A Step-indexed Semantics of Imperative Objects

TL;DR

This paper develops a step-indexed semantic framework for an imperative object calculus, enabling rigorous type safety proofs for complex features like objects, subtyping, recursion, and mutable state.

Contribution

It introduces a novel step-indexed semantics for a rich imperative object calculus, addressing challenges posed by dynamic allocation, higher-order store, and advanced type features.

Findings

Semantic interpretation of object types with subtyping and recursion

Handling stateful features in step-indexed semantics

Providing a foundation for type safety proofs in imperative object languages

Abstract

Step-indexed semantic interpretations of types were proposed as an alternative to purely syntactic proofs of type safety using subject reduction. The types are interpreted as sets of values indexed by the number of computation steps for which these values are guaranteed to behave like proper elements of the type. Building on work by Ahmed, Appel and others, we introduce a step-indexed semantics for the imperative object calculus of Abadi and Cardelli. Providing a semantic account of this calculus using more `traditional', domain-theoretic approaches has proved challenging due to the combination of dynamically allocated objects, higher-order store, and an expressive type system. Here we show that, using step-indexing, one can interpret a rich type discipline with object types, subtyping, recursive and bounded quantified types in the presence of state.