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Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…
This paper contains a discussion of a library of formalized mathematics for the proof assistant Coq which the author worked on in 2011-13.
Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…
The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when…
In this paper, we study two variations of the time discrete Taylor schemes for rough differential equations and for stochastic differential equations driven by fractional Brownian motions. One is the incomplete Taylor scheme which excludes…
Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial…
What research can be pursued with small models trained to complete true programs? Typically, researchers study program synthesis via large language models (LLMs) which introduce issues such as knowing what is in or out of distribution,…
We propose an automated verification technique for hypersafety properties, which express sets of valid interrelations between multiple finite runs of a program. The key observation is that constructing a proof for a small representative set…
Turing progressions have been often used to measure the proof-theoretic strength of mathematical theories. Turing progressions based on $n$-provability give rise to a $\Pi_{n+1}$ proof-theoretic ordinal. As such, to each theory $U$ we can…
Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…
Reliably knowing when a language model is correct is almost as important as being correct. We introduce prover-verifier deliberation (PVD), an inference-time protocol grounded in interactive proof theory, as a mechanism for selective…
Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for…
Formal theorem proving (FTP) has emerged as a critical foundation for evaluating the reasoning capabilities of large language models, enabling automated verification of mathematical proofs at scale. However, progress has been constrained by…
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…
Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to…
The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof…
This paper describes the Automated Reasoning for Mizar (MizAR) service, which integrates several automated reasoning, artificial intelligence, and presentation tools with Mizar and its authoring environment. The service provides ATP…
Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification, by learning from…