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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Syntax for Free: Representing Syntax with Binding Using Parametricity
verfasst von : Robert Atkey
Erschienen in: Typed Lambda Calculi and Applications
Verlag: Springer Berlin Heidelberg
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We show that, in a parametric model of polymorphism, the type ∀
α
. ((
α
→
α
) →
α
) →(
α
→
α
→
α
) →
α
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.