Stories with Tag program verification

• Clean, a formal verification DSL for ZK circuits in Lean4

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  Posted: 2025-03-27 18:33:00

  Verbose tl;dr

  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.

  The blog post "Clean, a formal verification DSL for ZK circuits in Lean4," introduces Clean, a new domain-specific language (DSL) designed for formally verifying zero-knowledge (ZK) circuits using the Lean4 theorem prover. ZK circuits are computational structures used in cryptography to prove the validity of a statement without revealing the underlying data. Verifying these circuits is crucial for ensuring their correctness and security, but existing methods often lack the rigor of formal verification. Clean aims to address this gap by providing a framework for building and verifying ZK circuits with a high degree of assurance.

  The post emphasizes the difficulty of formally verifying ZK circuits due to their complex nature and the need to reason about both low-level details like bit manipulations and high-level cryptographic concepts. Existing approaches often rely on informal methods or specialized tools limited in their expressive power. Clean, however, leverages the power and expressiveness of Lean4, a dependently-typed programming language and proof assistant, to offer a more robust and versatile solution.

  Clean's DSL embeds within Lean4, allowing developers to define circuits using a syntax similar to functional programming. The DSL provides abstractions for common circuit components, such as arithmetic operations, boolean logic, and cryptographic primitives, enabling concise and readable circuit descriptions. Importantly, these circuit descriptions are not merely specifications but executable code that can be compiled to various ZK proof systems. This facilitates a seamless workflow from circuit design to formal verification and deployment.

  A key aspect of Clean is its integration with Lean4's powerful theorem proving capabilities. Developers can formally specify the desired properties of their circuits using Lean4's logic and then construct proofs to demonstrate that these properties hold. This enables verification of various aspects, including circuit correctness, security properties, and even the soundness of the underlying cryptographic protocols. The dependent typing features of Lean4 play a crucial role in ensuring the consistency and completeness of these proofs.

  The blog post showcases a simple example of verifying a Schnorr signature within Clean, demonstrating how to define the circuit, specify the desired properties, and construct a formal proof of its correctness. While the post acknowledges that Clean is still in its early stages of development, it highlights the potential of the approach for improving the security and reliability of ZK circuits. The authors envision Clean as a valuable tool for researchers and developers working with ZK technology, enabling them to build and deploy formally verified ZK circuits with greater confidence. The ultimate goal is to bridge the gap between the theoretical foundations of ZK cryptography and its practical applications, fostering the development of more secure and trustworthy systems.

  • Formal Verification
  • ZK Circuits
  • zero-knowledge proofs
  • Lean4
  • theorem proving
  • domain specific language
  • DSL
  • Cryptography
  • Security
  • Clean Language
  • program verification
  • Automated Reasoning

  Summary of Comments ( 2 )
  https://news.ycombinator.com/item?id=43496577

  Verbose tl;dr

  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.

  The Hacker News post titled "Clean, a formal verification DSL for ZK circuits in Lean4" (https://news.ycombinator.com/item?id=43496577) has a moderate number of comments discussing various aspects of the project and its implications.

  Several commenters express enthusiasm for the use of Lean4, highlighting its potential for rigorous formal verification in the zero-knowledge proof space. They see the project as a positive step toward improving the security and reliability of ZK circuits. One commenter specifically praises the choice of Lean4 over other theorem provers, mentioning its speed and the active development community. This sentiment is echoed by another commenter who appreciates the metaprogramming capabilities of Lean4, suggesting it's a good fit for this kind of DSL development.

  There's a discussion around the practicality and usability of formal verification for ZK circuits. One commenter questions the scalability of this approach for larger, real-world circuits, wondering if the proof development overhead becomes too significant. Another commenter points out the inherent complexity of formally verifying cryptographic primitives and protocols, acknowledging the challenge but emphasizing the importance of this work for ensuring security.

  The conversation also touches upon the trade-offs between different formal verification approaches. One commenter contrasts the Lean4-based approach with other methods like Coq, highlighting potential benefits and drawbacks of each. They discuss the potential for integrating with existing tools and frameworks within the ZK ecosystem.

  Some commenters delve into more technical details, discussing the specific features of Lean4 that make it well-suited for this task, such as dependent types and its metaprogramming system. They also discuss the challenges of representing ZK circuits within a formal system and the potential for automated proof generation.

  Finally, there's a thread discussing the broader implications of formal verification in the context of blockchain technology and smart contracts. Commenters acknowledge the growing need for robust security guarantees in these systems and see projects like Clean as important contributions towards achieving this goal. One commenter expresses excitement about the potential for formally verified ZK circuits to enable more complex and secure smart contract applications.

