Free relative constructions in OT syntax

This paper is part of a research project on OT Syntax and the typology of the free relative (FR) construction. It concentrates on the details of an OT analysis and some of its consequences for OT syntax. I will not present a general discussion of the phenomenon and the many controversial issues it is famous for in generative syntax

Syntax for free: representing syntax with binding using parametricity

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