Programs Using Syntax with First-Class Binders

Abstract

We present a general methodology for adding support for higher-order abstract syntax definitions and first-class contexts to an existing ML-like language. As a consequence, low-level infrastructure that deals with representing variables and contexts can be factored out. This avoids errors in manipulating low-level operations, eases the task of prototyping program transformations and can have a major impact on the effort and cost of implementing such systems. We allow programmers to define syntax in a variant of the logical framework LF and to write programs that analyze these syntax trees via pattern matching as part of their favorite ML-like language. The syntax definitions and patterns on syntax trees are then eliminated via a translation using a deep embedding of LF that is defined in ML. We take advantage of GADTs which are frequently supported in ML-like languages to ensure our translation preserves types. The resulting programs can be type checked reusing the ML type checker, and compiled reusing its first-order pattern matching compilation. We have implemented this idea in a prototype written for and in OCaml and demonstrated its effectiveness by implementing a wide range of examples such as type checkers, evaluators, and compilation phases such as CPS translation and closure conversion.