Verus is a Rust verification framework designed for low-level systems programming. It extends Rust with features like specifications (preconditions, postconditions, and invariants) and data-race freedom proofs, allowing developers to formally verify the correctness and safety of their code. Verus integrates with existing Rust tools and aims to be practical for real-world systems development, leveraging SMT solvers to automate the verification process. It specifically targets areas like cryptography, operating systems kernels, and concurrent data structures, where rigorous correctness is paramount.
Clean is a new domain-specific language (DSL) built in Lean 4 for formally verifying zero-knowledge circuits. It aims to bridge the gap between circuit development and formal verification by offering a high-level, functional programming style for defining circuits, along with automated proofs of correctness within Lean's powerful theorem prover. Clean compiles to the intermediate representation used by the Circom zk-SNARK toolkit, enabling practical deployment of verified circuits. This approach allows developers to write circuits in a clear, maintainable way, and rigorously prove that these circuits correctly implement the desired logic, enhancing security and trust in zero-knowledge applications. The DSL includes features like higher-order functions and algebraic data types, enabling more expressive and composable circuit design than existing tools.
Several Hacker News commenters praise Clean's innovative approach to verifying zero-knowledge circuits, appreciating its use of Lean4 for formal proofs and its potential to improve the security and reliability of ZK systems. Some express excitement about Lean4's dependent types and metaprogramming capabilities, and how they might benefit the project. Others raise practical concerns, questioning the performance implications of using a theorem prover for this purpose, and the potential difficulty of debugging generated circuits. One commenter questions the comparison to other frameworks like Noir and Arkworks, requesting clarification on the specific advantages of Clean. Another points out the relative nascency of formal verification in the ZK space, emphasizing the need for further development and exploration. A few users also inquire about the tooling and developer experience, wondering about the availability of IDE support and debugging tools for Clean.
Niri is a new programming language designed for building distributed systems. It aims to simplify concurrent and parallel programming by introducing the concept of "isolated objects" which communicate via explicit message passing, eliminating shared mutable state and thus avoiding data races and other concurrency bugs. This approach, coupled with automatic memory management and a focus on performance, makes Niri suitable for developing robust and efficient distributed applications, potentially replacing complex actor models or other concurrency paradigms. The language is still under development, but shows promise for streamlining the creation of complex distributed systems.
Hacker News users discussed Niri's potential, focusing on its novel approach to UI design. Several commenters expressed excitement about the demo, praising its speed and the innovative concept of manipulating data directly within the interface. Concerns were raised about the practicality of text-based interaction for complex tasks and the potential learning curve. Some questioned the long-term viability of relying solely on a keyboard-driven interface, while others saw it as a powerful tool for experienced users. The discussion also touched upon comparisons to other tools like spreadsheets and the potential benefits for specific use cases like data analysis and programming. Some users expressed skepticism, finding the current implementation limited and wanting to see more concrete examples of its capabilities.
This paper explores using first-order logic (FOL) to detect logical fallacies in natural language arguments. The authors propose a novel approach that translates natural language arguments into FOL representations, leveraging semantic role labeling and a defined set of predicates to capture argument structure. This structured representation allows for the application of automated theorem provers to evaluate the validity of the arguments, thus identifying potential fallacies. The research demonstrates improved performance compared to existing methods, particularly in identifying fallacies related to invalid argument structure, while acknowledging limitations in handling complex linguistic phenomena and the need for further refinement in the translation process. The proposed system provides a promising foundation for automated fallacy detection and contributes to the broader field of argument mining.
Hacker News users discussed the potential and limitations of using first-order logic (FOL) for fallacy detection as described in the linked paper. Some praised the approach for its rigor and potential to improve reasoning in AI, while also acknowledging the inherent difficulty of translating natural language to FOL perfectly. Others questioned the practical applicability, citing the complexity and ambiguity of natural language as major obstacles, and suggesting that statistical/probabilistic methods might be more robust. The difficulty of scoping the domain knowledge necessary for FOL translation was also brought up, with some pointing out the need for extensive, context-specific knowledge bases. Finally, several commenters highlighted the limitations of focusing solely on logical fallacies for detecting flawed reasoning, suggesting that other rhetorical tactics and nuances should also be considered.
