https://vouillon.github.io/blog/tags/formal-methods/Recent content in Formal-Methods on Jérôme VouillonHugoenTue, 21 Jul 2026 12:00:00 +0200https://vouillon.github.io/blog/posts/theo/Tue, 21 Jul 2026 12:00:00 +0200https://vouillon.github.io/blog/posts/theo/<p>What if checking whether two formulas with a million nodes are logically equivalent took exactly one machine instruction? Binary Decision Diagrams (BDDs) make this possible. They give you a <strong>canonical</strong> representation of boolean functions (two logically equivalent formulas always produce the exact same structure), which turns equivalence checking into a pointer comparison.</p> <p><a href="https://github.com/vouillon/theo" target="_blank" rel="noreferrer">Theo</a> is an OCaml library that implements BDDs with two key extensions: <strong>complement edges</strong> for compact representation, and <strong>theory support</strong> for reasoning about linear orders and equality. Consider a package manager checking whether <code>(ocaml &gt;= 4.14 AND dune &gt;= 3.0) OR (ocaml &gt;= 5.0)</code> is compatible with <code>ocaml &lt; 5.0</code>. With Theo, you write this directly using version constraints as atoms, and the engine automatically simplifies: it knows <code>ocaml &gt;= 4.14</code> is redundant when <code>ocaml &gt;= 5.0</code> holds, detects that the second disjunct contradicts <code>ocaml &lt; 5.0</code>, and can find the simplest satisfying assignment (<code>ocaml &gt;= 4.14, ocaml &lt; 5.0, dune &gt;= 3.0</code>).</p>