Abstract: |
Studies of the mathematical properties of impredicatively polymorphic
types have for the most part focused on the polymorphic lambda
calculus of Girard-Reynolds, which is a calculus of total polymorphic
functions. This talk considers polymorphic types from a functional
programming perspective, where the partialness arising from the
presence of fixpoint recursion complicates the nature of potentially
infinite (`lazy') datatypes. An operationally-based approach to
Reynolds' notion of relational parametricity is developed for an
extension of Plotkin's PCF with universally quantified types and lazy
lists. The resulting logical relation is shown to be a useful tool for
proving properties of polymorphic types up to a notion of operational
equivalence based on Morris-style contextual equivalence.
Slides,
paper.
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