The Design and Implementation of Typed Scheme: From Scripts to Programs

TL;DR

Typed Scheme introduces an explicitly typed extension to an untyped scripting language, using occurrence typing and refinement types to improve program maintainability and correctness.

Contribution

It presents a novel type system based on occurrence typing, formalizes it, and demonstrates its implementation in Typed Scheme with refinement types and subtyping.

Findings

Type system is sound and formalized

Refinement types enable precise value tracking

Implementation improves program safety and maintainability

Abstract

When scripts in untyped languages grow into large programs, maintaining them becomes difficult. A lack of explicit type annotations in typical scripting languages forces programmers to must (re)discover critical pieces of design information every time they wish to change a program. This analysis step both slows down the maintenance process and may even introduce mistakes due to the violation of undiscovered invariants. This paper presents Typed Scheme, an explicitly typed extension of PLT Scheme, an untyped scripting language. Its type system is based on the novel notion of occurrence typing, which we formalize and mechanically prove sound. The implementation of Typed Scheme additionally borrows elements from a range of approaches, including recursive types, true unions and subtyping, plus polymorphism combined with a modicum of local inference. The formulation of occurrence typing naturally leads to a simple and expressive version of predicates to describe refinement types. A Typed Scheme program can use these refinement types to keep track of arbitrary classes of values via the type system. Further, we show how the Typed Scheme type system, in conjunction with simple recursive types, is able to encode refinements of existing datatypes, thus expressing both proposed variations of refinement types.