https://theorem.dev/blog/ Recent content in Blog on Theorem Hugo en-us Thu, 05 Feb 2026 00:00:00 +0000 https://theorem.dev/blog/lf-lean/ Thu, 05 Feb 2026 00:00:00 +0000 https://theorem.dev/blog/lf-lean/ <style> /* Hide the scrolling table of contents */ .distill-toc { display: none !important; } /* Abstract is manually placed after the hero image */ .distill-subtitle { display: none !important; } .distill-header { border-bottom: none !important; padding-bottom: 0 !important; margin-bottom: 0 !important; } .post-abstract { font-family: var(--font-sans); font-size: 1.05rem; font-weight: 400; line-height: 1.5; color: var(--text-light); margin: 0 0 1.5rem 0; } @media (max-width: 768px) { .post-abstract { font-size: 1rem; } } @media (max-width: 480px) { .post-abstract { font-size: 0.95rem; } } .figure-container { --fig-w: 100%; --capped-w: min(var(--fig-w), calc(100vw - 2rem)); width: var(--capped-w); margin: 2rem 0; margin-left: calc((100% - var(--capped-w)) / 2); text-align: center; } .figure-container img { max-width: 100%; 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white-space: pre;"><tspan style="font-weight:bold">Verina</tspan></text></g></g></g><g class="annotation" data-index="17" style="opacity: 1;"><g class="annotation-text-g" transform="rotate(0,1054.51,320.68)"><g class="cursor-pointer" transform="translate(1028,312)"><rect class="bg" x="0.5" y="0.5" width="53" height="17" style="stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 0; fill: rgb(0, 0, 0); fill-opacity: 0;"/><text class="annotation-text" text-anchor="middle" x="27.21875" y="12" style="font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji'; font-size: 12px; fill: rgb(29, 78, 216); fill-opacity: 1; white-space: pre;"><tspan style="font-weight:bold"><tspan style="font-family: monospace">lf-lean</tspan></tspan></text></g></g></g><g class="annotation" data-index="18" style="opacity: 1;"><g class="annotation-text-g" transform="rotate(0,480.15,254.02999999999997)"><g class="cursor-pointer" transform="translate(284,227)"><rect class="bg" x="0.5" y="0.5" width="391" height="53" style="stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 0; fill: rgb(0, 0, 0); fill-opacity: 0;"/><text class="annotation-text" text-anchor="middle" x="195.671875" y="21" style="font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji'; font-size: 20px; fill: rgb(13, 148, 136); fill-opacity: 1; white-space: pre;"><tspan class="line" dy="0em" x="195.671875" y="21"><tspan style="font-weight:bold">Verified software engineering,</tspan></tspan><tspan class="line" dy="1.3em" x="195.671875" y="21"><tspan style="font-weight:bold">code automatically proven correct</tspan></tspan></text></g></g><g class="annotation-arrow-g" style="opacity: 0.75;"><path d="M480.15,281.03L480.15,515.03" style="stroke-width: 2px; stroke: rgb(13, 148, 136); stroke-opacity: 1; stroke-dasharray: 0px, 0px, 230.88px, 234px;"/><path d="M-3.7,-2.5V2.5L1.3,0Z" transform="translate(480.1499938964844,511.9100341796875)rotate(90)scale(2.4)" style="fill: rgb(13, 148, 136); stroke-width: 0;"/></g></g><g class="annotation" data-index="19" style="opacity: 1;"><g class="annotation-text-g" transform="rotate(0,838.83,193.26)"><g class="cursor-pointer" transform="translate(650,166)"><rect class="bg" x="0.5" y="0.5" width="376" height="53" style="stroke-width: 1px; stroke: rgb(0, 0, 0); stroke-opacity: 0; fill: rgb(0, 0, 0); fill-opacity: 0;"/><text class="annotation-text" text-anchor="middle" x="188.484375" y="21" style="font-family: system-ui, 'Segoe UI', Roboto, Helvetica, Arial, sans-serif, 'Apple Color Emoji', 'Segoe UI Emoji'; font-size: 20px; fill: rgb(180, 83, 9); fill-opacity: 1; white-space: pre;"><tspan class="line" dy="0em" x="188.484375" y="21"><tspan style="font-weight:bold">Unverified software engineering,</tspan></tspan><tspan class="line" dy="1.3em" x="188.484375" y="21"><tspan style="font-weight:bold">bottlenecked on human review</tspan></tspan></text></g></g><g class="annotation-arrow-g" style="opacity: 0.8;"><path