This paper explores the potential of Large Language Models (LLMs) as tools for mathematicians. It examines how LLMs can assist with tasks like generating conjectures, finding proofs, simplifying expressions, and translating between mathematical formalisms. While acknowledging current limitations such as occasional inaccuracies and a lack of deep mathematical understanding, the authors demonstrate LLMs' usefulness in exploring mathematical ideas, automating tedious tasks, and providing educational support. They argue that future development focusing on formal reasoning and symbolic computation could significantly enhance LLMs' capabilities, ultimately leading to a more symbiotic relationship between mathematicians and AI. The paper also discusses the ethical implications of using LLMs in mathematics, including concerns about plagiarism and the potential displacement of human mathematicians.
Hacker News users discussed the potential for LLMs to assist mathematicians, but also expressed skepticism. Some commenters highlighted LLMs' current weaknesses in formal logic and rigorous proof construction, suggesting they're more useful for brainstorming or generating initial ideas than for producing finalized proofs. Others pointed out the importance of human intuition and creativity in mathematics, which LLMs currently lack. The discussion also touched upon the potential for LLMs to democratize access to mathematical knowledge and the possibility of future advancements enabling more sophisticated mathematical reasoning by AI. There was some debate about the specific examples provided in the paper, with some users questioning their significance. Overall, the sentiment was cautiously optimistic, acknowledging the potential but emphasizing the limitations of current LLMs in the field of mathematics.
This article dissects the structure of a formal mathematical proof, illustrating it with a simple example about even and odd numbers. It emphasizes the distinction between informal proofs aimed at human understanding and formal proofs designed for automated verification. Formal proofs meticulously lay out every logical step, referencing specific axioms and inference rules within a chosen formal system. This detailed approach, while tedious for humans, enables computer-assisted verification and eliminates ambiguity, ensuring absolute rigor. The article highlights the importance of choosing appropriate axioms and the role of proof assistants in constructing and checking these complex formal structures, ultimately increasing confidence in mathematical results.
HN commenters discuss the accessibility of formal proof systems, particularly referencing Lean. Some express excitement about the potential of formal proofs to revolutionize mathematics, while others are more skeptical, citing the steep learning curve and questioning the practical benefits for most mathematicians. Several commenters debate the role of intuition versus rigor in mathematical practice, with some arguing that formalization can enhance understanding and others suggesting it might stifle creativity. The feasibility of formalizing existing mathematical knowledge is also discussed, with varying opinions on the timescale and resources required for such a project. Some users highlight the potential of AI in assisting with formalization efforts, while others remain cautious about its current capabilities. The overall tone is one of cautious optimism, acknowledging the challenges but also recognizing the potential transformative power of formal proof systems.
Dusa is a logic programming language based on finite-choice logic, designed for declarative problem solving and knowledge representation. It emphasizes simplicity and approachability, with a Python-inspired syntax and built-in support for common data structures like lists and dictionaries. Dusa programs define relationships between facts and rules, allowing users to describe problems and let the system find solutions. Its core features include backtracking search, constraint satisfaction, and a type system based on logical propositions. Dusa aims to be both a practical tool for everyday programming tasks and a platform for exploring advanced logic programming concepts.
Hacker News users discussed Dusa's novel approach to programming with finite-choice logic, expressing interest in its potential for formal verification and constraint solving. Some questioned its practicality and performance compared to established Prolog implementations, while others highlighted the benefits of its clear semantics and type system. Several commenters drew parallels to miniKanren, another logic programming language, and discussed the trade-offs between Dusa's finite-domain focus and the more general approach of Prolog. The static typing and potential for compile-time optimization were seen as significant advantages. There was also a discussion about the suitability of Dusa for specific domains like game AI and puzzle solving. Some expressed skepticism about the claim of "blazing fast performance," desiring benchmarks to validate it. Overall, the comments reflected a mixture of curiosity, cautious optimism, and a desire for more information, particularly regarding real-world applications and performance comparisons.
