papers/hanzo-formal-verification/sections/01-introduction.tex

\section{Introduction}

\label{sec:intro}
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Testing demonstrates the presence of bugs; formal verification demonstrates
their absence. Hanzo infrastructure handles authentication for 2,800+
applications, manages 12,000+ secrets, routes 47M+ inference requests per
month, and delegates credentials to autonomous AI agents. A single
vulnerability in any of these systems can compromise the entire platform.

Testing, no matter how thorough, cannot cover all possible states. Formal
verification provides mathematical guarantees that critical properties hold
for \emph{all} inputs and \emph{all} execution paths. We use Lean
4~\cite{lean4} as our proof assistant because:
\begin{enumerate}[leftmargin=1.4em]
    \item \textbf{Small trusted kernel}: Lean 4's type checker is the only
    trusted component. All proof steps are verified by the kernel.
    \item \textbf{Dependent types}: Enable precise specifications that capture
    security invariants as types.
    \item \textbf{Metaprogramming}: Lean 4's tactic framework enables
    automation of repetitive proof steps.
    \item \textbf{Executable specifications}: Lean 4 code can be extracted to
    executable programs, enabling specification-implementation comparison.
\end{enumerate}

\subsection{Scope and Methodology}

We verify properties at the specification level: we formalize the intended
behavior of each system as Lean 4 definitions and prove theorems about those
specifications. This catches design-level bugs (incorrect algorithms, missing
edge cases, violated invariants) but does not verify the implementation code
directly.

The verification process for each system follows four steps:
\begin{enumerate}[leftmargin=1.4em]
    \item \textbf{Formalize}: Encode the system's data structures, state
    transitions, and external interfaces as Lean 4 types and functions.
    \item \textbf{Specify}: State the desired properties as Lean 4 theorems.
    \item \textbf{Prove}: Construct proofs accepted by the Lean 4 kernel.
    \item \textbf{Audit}: Map proved properties back to implementation code
    and verify that the implementation matches the formalization.
\end{enumerate}

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