d="M838.83,220.26L838.83,392.26" style="stroke-width: 2px; stroke: rgb(180, 83, 9); stroke-opacity: 1; stroke-dasharray: 0px, 0px, 168.88px, 172px;"/><path d="M-3.7,-2.5V2.5L1.3,0Z" transform="translate(838.8300170898438,389.1400146484375)rotate(90)scale(2.4)" style="fill: rgb(180, 83, 9); stroke-width: 0;"/></g></g></g></svg></div></div><figcaption class="plotly-caption">Figure 1: Closing the Gap Between Verified and Unverified Software Engineering. Adapted from METR&rsquo;s Time Horizon plot, including software verification benchmarks where AIs write code and then prove it correct. We plot only the time horizon for software implementation (not verification) for an an apples-to-apples comparison of how much functionality is implemented via each method of software development. <code>lf-lean</code> gives us an encouraging measurement of where verified software engineering capability is.</figcaption></figure><script> document.addEventListener('DOMContentLoaded', function() {loadPlotlyChart('plotly-fdb1d3d31c4492291fc111fec0abbe0c', 'hero-image', { height: '600px', inlineData: { "colorScheme": null, "data": [ { "type": "scatter", "mode": "lines", "name": "", "hovertemplate": "", "x": [ "2024-11-30", "2024-12-15", "2024-12-22", "2024-12-29", "2025-01-05", "2025-01-12", "2025-01-19", "2025-01-26", "2025-02-02", "2025-02-09", "2025-02-16", "2025-02-23", "2025-03-02", "2025-03-09", "2025-03-16", "2025-03-23", "2025-03-30", "2025-04-06", "2025-04-13", "2025-04-20", "2025-04-27", "2025-05-04", "2025-05-11", "2025-05-18", "2025-05-25", "2025-06-01", "2025-06-08", 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"#1D4ED8", "weight": "bold" } }, { "x": "2025-05-15", "y": 3.5, "text": "<b>Verified software engineering,<br>code automatically proven correct</b>", "showarrow": true, "arrowhead": 2, "arrowsize": 1.2, "arrowwidth": 2, "arrowcolor": "rgba(13, 148, 136, 0.75)", "ax": 0, "ay": -234, "xanchor": "center", "yanchor": "bottom", "font": { "size": 20, "color": "#0D9488" } }, { "x": "2025-10-15", "y": 90, "text": "<b>Unverified software engineering,<br>bottlenecked on human review</b>", "showarrow": true, "arrowhead": 2, "arrowsize": 1.2, "arrowwidth": 2, "arrowcolor": "rgba(180, 83, 9, 0.8)", "ax": 0, "ay": -172, "xanchor": "center", "yanchor": "bottom", "font": { "size": 20, "color": "#B45309" } } ] } } });}); </script> </div> <p class="post-abstract">We present <code>lf-lean</code>, a verified translation of all 1,276 statements of the Logical Foundations textbook from Rocq to Lean, produced by frontier AI with ~2 person-days of human effort versus an estimated ~2.75 person-years manually (a 350x speed-up). We achieve this through task-level specification generators: because many software transformations are semantics-preserving, correctness can be defined once for an entire task class and checked automatically across all instances and codebases. This scales human oversight from 𝒪(𝓃) to 𝒪(1) regardless of program complexity. Placed on METR's time horizon graph, our result suggests verified software engineering is advancing faster than expected.</p> https://theorem.dev/blog/anthropic-bug-test/ Tue, 07 Oct 2025 00:00:00 +0000 https://theorem.dev/blog/anthropic-bug-test/ <p>Most large projects have a limited compute budget for testing, lest it slows down the CI pipeline. This means missing rare edge cases until customers find them in production.</p> <p>I love formal verification! And I want to bring the power of reasoning about program structure to testing. In this blog post, I will briefly introduce fractional proof decomposition, our new technique that makes testing compute scale logarithmically with bug rarity instead of linearly.</p> <p>As a demo, I&rsquo;ll walk through how this approach would have caught Anthropic&rsquo;s recent <a href="https://www.anthropic.com/engineering/a-postmortem-of-three-recent-issues">approximate top-K bug</a>. Note that we generate these unit tests without relying on the bug reproducer code, using just the high-level specification of top-K sampling.</p>