Abstract Representation of Binders in OCaml using the Bindlib Library

TL;DR

The paper discusses the Bindlib library for OCaml, which efficiently manages data structures with variable binding, supporting substitution and renaming without variable capture issues, useful for implementing languages and proof systems.

Contribution

It introduces Bindlib's approach to representing binders in OCaml, emphasizing its efficiency and handling of variable capture in abstract syntax trees.

Findings

Supports fast substitution and variable renaming

Prevents variable capture during substitution

Enables explicit recomputation of variable names

Abstract

The Bindlib library for OCaml provides a set of tools for the manipulation of data structures with variable binding. It is very well suited for the representation of abstract syntax trees, and has already been used for the implementation of half a dozen languages and proof assistants (including a new version of the logical framework Dedukti). Bindlib is optimised for fast substitution, and it supports variable renaming. Since the representation of binders is based on higher-order abstract syntax, variable capture cannot arise during substitution. As a consequence, variable names are not updated at substitution time. They can however be explicitly recomputed to avoid "visual capture" (i.e., distinct variables with the same apparent name) when a data structure is displayed.