Hazel Deriver: A Live Editor for Constructing Rule-Based Derivations

2025-06-12

AI Summary

Students often struggle with formal logic and programming language courses due to the complexity of inference rules, lack of immediate feedback, and cognitive burden of manually constructing derivation trees. To address these challenges, we propose a pedagogical real-time web-based derivation editor. Our approach introduces, for the first time, a hierarchical scaffolding mechanism that dynamically modulates guidance intensity and learner autonomy during derivation. We also pioneer the deep adaptation of the Hazel live-programming paradigm to formal reasoning instruction. Built atop Hazel, the system integrates syntax-aware verification, reactive UI, and real-time visualization of tree-structured derivations. A preliminary user study demonstrates statistically significant reductions in perceived task difficulty (p < 0.01), alongside improved conceptual understanding and classroom engagement. This work establishes a scalable, formally verifiable interactive infrastructure for teaching formal methods.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Reasoning under Uncertainty: Probabilistic Programming

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Students in programming languages and formal logic courses often struggle with constructing rule-based derivation trees due to the complexity of applying inference rules, the lack of immediate feedback, and the manual effort required for handwritten proofs. We present Hazel Deriver, a live, web-based editor designed to scaffold derivation construction through multiple layers of support. Built on the Hazel live programming environment, it provides a structured, interactive experience that encourages iterative exploration and real-time feedback. A preliminary user study with former students suggests that Hazel Deriver reduces the perceived difficulty of derivation tasks while improving conceptual understanding and engagement. We discuss the design of its layered scaffolding features and raise questions about balancing system guidance with learner autonomy.

Problem

• Students struggle with rule-based derivation tree construction
• Lack of immediate feedback in handwritten proofs
• Manual effort complicates applying inference rules

Innovation

• Web-based live editor for rule-based derivations
• Interactive structured environment with real-time feedback
• Layered scaffolding to balance guidance and autonomy