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Bunched polymorphism

Published online by Cambridge University Press:  01 December 2008

MATTHEW COLLINSON ,
DAVID PYM  and
EDMUND ROBINSON
MATTHEW COLLINSON
Affiliation:
Hewlett-Packard Laboratories, Bristol, BS34 8QZ, United Kingdom Email: david.pym@hp.com
DAVID PYM
Affiliation:
Hewlett-Packard Laboratories, Bristol, BS34 8QZ, United Kingdom Email: david.pym@hp.com
EDMUND ROBINSON
Affiliation:
Queen Mary, University of London, E1 4NS, United Kingdom
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Abstract

We describe a polymorphic, typed lambda calculus with substructural features. This calculus extends the first-order substructural lambda calculus αλ 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.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 6 , December 2008 , pp. 1091 - 1132
Copyright
Copyright © Cambridge University Press 2008

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