym;Edmund Robinson
Affiliations:
University of Bath, UK;University of Bath, UK;Queen Mary, University of London, UK
Venue:
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
Year:
2005

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Abstract

We describe a polymorphic extension of the substructural lambda calculus αλ associated with the logic of bunched implications. This extension is particularly novel in that both variables and type variables are treated substructurally, being maintained through a system of zoned, bunched contexts. Polymorphic universal quantifiers are introduced in both additive and multiplicative forms, and then metatheoretic properties, including subject-reduction and normalization, are established. A sound interpretation in a class of indexed category models is defined and the construction of a generic model is outlined, yielding completeness. A concrete realization of the categorical models is given using pairs of partial equivalence relations on the natural numbers. Polymorphic existential quantifiers are presented, together with some metatheory. Finally, potential applications to closures and memory-management are discussed.