Related papers: Interactive Simplifier Tracing and Debugging in Is…
We significantly improve the performance of the E automated theorem prover on the Isabelle Sledgehammer problems by combining learning and theorem proving in several ways. In particular, we develop targeted versions of the ENIGMA guidance…
Proof competence, i.e. the ability to write and check (mathematical) proofs, is an important skill in Computer Science, but for many students it represents a difficult challenge. The main issues are the correct use of formal language and…
Recent advances in Large Language Models have led to Large Reasoning Models, which produce step-by-step reasoning traces. These traces offer insight into how models think and their goals, improving explainability and helping users follow…
Auto2 is a recently introduced prover for the proof assistant Isabelle. It is designed to be both highly customizable from within Isabelle, and also have a powerful proof search mechanism. In this paper, we apply auto2 to the verification…
We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA. In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to…
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…
The Isabelle Archive of Formal Proofs (AFP) has grown to over 500 articles in late 2019. Meanwhile, finding formalizations in it has not exactly become easier. At the time of writing, the site-specific AFP google search and the Isabelle…
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…
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,…
A large class of data questions can be modeled as identifying important slices of data driven by user defined metrics. This paper presents TRACE, a Time-Relational Approximate Cubing Engine that enables interactive analysis on such slices…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
In this paper, we propose the use of interactive theorem proving for explainable machine learning. After presenting our proposition, we illustrate it on the dedicated application of explaining security attacks using the Isabelle…
Exploring data relations across multiple views has been a common task in many domains such as bioinformatics, cybersecurity, and healthcare. To support this, various techniques (e.g., visual links and brushing and linking) are used to show…
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
We present a novel iterative, edit-based approach to unsupervised sentence simplification. Our model is guided by a scoring function involving fluency, simplicity, and meaning preservation. Then, we iteratively perform word and phrase-level…
Although modern recommendation systems can exploit the structure in users' item feedback, most are powerless in the face of new users who provide no structure for them to exploit. In this paper we introduce ImplicitCE, an algorithm for…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
Systematic reviews provide comprehensive syntheses of research fields. As a result, systematic reviews often emphasize synthesizing across the large bodies of literature rather than just describing the studies from which the conclusions…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider…
Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…