Binders unbound

Abstract

Implementors of compilers, program refactorers, theorem provers, proof checkers, and other systems that manipulate syntax know that dealing with name binding is difficult to do well. Operations such as α-equivalence and capture-avoiding substitution seem simple, yet subtle bugs often go undetected. Furthermore, their implementations are tedious, requiring "boilerplate" code that must be updated whenever the object language definition changes. Many researchers have therefore sought to specify binding syntax declaratively, so that tools can correctly handle the details behind the scenes. This idea has been the inspiration for many new systems (such as Beluga, Delphin, FreshML, FreshOCaml, Cαml, FreshLib, and Ott) but there is still room for improvement in expressivity, simplicity and convenience. In this paper, we present a new domain-specific language, Unbound , for specifying binding structure. Our language is particularly expressive - it supports multiple atom types, pattern binders, type annotations, recursive binders, and nested binding (necessary for telescopes, a feature found in dependently-typed languages). However, our specification language is also simple, consisting of just five basic combinators. We provide a formal semantics for this language derived from a locally nameless representation and prove that it satisfies a number of desirable properties. We also present an implementation of our binding specification language as a GHC Haskell library implementing an embedded domain specific language (EDSL). By using Haskell type constructors to represent binding combinators, we implement the EDSL succinctly using datatype-generic programming. Our implementation supports a number of features necessary for practical programming, including flexibility in the treatment of user-defined types, best-effort name preservation (for error messages), and integration with Haskell's monad transformer library.

αCheck: A mechanized metatheory model checker

“…Lazy SmallCheck can also generate and evaluate partially-defined inputs, by using a form of needed narrowing. In conjunction with an implementation of nominal abstract syntax (such as FreshLib (Cheney 2005b) or Binders Unbound (Weirich et al 2011)), Quick/SmallCheck could be used to implement metatheory model-checking, although this would build several levels of indirectness that may make counter-example search rather problematic. Compared to us, QuickCheck is a widely used library for general purpose programming, while we have so far put little effort into making our counter-example search more efficient.…”

Generic datatypes à la carte

“…One very interesting idea is to use datatype-generic programming to handle variable binding [9,28]. Variable binding is an ubiquitous aspect of programming languages.…”

The HERMIT in the machine

“…There has been a good deal of work in this area, with Unbound (Weirich et al 2011b), a Haskell-hosted DSL for specifying binding structure, being a recent solution. HERMIT uses congruence combinators for this task, which are a general mechanism for encapsulating the maintenance of any sort of contextual information, of which bindings are just one example.…”