Related papers: Developments in Formal Proofs
In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of…
This paper expands upon the finite state machine approach for the formal analysis of digital evidence. The proposed method may be used to support the feasibility of a given statement by testing it against a relevant system model. To achieve…
We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable…
This paper describes a formal theory of smooth vector fields, Lie groups and the Lie algebra of a Lie group in the theorem prover Isabelle. Lie groups are abstract structures that are composable, invertible and differentiable. They are…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous…
We present a simple and concise semantics for temporal planning. Our semantics are developed and formalised in the logic of the interactive theorem prover Isabelle/HOL. We derive from those semantics a validation algorithm for temporal…
This position paper provides a critical but constructive discussion of current practices in benchmarking and evaluative practices in the field of formal reasoning and automated theorem proving. We take the position that open code, open…
The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…
Recent advances in automated theorem proving use Large Language Models (LLMs) to translate informal mathematical statements into formal proofs. However, informal cues are often ambiguous or lack strict logical structure, making it hard for…
Capitalizing on previous encodings and formal developments about nominal calculi and type systems, we propose a weak Higher-Order Abstract Syntax formalization of the type language of pure System F<: within Coq, a proof assistant based on…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Modern separation logics allow one to prove rich properties of intricate code, e.g. functional correctness and linearizability of non-blocking concurrent code. However, this expressiveness leads to a complexity that makes these logics…
We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and…
Proof engineering is notoriously labor-intensive: proofs that are straightforward on paper often require lengthy scripts in theorem provers. Recent advances in large language models (LLMs) create new opportunities for proof automation:…
Description Logics (DLs) are a family of languages used for the representation and reasoning on the knowledge of an application domain, in a structured and formal manner. In order to achieve this objective, several provers, such as RACER…
In this article we describe the formalisation of the Bruhat-Tits tree - an important tool in modern number theory - in the Lean Theorem Prover. Motivated by the goal of connecting to ongoing research, we apply our formalisation to verify a…
The algebraic properties of the combination of probabilistic choice and nondeterministic choice have long been a research topic in program semantics. This paper explains a formalization in the Coq proof assistant of a monad equipped with…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
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…