Why higher-order logic is a good formalisation for hardware (www.cl.cam.ac.uk)

Mike Gordon’s 1985 technical report argues that higher-order logic (HOL) — originally a foundation for mathematics — is a natural and practical formalism for both describing hardware and proving that designs meet their specifications. The paper demonstrates how HOL can model combinational and sequential circuits at varying abstraction levels, giving worked examples from transistor-level CMOS inverter and full adder to an n‑bit ripple‑carry adder, a sequential multiplier, and an edge‑triggered D‑type register. These case studies show how functional types, higher-order quantification and explicit modeling of state and time let designers state precise specifications and carry out compositional, machine-checked correctness proofs. The significance for the AI/ML and broader systems community is twofold: technically, HOL’s expressivity supports rigorous, reusable proofs of circuit behavior (including temporal and stateful properties) that go beyond what purely syntactic HDLs or model checkers easily capture; practically, the approach paved the way for interactive theorem provers and mechanized verification toolchains (the HOL family and successors) that underpin trustworthy hardware design. For AI/ML this matters because formally verified accelerators and safety-critical inference pipelines benefit from the same proof techniques — enabling higher confidence in correctness, composability, and provenance of hardware used for ML workloads.