Related papers: PaMpeR: Proof Method Recommendation System for Isa…
We introduce Prove-It, a Python-based general-purpose interactive theorem-proving assistant designed with the goal of making formal theorem proving as easy and natural as informal theorem proving (with moderate training). Prove-It uses a…
For a considerable number of software projects, the creation of effective test cases is hindered by design documentation that is either lacking, incomplete or obsolete. The exploratory testing approach can serve as a sound method in such…
Assurance cases are often required to certify critical systems. The use of formal methods in assurance can improve automation, increase confidence, and overcome errant reasoning. However, assurance cases can never be fully formalised, as…
In logical reasoning, it is often the case that only some of a collection of assumptions are needed to reach a conclusion. A strengthening lemma is an assertion that a given conclusion is independent in this sense of a particular…
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…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
In many statistical applications, particularly in clinical studies, hypotheses may carry different levels of importance, motivating the use of weighted multiple testing procedures (wMTPs) to control the familywise error rate (FWER). Among…
The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not…
We present a tool called HHLPar for verifying hybrid systems modelled in Hybrid Communicating Sequential Processes (HCSP). HHLPar is built upon a Hybrid Hoare Logic for HCSP, which is able to reason about continuous-time properties of…
Type annotations are essential when printing terms in a way that preserves their meaning under reparsing and type inference. We study the problem of complete and minimal type annotations for rank-one polymorphic $\lambda$-calculus terms, as…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
In this article we present an ongoing effort to formalise quantum algorithms and results in quantum information theory using the proof assistant Isabelle/HOL. Formal methods being critical for the safety and security of algorithms and…
Model execution allows us to prototype and analyse software engineering models by stepping through their possible behaviours, using techniques like animation and simulation. On the other hand, deductive verification allows us to construct…
Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…
This paper explores verification of constituent systems within the context of the Symphony tool platform for Systems of Systems (SoS). Our SoS modelling language, CML, supports various contractual specification elements, such as state…
This article presents a pattern-based language designed to select (a set of) subterms of a given term in a concise and robust way. Building on this language, we implement a single-step rewriting tactic in the Isabelle theorem prover, which…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…
We report on our formalization of matrix-interpretation in Isabelle/HOL. Matrices are required to certify termination proofs and we wish to utilize them for complexity proofs, too. For the latter aim, only basic methods have already been…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…