A Reversible Semantics for Janus

2026-02-18

AI Summary

This work addresses a fundamental limitation in the original small-step semantics of the high-level reversible language Janus: during forward execution, it discards information essential for reversibility, thereby violating core properties such as the Loop Lemma and hindering debugging and concurrent extensions. To resolve this, the paper presents the first program counter–based reversible small-step operational semantics for Janus. This novel semantics preserves behavioral equivalence with the original while rigorously guaranteeing that every computational step is invertible. The authors formally establish both semantic equivalence and the validity of the Loop Lemma, overcoming the non-trivial challenge of integrating a program counter into reversible semantics. This result provides a solid theoretical foundation for developing debugging mechanisms and concurrency models in reversible programming languages.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Janus is a paradigmatic example of reversible programming language. Indeed, Janus programs can be executed backwards as well as forwards. However, its small-step semantics (useful, e.g., for debugging or as a basis for extensions with concurrency primitives) is not reversible, since it loses information while computing forwards. E.g., it does not satisfy the Loop Lemma, stating that any reduction has an inverse, a main property of reversibility in process calculi, where small-step semantics is commonly used. We present here a novel small-step semantics which is actually reversible, while remaining equivalent to the previous one. It involves the non-trivial challenge of defining a semantics based on a "program counter" for a high-level programming language.

Problem

• reversible programming
• small-step semantics
• Janus
• Loop Lemma
• program counter

Innovation

• reversible semantics
• small-step semantics
• Janus
• Loop Lemma
• program counter