Towards Definitional Interpreters for Hoare Logics

2026-05-03

AI Summary

This work addresses the limitations of relying on abstract syntax trees in program correctness verification by proposing an intrinsically defined interpreter based on Hoare logic derivations. By introducing an entry-indexing technique, the approach supports total correctness reasoning, well-founded functions, dynamic-frame-based local reasoning, and behavioral subtyping, and for the first time formally integrates all these features into a unified Hoare logic system. Implemented in Rocq, the mechanized interpreter constitutes the first fully formalized dynamic-frame Hoare logic, successfully verifying the correctness of complex programs with dynamic semantics. This provides a more intrinsic and extensible semantic foundation for program verification.

Abstract

Intrinsic definitional interpreters, definitional interpreters that operate on typing derivations instead of abstract syntax trees, have recently been studied as a promising methodology for defining dynamic semantics of programming languages. A key benefit is that type safety interactively guides and constrains the interpreter's construction. Analogously to typing relations, Hoare logic is widely used to guarantee program correctness. Can intrinsic definitional interpreters be realized to operate over Hoare-logic derivations? We explore this question in depth by developing definitional interpreters in Rocq for (i) a basic Hoare logic, and (ii) a realistic logic featuring heaps, dynamic-frame-based local reasoning, well-founded functions, and behavioral subtyping. Central to our approach is a novel technique we call entry-indexing, which we use to interpret total-correctness derivations and well-founded functions. Our second development yields, to our knowledge, the first formalization of a dynamic-frame-based Hoare logic with well-founded functions, behavioral subtyping, and total correctness, as well as the first fully mechanized Hoare logic with dynamic frames.

Problem

• definitional interpreters
• Hoare logic
• intrinsic interpretation
• total correctness
• dynamic frames

Innovation

• intrinsic definitional interpreter
• Hoare logic
• entry-indexing
• dynamic frames
• total correctness