Phantom Types and Subtyping in Programming Languages

Title: Phantom Types and Subtyping in Programming Languages

Abstract: This research explores a technique called the "phantom types technique" that uses parametric polymorphism, type constraints, and unification of polymorphic types to create a subtyping hierarchy in programming languages. This technique is particularly useful for capturing subtyping relationships and can be applied to a wide range of programming languages and applications.

Research Question: How can we use the phantom types technique to create a subtyping hierarchy and capture programming invariants associated with user-defined data types?

Methodology: The study uses a Hindley-Milner type system, such as the one found in Standard ML, to enforce the subtyping relation. The authors demonstrate the suitability of the phantom types technique by presenting a type-preserving translation from a simple calculus with bounded polymorphism to a calculus embodying the type system of Standard ML. They also illustrate the technique's use in capturing programming invariants through statically-enforced data type specializations.

Results: The research shows that the phantom types technique can be used to create any finite subtyping hierarchy, including those arising from multiple interface inheritance. It also demonstrates that the technique can be used to capture programming invariants associated with user-defined data types, reducing the need for run-time checks and improving the overall performance of the program.

Implications: The phantom types technique offers a powerful and flexible approach to capturing subtyping relationships and programming invariants in programming languages. It can be applied to a wide range of languages and applications, leading to more robust, efficient, and maintainable software systems. The technique's ability to encode subtyping information and reflect user-defined restrictions in the constrained types of values and functions makes it an essential tool for modern type-based programming.

Link to Article: https://arxiv.org/abs/0403034v1 Authors: arXiv ID: 0403034v1