Rishi Mehta reflects on the key contributions and learnings from AlphaProof, his AI research project focused on automated theorem proving. He highlights the successes of AlphaProof in tackling challenging mathematical problems, particularly in abstract algebra and group theory, emphasizing its unique approach of combining language models with symbolic reasoning engines. The post delves into the specific techniques employed, such as the use of chain-of-thought prompting and iterative refinement, and discusses the limitations encountered. Mehta concludes by emphasizing the significant progress made in bridging the gap between natural language and formal mathematics, while acknowledging the open challenges and future directions for research in automated theorem proving.
Hacker News users discuss AlphaProof's approach to testing, questioning its reliance on property-based testing and mutation testing for catching subtle bugs. Some commenters express skepticism about the effectiveness of these techniques in real-world scenarios, arguing that they might not be as comprehensive as traditional testing methods and could lead to a false sense of security. Others suggest that AlphaProof's methodology might be better suited for specific types of problems, such as concurrency bugs, rather than general software testing. The discussion also touches upon the importance of code review and the potential limitations of automated testing tools. Some commenters found the examples provided in the original article unconvincing, while others praised AlphaProof's innovative approach and the value of exploring different testing strategies.
Summary of Comments ( 30 )
https://news.ycombinator.com/item?id=43745987
Hacker News users discussed Verus's potential and limitations. Some expressed excitement about its ability to verify low-level code, seeing it as a valuable tool for critical systems. Others questioned its practicality, citing the complexity of verification and the potential for performance overhead. The discussion also touched on the trade-offs between verification and traditional testing, with some arguing that testing remains essential even with formal verification. Several comments highlighted the challenge of balancing the strictness of verification with the flexibility needed for practical systems programming. Finally, some users were curious about Verus's performance characteristics and its suitability for real-world projects.
The Hacker News post "Verus: Verified Rust for low-level systems code" (https://news.ycombinator.com/item?id=43745987) has generated several comments discussing various aspects of the Verus verification system for Rust.
Several commenters express interest in the project and its potential. One notes the significance of bringing verification tools to a language like Rust, which is gaining traction in systems programming, suggesting it could lead to more robust and reliable systems. Another appreciates the focus on low-level code, acknowledging the challenge of verification in this domain and hoping for positive outcomes. Someone also mentions the potential of combining Verus with other Rust-based verification efforts for a comprehensive solution.
Some discussion revolves around the practicality and usability of formal verification tools. One commenter highlights the steep learning curve associated with formal verification, suggesting that broader adoption hinges on simplifying the process. Another expresses concern about the potential for proofs to become overly complex and difficult to manage, particularly in large projects. There's also a question about the performance overhead introduced by verification and whether it's acceptable for performance-sensitive applications.
The integration of Verus with existing Rust development workflows is another topic of discussion. A commenter inquires about IDE support for Verus, specifically within Visual Studio Code, emphasizing the importance of tooling for practical use. Another raises the point that effective verification often requires significant changes to coding style and project structure, potentially impacting development practices.
A few comments delve into the technical details of Verus. One commenter mentions the use of SMT solvers (Satisfiability Modulo Theories) and their role in the verification process. Another asks about the specific logic used by Verus, such as higher-order logic or separation logic. There's also a comment inquiring about the handling of concurrency and parallelism in Verus, recognizing the challenges of verifying concurrent code.
Finally, a commenter points out the connection between Verus and the Dafny verification system, suggesting that Verus builds upon some of the concepts and ideas from Dafny. They express curiosity about the differences and improvements introduced by Verus.
In summary, the comments reflect a mixture of enthusiasm, cautious optimism, and pragmatic concerns about the challenges of integrating formal verification into real-world Rust projects. They touch upon topics ranging from usability and tooling to technical aspects of the verification process and its potential impact on performance and development workflows.