We present a system for virtual programming tutoring powered by large language models. We specify functional and quality requirements, propose a modular architecture with an isolated code execution environment and a unified LLM wrapper, and describe data construction methods and model adaptation techniques suitable for educational goals. We provide knowledge-tracing algorithms, a metric scheme for learner progress, and an observability pipeline that supports A/B experiments and analysis of tutoring usefulness. As a contribution, we introduce a two-loop tutor that pairs a dialog LLM with an instrumental agent in a sandbox to verify recommendations via tests, together with an engagement-aware hint policy. The design is grounded in prior work on intelligent tutoring systems, transformer models, RLHF, and learning analytics, yielding a system ready for implementation in real courses.