CktFormalizer: Autoformalization of Natural Language into Circuit Representations

Hardware infrastructure is a critical bottleneck for LLM-driven circuit design, limiting what agents can express, compile, and iteratively refine within an agentic loop. To address this bottleneck, we introduce CktLean, a typed hardware infrastructure embedded in Lean. It supports hardware description, compilation to SystemVerilog, and interactive type-checking and proof feedback through a persistent read-eval-print loop (REPL). On this foundation, we build CktFormalizer, an agent framework for hardware generation, repair, optimization, and source-level equivalence proving. We evaluate structural correctness through compilation, functional correctness through RTL and gate-level simulation, and formal correctness through proofs relative to stated specifications. Across VerilogEval, RTLLM, ResBench, and CVDP, CktFormalizer with CktLean achieves compilation rates of 91.1%–99.4%. Among designs that pass RTL simulation, 95.4%–100.0% jointly complete synthesis and place-and-route and pass design-rule and layout-versus-schematic checks. In a separate evaluation on 30 VerilogEval problems, interactive proof-state feedback raises kernel-accepted equivalence proof completion from 53.3% to 63.3%. Hardware evaluation feedback also guides architecture exploration and iterative power, performance, and area (PPA) optimization, with synthesis-area reductions of up to 58.6% in the optimization loop. These results suggest that typed representations and explicit proof-state feedback help structure the agentic loop: compiler diagnostics guide targeted repairs, while proof-state feedback helps agents identify what remains to be proved and determine the next proof step. Our code is available anonymously at https://anonymous.4open.science/r/CKT-D51D/.