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SSGIP'10 Proceedings of the 2010 international spring school conference on Generic and Indexed Programming
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POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Names for free: polymorphic views of names and binders
Proceedings of the 2013 ACM SIGPLAN symposium on Haskell
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We show that, in a parametric model of polymorphism, the type *** *** . ((*** ****** ) ****** ) ***(*** ****** ****** ) ****** is isomorphic to closed de Bruijn terms. That is, the type of closed higher-order abstract syntax terms is isomorphic to a concrete representation. To demonstrate the proof we have constructed a model of parametric polymorphism inside the Coq proof assistant. The proof of the theorem requires parametricity over Kripke relations. We also investigate some variants of this representation.