A fresh look at programming with names and binders

Abstract

A wide range of computer programs, including compilers and theorem provers, manipulate data structures that involve names and binding. However, the design of programming idioms which allow performing these manipulations in a safe and natural style has, to a large extent, remained elusive.In this paper, we present a novel approach to the problem. Our proposal can be viewed either as a programming language design or as a library: in fact, it is currently implemented within Agda. It provides a safe and expressive means of programming with names and binders. It is abstract enough to support multiple concrete implementations: we present one in nominal style and one in de Bruijn style. We use logical relations to prove that "well-typed programs do not mix names with different scope". We exhibit an adequate encoding of Pitts-style nominal terms into our system.

A unified treatment of syntax with binders

“…We need not throw anything away. This is in contrast with our first conference paper (Pouillard & Pottier, 2010), where we presented two distinct implementations of a common interface. Here, there is no need to make a monolithic choice between the nominal style and de Bruijn's style.…”

“…Our previous papers This paper combines and extends two conference papers (Pouillard & Pottier, 2010;Pouillard, 2011a). Here is a summary of the differences between these papers and the present work and of the path that we have followed.…”

“…Our first conference paper (Pouillard & Pottier, 2010) contains a mistake that we would like to briefly explain because it emphasizes why it can be interesting to have both + W and ↑ instead of just the latter.…”

“…In the conference paper (Pouillard & Pottier, 2010), we fell into this trap and defined a function (called shiftName there) with the behavior of unprotectedAdd, whereas the intended behavior was that of protectedAdd↑. We did not notice the bug, and indeed were quite confident that there was no bug, because the soundness proof based on logical relations went through.…”

“…Incidentally, Cave and Pientka use a version of our system in order to establish the meta-theoretic properties of Beluga µ in the COQ proof assistant. They use a simplified version of the "links" found in our first conference paper (Pouillard & Pottier, 2010) which corresponds to the "little link library" that we have mentioned above.…”