Related papers: Lean-auto: An Interface between Lean 4 and Automat…
Interactive theorem provers such as Coq are powerful tools to formally guarantee the correctness of software. However, using these tools requires significant manual effort and expertise. While Large Language Models (LLMs) have shown promise…
Generating code from natural-language requirements has become a primary route for LLM-assisted software development. Although LLMs can successfully complete small programming tasks, generating an entire complex project remains unreliable…
Automated theorem proving (ATP) benchmarks largely consist of problems formalized in MathLib, so current ATP training and evaluation are heavily biased toward MathLib's definitional framework. However, frontier mathematics is often…
Large language models (LLMs) have significantly advanced formal theorem proving, yet the scarcity of high-quality training data constrains their capabilities in complex mathematical domains. Combinatorics, a cornerstone of mathematics,…
Can large language models be used to complete mathematical tasks that are traditionally performed either manually or with the aid of theorem provers? To answer this question, a state-of-the-art system, GPT-4, was provided with a concise…
Large-scale formalization projects in Lean rely on blueprints: structured dependency graphs linking informal mathematical exposition to formal declarations. While blueprints are central to human collaboration, existing tooling treats the…
In the recent years, the Metis prover based on ordered paramodulation and model elimination has replaced the earlier built-in methods for general-purpose proof automation in HOL4 and Isabelle/HOL. In the annual CASC competition, the leanCoP…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Large Language Models (LLMs) demonstrate impressive mathematical reasoning abilities, but their solutions frequently contain errors that cannot be automatically checked. Formal theorem proving systems such as Lean 4 offer automated…
The broader goal of this research, on the one hand, is to obtain the State of the Art in Automated Test Production (ATP), to find the open questions and related problems and to track the progress of researchers in the field, and on the…
Large Language Models (LLMs) hold the potential to revolutionize autoformalization. The introduction of Lean4, a mathematical programming language, presents an unprecedented opportunity to rigorously assess the autoformalization…
Nowadays, formal theorem provers have made monumental progress on high-school and competition-level mathematics, but few of them generalize to more advanced mathematics. In this paper, we present REAL-Prover, a new open-source stepwise…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
Proof by induction plays a central role in formal verification. However, its automation remains as a formidable challenge in Computer Science. To solve inductive problems, human engineers often have to provide auxiliary lemmas manually. We…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
LLMs excel at reasoning, but validating their steps remains challenging. Formal verification offers a solution through mechanically checkable proofs. Interactive theorem provers (ITPs) dominate mathematical reasoning but require detailed…
Recent advances in large language models (LLMs) have shown promise in formal theorem proving, yet evaluating semantic correctness remains challenging. Existing evaluations rely on indirect proxies such as lexical overlap with…
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…
Assurance cases (ACs) are structured arguments that support the verification of the correct implementation of systems' non-functional requirements, such as safety and security, thereby preventing system failures which could lead to…