Procedural Refinement by LLM-driven Algorithmic Debugging for ARC-AGI-2

In complex code-generation tasks, conversation-based LLM code repair exhibits limited ability to recover from first-pass programming errors, as such code revisions are usually driven by LLMs' "plausible reasoning" rather than a formal, algorithmic debugging procedure. However, a formal foundation for such debugging exists in Udi Shapiro's theory of algorithmic program debugging (APD), which frames program repair as an explicit, stepwise procedural refinement process. In this paper, we propose a neuro-symbolic procedural refinement approach, Abduction-Based Procedural Refinement (ABPR), which couples an LLM with a meta-interpreter that materialises program execution into compact, declarative tree-structured traces, following the principles of APD. We evaluate ABPR on ARC-AGI-2, a benchmark requiring strong abstraction and debugging capabilities, and adopt Prolog as the target language due to its declarative semantics, which are well-suited to algorithmic program debugging. Our experiments show that ABPR paired with Gemini-3-Flash achieves a Pass@2 score of 56.67\% even in a language in which contemporary LLMs typically underperform. These results point towards a more auditable paradigm for program repair by integrating LLMs with classical formal methods.