• Long division verified via Hoare logic

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  Posted: 2025-02-26 16:15:17

  Verbose tl;dr

  The blog post details a formal verification of the standard long division algorithm using the Dafny programming language and its built-in Hoare logic capabilities. It walks through the challenges of representing and reasoning about the algorithm within this formal system, including defining loop invariants and handling edge cases like division by zero. The core difficulty lies in proving that the quotient and remainder produced by the algorithm are indeed correct according to the mathematical definition of division. The author meticulously constructs the necessary pre- and post-conditions, and elaborates on the specific insights and techniques required to guide the verifier to a successful proof. Ultimately, the post demonstrates the power of formal methods to rigorously verify even relatively simple, yet subtly complex, algorithms.

  The blog post "Long story of division" details a rigorous verification of the long division algorithm using Hoare logic. The author meticulously demonstrates how to prove the correctness of this fundamental arithmetic operation, a process more complex than its commonplace usage might suggest. The post begins by acknowledging the seemingly trivial nature of long division, a procedure learned early in education, yet highlights the underlying logical intricacies that often go unnoticed. It then introduces Hoare logic as the chosen verification method, explaining its basic principles: preconditions, postconditions, and loop invariants. These concepts form the framework for guaranteeing that a program, or in this case an algorithm, behaves as intended.

  The core of the post delves into the specific application of Hoare logic to the long division algorithm. The author carefully constructs a loop invariant – a condition that holds true before, during, and after each iteration of the division loop – which captures the essence of the algorithm's progressive refinement of the quotient. This invariant, expressed mathematically, relates the dividend, divisor, current quotient, and remainder at each step. The post rigorously demonstrates that this invariant is preserved across all iterations, proving that the algorithm correctly computes the quotient and remainder.

  The argument proceeds step-by-step through the long division process, mirroring the manual calculation one might perform with pencil and paper. Each stage of the division – from bringing down the next digit of the dividend to subtracting the product of the divisor and the current quotient digit – is formalized within the Hoare logic framework. Preconditions and postconditions are established for each step, and the preservation of the loop invariant is meticulously verified. This detailed approach ensures that no aspect of the algorithm's operation is left unchecked.

  The author further explains how the initial condition before the loop begins and the final condition after the loop terminates are connected by the carefully constructed loop invariant. This connection provides the crucial link that demonstrates the overall correctness of the long division algorithm. By establishing that the invariant holds throughout the process and connects the initial and final states, the proof guarantees that the final quotient and remainder are indeed the correct results of the division operation. The post concludes by having successfully proven the correctness of the long division algorithm using formal methods, highlighting the power of Hoare logic to provide rigorous assurance even for seemingly simple procedures. This detailed verification process showcases how formal methods can be applied to ensure the reliability of fundamental algorithms.

  • long division
  • Hoare logic
  • program verification
  • formal methods
  • mathematics
  • Computer Science
  • algorithms
  • proofs
  • verification
  • software engineering

  Summary of Comments ( 1 )
  https://news.ycombinator.com/item?id=43185059

  Verbose tl;dr

  Hacker News users discussed the application of Hoare logic to verify long division, with several expressing appreciation for the clear explanation and visualization of the algorithm. Some commenters debated the practical benefits of formal verification for such a well-established algorithm, questioning the likelihood of uncovering unknown bugs. Others highlighted the educational value of the exercise, emphasizing the importance of understanding foundational algorithms. A few users delved into the specifics of the chosen proof method and its implications. One commenter suggested exploring alternative verification approaches, while another pointed out the potential for applying similar techniques to other arithmetic operations.

  The Hacker News post "Long division verified via Hoare logic" discussing the article about verifying long division using Hoare logic sparked a small but focused conversation. Several commenters express appreciation for the clear explanation of both Hoare logic and its application to a concrete example like long division. One commenter highlights the pedagogical value of such demonstrations, suggesting it's a good way to teach people about formal verification methods. They appreciate the author's approach of starting with a simple example and gradually introducing complexities, making the concepts more accessible.

  Another commenter delves into the practical implications, pondering whether such verified algorithms could find their way into real-world applications like optimizing compilers. They acknowledge the potential benefits of guaranteed correctness for critical operations like division, especially in performance-sensitive contexts.

  A different user questions the choice of long division as the example, wondering if simpler algorithms might have served the illustrative purpose equally well while requiring less intricate proofs. This commenter suggests that the complexity of the long division algorithm might overshadow the core principles of Hoare logic being demonstrated.

  Finally, a comment points out the historical context, mentioning Edsger W. Dijkstra's early work on formal program verification and how the article's approach aligns with Dijkstra's vision. This comment connects the present work to the foundational ideas in the field.

  Overall, the comments demonstrate a positive reception of the article, praising its clarity and educational value. The discussion also touches upon practical considerations and historical context, enriching the understanding of the presented work.