Related papers: Metamath Zero: The Cartesian Theorem Prover
The recent development of fact verification systems with natural logic has enhanced their explainability by aligning claims with evidence through set-theoretic operators, providing faithful justifications. Despite these advancements, such…
Neural theorem proving has advanced rapidly in the past year, reaching IMO gold-medalist capabilities and producing formal proofs that span thousands of lines. Although such proofs are mechanically verified by formal systems like Lean,…
The problem of mechanically formalizing and proving metatheoretic properties of programming language calculi, type systems, operational semantics, and related formal systems has received considerable attention recently. However, the dual…
We introduce a technology to formally verify that a software system satisfies a temporal specification of functional correctness, without revealing the system itself. Our method combines a deductive approach to model checking to obtain a…
Zero-knowledge proofs allow verification of computations without revealing private information. However, existing systems require memory proportional to the computation size, which has historically limited use in large-scale applications…
By a pure logical framework we mean a framework which does not rely on any particular formal calculus. For example, Metamath is an instance of a pure logical framework. Another example is the Russell system…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
We introduce Meta-F*, a tactics and metaprogramming framework for the F* program verifier. The main novelty of Meta-F* is allowing the use of tactics and metaprogramming to discharge assertions not solvable by SMT, or to just simplify them…
Reliable verification of proofs remains a bottleneck for training and evaluating AI systems on hard mathematical reasoning. Fully formal proofs, in languages like Lean, are easy to verify because they are unambiguous and modular. Most…
Large language models are often adapted through parameter efficient fine tuning, but current release practices provide weak assurances about what data were used and how updates were computed. We present Verifiable Fine Tuning, a protocol…
Unlike some other formal systems, the proof system Metamath has no built-in concept of "decimal number" in the sense that arbitrary digit strings are not recognized by the system without prior definition. We present a system of theorems and…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
Static verification relying on an automated theorem prover can be very slow and brittle: since static verification is undecidable, correct code may not pass a particular static verifier. In this work we use metaprogramming to generate code…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
With the rise of machine learning techniques, ensuring the fairness of decisions made by machine learning algorithms has become of great importance in critical applications. However, measuring fairness often requires full access to the…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…