相关论文: Certified HLints with Isabelle/HOLCF-Prelude

Language models (LMs) hallucinate. We inquire: Can we detect and mitigate hallucinations before they happen? This work answers this research question in the positive, by showing that the internal representations of LMs provide rich signals…

Large Language Models (LLMs) are reported to hold undesirable attestation bias on inference tasks: when asked to predict if a premise P entails a hypothesis H, instead of considering H's conditional truthfulness entailed by P, LLMs tend to…

We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…

We present an Isabelle/HOL formalization of a characterization of confluence for quasi-reductive strongly deterministic conditional term rewrite systems, due to Avenhaus and Lor\'ia-S\'aenz.

We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that integrates large language models as reasoning assistants…

Automatic software verifiers have become increasingly effective at the task of checking software against (formal) specifications. Yet, their adoption in practice has been hampered by the lack of such specifications in real world code. Large…

This paper proposes a natural language translation method for machine-verifiable formal proofs that leverages the informalization (verbalization of formal language proof steps) and summarization capabilities of LLMs. For evaluation, it was…

If a code base is so big and complicated that complete mechanical verification is intractable, can we still apply and benefit from verification methods? We show that by allowing a deliberate mechanized formalization gap we can shrink and…

Large Language Models (LLMs) excel in fluency but risk producing inaccurate content, called "hallucinations." This paper outlines a standardized process for categorizing fine-grained hallucination types and proposes an innovative…

We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As…

We present a method for automatic inference of conditions on the initial states of a program that guarantee that the safety assertions in the program are not violated. Constrained Horn clauses (CHCs) are used to model the program and…

A principled approach to the design of program verification and con- struction tools is applied to separation logic. The control flow is modelled by power series with convolution as separating conjunction. A generic construction lifts…

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about…

Linear programming describes the problem of optimising a linear objective function over a set of constraints on its variables. In this paper we present a solver for linear programs implemented in the proof assistant Isabelle/HOL. This…

New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In…

As Large Language Models (LLMs) have advanced, they have brought forth new challenges, with one of the prominent issues being LLM hallucination. While various mitigation techniques are emerging to address hallucination, it is equally…

Verification of higher-order probabilistic programs is a challenging problem. We present a verification method that supports several quantitative properties of higher-order probabilistic programs. Usually, extending verification methods to…

Despite the recent breakthroughs achieved by Large Vision Language Models (LVLMs) in understanding and responding to complex visual-textual contexts, their inherent hallucination tendencies limit their practical application in real-world…

Hidden Markov Models (HMMs) are foundational tools for modeling sequential data with latent Markovian structure, yet fitting them to real-world data remains computationally challenging. In this work, we show that pre-trained large language…

Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just…