Names For Free - Polymorphic Views of Names and Binders

Paper in proceedings, 2013

We propose a novel technique to represent names and binders in Haskell. The dynamic (run-time) representation is based on de Bruijn indices, but it features an interface to write and manipulate variables conviently, using Haskell-level lambdas and variables. The key idea is to use rich types: a subterm with an additional free variable is viewed either as $\forall v. v \rightarrow \mathsf{Term} (a + v)$ or $\exists v. v \times \mathsf{Term} (a + v)$ depending on weather it is constructed or analysed. We demonstrate on a number of examples how this approach approach permits to express terms construction and manipulation in a natural way, while retaining the good properties of representations based on de Bruijn indices.