Scopes as types

Hendrik Van Antwerpen,Casper Bach Poulsen,Eelco Visser,Arjen Rouvoet

doi:10.1145/3276484

Scopes as types

Hendrik Van Antwerpen, Casper Bach Poulsen + Show 2 more

Open Access

https://doi.org/10.1145/3276484

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Abstract

Scope graphs are a promising generic framework to model the binding structures of programming languages, bridging formalization and implementation, supporting the definition of type checkers and the automation of type safety proofs. However, previous work on scope graphs has been limited to simple, nominal type systems. In this paper, we show that viewing scopes as types enables us to model the internal structure of types in a range of non-simple type systems (including structural records and generic classes) using the generic representation of scopes. Further, we show that relations between such types can be expressed in terms of generalized scope graph queries. We extend scope graphs with scoped relations and queries. We introduce Statix, a new domain-specific meta-language for the specification of static semantics, based on scope graphs and constraints. We evaluate the scopes as types approach and the Statix design in case studies of the simply-typed lambda calculus with records, System F, and Featherweight Generic Java.

Highlights

The goal of our work is to support high-level specification of type systems that can be used for multiple purposes, including reasoning and the implementation of type checkers [Visser et al 2014]
We present an approach based on scopes with explicit substitutions that are lazily applied during name resolution, as opposed to eager application before name resolution
We have developed a full fledged Statix programming language with a concrete ASCII notation embodying the design described in this paper

Summary

Introduction

The goal of our work is to support high-level specification of type systems that can be used for multiple purposes, including reasoning (about type safety among other things) and the implementation of type checkers [Visser et al 2014]. Traditional approaches to type system specification do not reflect the commonality underlying the name binding mechanisms for different languages. Operationalizing name binding in a type checker requires carefully staging the traversals of the abstract syntax tree in order to collect information before it is needed. We introduce an approach to the declarative specification of type systems that is close in abstraction to traditional type system specifications, but can be directly interpreted as type checking rules. The approach is based on scope graphs for name resolution, and constraints to separate traversal order from solving order.

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