Syntax for free: representing syntax with binding using parametricity

Atkey, Robert; Curien, Pierre-Louis, ed. (2009) Syntax for free: representing syntax with binding using parametricity. In: Typed Lambda Calculi and Applications, 9th International Conference, TLCA 2009. Lecture Notes in Computer Science, 5608 . Springer, pp. 35-49. ISBN 978-3-642-02272-2

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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.

    ORCID iDs

    Atkey, Robert ORCID logoORCID:; Curien, Pierre-Louis