K-CIRCT: A Layered, Composable, and Executable Formal Semantics for CIRCT Hardware IRs

TL;DR

This paper presents K-CIRCT, a layered formal semantics framework for CIRCT, enabling rigorous hardware verification and simulation of RISC-V processors within an open-source hardware design environment.

Contribution

It introduces the first formal semantics for CIRCT in { extbackslash}K, structured into multiple layers for different dialects, enhancing verification and extensibility.

Findings

Achieved full-rule coverage in semantics validation.

Successfully modeled RISC-V processor in CIRCT semantics.

Demonstrated practical applicability with riscv-mini design.

Abstract

CIRCT, an open-source EDA framework akin to LLVM for software, is a foundation for various hardware description languages. Despite its crucial role, CIRCT's lack of formal semantics challenges necessary rigorous hardware verification. Thus, this paper introduces K-CIRCT, the first formal semantics in {\K} for a substantial CIRCT subset adequate for simulating a RISC-V processor. Our semantics are structured into multiple layers: (1) MLIR static semantics, which covers fundamental MLIR concepts across domains; (2) CIRCT common semantics, featuring a generic hardware model that captures key hardware features across dialects; and (3) composable and extensible semantics for specific dialects, formalized individually using a unified approach. This approach has been applied to formalize CIRCT core dialects. We validated our semantics through full-rule coverage tests and assessed its practicality using the popular RISC-V hardware design, riscv-mini.