Related papers: SeCaV: A Sequent Calculus Verifier in Isabelle/HOL
Combining higher-order abstract syntax and (co)induction in a logical framework is well known to be problematic. Previous work described the implementation of a tool called Hybrid, within Isabelle HOL, which aims to address many of these…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to de-Bruijn indices). In…
Assurance cases are often required as a means to certify a critical system. Use of formal methods in assurance can improve automation, and overcome problems with ambiguity, faulty reasoning, and inadequate evidentiary support. However,…
Proof assistants are computer softwares that allow us to write mathematical proofs so as to assess their correctness. In November 2021, I started the project of checking the simplicity of the alternating groups within the Lean theorem…
Human beings learn and accumulate hierarchical knowledge over their lifetime. This knowledge is associated with previous concepts for consolidation and hierarchical construction. However, current incremental learning methods lack the…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
Smart contracts manage a large number of digital assets nowadays. Bugs in these contracts have led to significant financial loss. Verifying the correctness of smart contracts is, therefore, an important task. This paper presents an…
We see how nested sequents, a natural generalisation of hypersequents, allow us to develop a systematic proof theory for modal logics. As opposed to other prominent formalisms, such as the display calculus and labelled sequents, nested…
OnlineProver is an interactive proof assistant tailored for the educational setting. Its main features include a user-friendly interface for editing and checking proofs. The user interface provides feedback directly within the derivation,…
In this paper, we introduce a general family of sequent-style calculi over the modal language and its fragments to capture the essence of all constructively acceptable systems. Calling these calculi \emph{constructive}, we show that any…
Informal arguments that cryptographic protocols are secure can be made rigorous using inductive definitions. The approach is based on ordinary predicate calculus and copes with infinite-state systems. Proofs are generated using…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Albeit being a central notion of every programming language, formally and modularly reasoning about iteration proves itself to be a non-trivial feat, specially in the context of higher-order iteration. In this paper, we present a generic…
Isabelle/HOL augments classical higher-order logic with ad-hoc overloading of constant definitions---that is, one constant may have several definitions for non-overlapping types. In this paper, we present a mechanised proof that HOL with…
Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof…
Sarcasm detection is a crucial yet challenging Natural Language Processing task. Existing Large Language Model methods are often limited by single-perspective analysis, static reasoning pathways, and a susceptibility to hallucination when…
Simulation and formal verification are important complementary techniques necessary in high assurance model-based systems development. In order to support coherent results, it is necessary to provide unifying semantics and automation for…
In systems verification we are often concerned with multiple, inter-dependent properties that a program must satisfy. To prove that a program satisfies a given property, the correctness of intermediate states of the program must be…