Bend 2: a fast language that blocks AI mistakes via proof. Install: curl -fsSL https://bend-lang.com/install.sh | sh
bendlang/bend
Bend 2: a fast language that blocks AI mistakes via proof. Install: curl -fsSL https://bend-lang.com/install.sh | sh
bend/paper/BendTT.pdf at main · bendlang/bend
Bend 2: a fast language that blocks AI mistakes via proof. Install: curl -fsSL https://bend-lang.com/install.sh | sh - bendlang/bend
Palomar – a registry of Lean verified mathematics
In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking tha…
GNU and the AI reimplementations - <antirez>
goose | Your open source AI agent
Your native open source AI agent. Desktop app, CLI, and API — for code, workflows, and everything in between.
goose | Your open source AI agent
Your native open source AI agent. Desktop app, CLI, and API — for code, workflows, and everything in between.
Advancing Mathematics Research with AI-Driven Formal Proof Search
Large language models (LLMs) increasingly excel at mathematical reasoning, but their unreliability limits their utility in mathematics research. A mitigation is using LLMs to generate formal proofs in languages like Lean. We perform the first large-scale evaluation of this method's ability to solve open problems. Our most capable agent autonomously resolved 9 of 353 open Erdős problems at the per-problem cost of a few hundred dollars, proved 44/492 OEIS conjectures, and is being deployed in combinatorics, optimization, graph theory, algebraic geometry, and quantum optics research. A basic agent alternating LLM-based generation with Lean-based verification replicated the Erdős successes but proved costlier on the hardest problems. These findings demonstrate the power of AI-aided formal proof search and shed light on the agent designs that enable it.
Prove2Me: An Open Collaborative Platform for Scaling Math Formalization
Proof assistants such as Lean 4 promise the paradigm of formally verified mathematics, but large-scale formalization projects have faced major barriers to entry, including the need for expertise in formal verification (as well as the underlying mathematics) and the significant time required for writing formal proofs. AI coding agents have dramatically reduced these barriers; human users can now use natural language to prompt agents to write complex proofs in Lean. This opens up the intriguing possibility of internet-scale mathematical collaboration involving both humans and AI agents, where correctness is machine-checked. To realize this possibility, we introduce Prove2Me (https://prove2.me), an open collaborative platform for formalizing mathematics. Users launch formalization "missions", to which AI agents contribute formal proofs toward completion. We designed mechanisms and a specialized harness in Prove2Me that enable large-scale collaboration so that agents can build on one another's work and freely reuse existing results. In doing so, Prove2Me aims to turn math formalization into a scalable, crowd-sourced effort open to anyone with an agent.
Towards autonomous biology: Compiler-Verified Protocols as a Foundation for Real-World AI Execution
Artificial intelligence has advanced from analyzing experimental data to autonomously generating hypotheses, designing experiments, and coordinating closed loop discovery. Yet the translation from computational reasoning to physical execution remains bottlenecked by the experimental protocol, which in biology still relies on ambiguous natural-language descriptions: a medium other engineering disciplines abandoned decades ago in favor of compiler verified specification languages. This deficit fragments reproducibility along three axes: protocol accuracy, pre execution verification, and cross platform portability. Existing formalisms address only subsets of these challenges, trading expressiveness for rigor, portability for standardization, or usability for provenance. Here we introduce the Biology Protocol Language (BPL), a domain specific language with a biology-native type system in which every quantity carries physical units, every reagent declares its physical form, and every container maintains compiler-tracked state, so that implicit assumptions must be stated explicitly and physically impossible operations are rejected at compile time. We further develop BPL-COGEN, a pipeline that couples a fine tuned 30 billion parameter language model with the deterministic compiler in a closed generate validate repair loop, iteratively correcting the translation from natural language SOPs to BPL through compiler diagnostics until all physical, dimensional, and state constraints are satisfied. On a benchmark of 300 published Nature Protocols papers, BPL COGEN achieved an overall fidelity score of 95.1 against the source protocols as ground truth. Wet-lab experiment and cross-platform validation in GFP expression library construction and HPLC to UHPLC method translation confirmed that a single BPL source yielded reproducible execution across manual and liquid handler assisted contexts. The results established a novel pipeline that generates compiler-verified protocols, which is an essential prerequisite for physically embodied AI in biology.
Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs
Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations. In this process, an AI system translates the text from a natural language (NL) into a formal language such as Lean. Once this translation is done, the argument expressed in the formal language can easily be mechanically verified. The purpose of this article is to demonstrate why this process may offer no confidence in the original NL argument, owing to the various difficulties in performing the translation semantically faithfully. In particular, we highlight that the problem of resolving ambiguities in mathematical NL text, which is necessary in order to provide semantically faithful translation, is arbitrarily high up in the Solvability Complexity Index (SCI) hierarchy/arithmetical hierarchy (the SCI $= \infty$). Hence, informally, providing semantically faithful AI autoformalisation is harder than any computational problem including the Halting problem (which has SCI $= 1$). To demonstrate the effect of this result we provide several examples of AI mistranslations of NL statements and proofs into Lean in practice, resulting in mismatches between NL proofs and their Lean `verifications'. These include OpenAI's announced Navier-Stokes proof. In particular, we show that the formalised Lean proof does not correspond to the NL proof of blow-up of solutions to the Navier-Stokes equations.
Taelin on Twitter / X
RELEASE DAYAfter almost 10 years of hard work, tireless research, and a dive deep into the kernels of computer science, I finally realized a dream: running a high-level language on GPUs. And I'm giving it to the world!Bend compiles modern programming features, including:-… pic.twitter.com/Q2tcH8Q6nq— Taelin (@VictorTaelin) May 16, 2024
