https://emsenn.net/tags/formalverification/ Recent content in FormalVerification on emsenn.net Hugo en-us Sun, 01 Mar 2026 00:00:00 +0000 https://emsenn.net/library/domains/engineering/domains/tech/domains/computing/domains/formal-math/domains/agda/texts/write-agda-proof/ Sun, 01 Mar 2026 00:00:00 +0000 https://emsenn.net/library/domains/engineering/domains/tech/domains/computing/domains/formal-math/domains/agda/texts/write-agda-proof/ <h1 id="write-agda-proof">Write Agda Proof</h1> <h2 id="prerequisites">Prerequisites</h2> <p>Read the <a href="https://emsenn.net/mathematics/concepts/proof/skills/write-formal-proof/SKILL.md" class="link-internal">write-formal-proof</a> skill first. It contains the anti-slop checklist that must pass before any proof is considered complete.</p> <h2 id="agda-specific-workflow">Agda-specific workflow</h2> <ol> <li> <p><strong>State the proposition</strong> as an Agda type signature with explicit universe levels and parameters.</p> </li> <li> <p><strong>Identify standard library imports.</strong> Common ones:</p> <ul> <li><code>Relation.Binary.PropositionalEquality</code> — <code>_≡_</code>, <code>refl</code>, <code>cong</code>, <code>sym</code>, <code>trans</code>, <code>subst</code></li> <li><code>Data.Nat</code>, <code>Data.List</code> — basic data types</li> <li><code>Data.Product</code> — <code>_×_</code>, <code>_,_</code>, <code>proj₁</code>, <code>proj₂</code></li> <li><code>Data.Sum</code> — <code>_⊎_</code>, <code>inj₁</code>, <code>inj₂</code></li> <li><code>Level</code> — universe level management</li> <li><code>Function</code> — <code>id</code>, <code>_∘_</code>, <code>case_of_</code></li> </ul> </li> <li> <p><strong>Write the proof as a function definition.</strong> Agda has no tactic mode — proofs are terms. Use:</p>