A Formally Verified Procedure for Width Inference in FIRRTL

2026-01-19

AI Summary

This work addresses the incompleteness of existing FIRRTL compilers, such as firtool, which may fail to infer bit widths even for simple programs. We propose a complete width inference method that guarantees a unique minimal solution whenever the underlying constraints are satisfiable, and we formalize this inference procedure accordingly. For the first time, we implement and formally verify the InferWidths compiler pass within the interactive theorem prover Rocq, from which we extract correct-by-construction OCaml executable code. Experimental evaluation demonstrates that our approach handles a strictly larger set of benchmarks than firtool while maintaining high performance.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Machine Learning: Hardware-aware ML

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

FIRRTL is an intermediate representation language for Register Transfer Level (RTL) hardware designs. In FIRRTL programs, the bit widths of many components are not specified explicitly and must be inferred during compilation. In mainstream FIRRTL compilers, such as the official compiler firtool, width inference is conducted by a compilation pass referred to as InferWidths, which may fail even for simple FIRRTL programs. In this paper, we thoroughly investigate the width inference problem for FIRRTL programs. We show that, if the constraints obtained from a FIRRTL program are satisfiable, there exists a unique least solution. Based on this result, we propose a complete procedure for solving the width inference problem. We implement it in the interactive theorem prover Rocq and prove its functional correctness. From the Rocq implementation, we extract an OCaml implementation, which is the first formally verified implementation of the InferWidths pass. Extensive experiments demonstrate that our approach can solve more instances than the official InferWidths pass in firtool, normally with high efficiency.

Problem

• FIRRTL
• width inference
• RTL
• bit width
• compiler

Innovation

• FIRRTL
• width inference
• formal verification
• constraint solving
• compiler pass