Relational Parametricity for Computational Effects

TL;DR

This paper extends the concept of relational parametricity, traditionally used in pure functional programming, to include programming languages with computational effects, providing a foundational framework for such extensions.

Contribution

It introduces a new theoretical framework that adapts relational parametricity to effectful programming languages, bridging a gap in existing theory.

Findings

Framework for relational parametricity with effects

Enhanced data abstraction properties for effectful programs

Formal proofs of program equivalences with effects

Abstract

According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible mathematical formulation of this idea. Relational parametricity provides a powerful tool for establishing data abstraction properties, proving equivalences of datatypes, and establishing equalities of programs. Such properties have been well studied in a pure functional setting. Many programs, however, exhibit computational effects, and are not accounted for by the standard theory of relational parametricity. In this paper, we develop a foundational framework for extending the notion of relational parametricity to programming languages with effects.