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Proof assistants offer tactics to facilitate inductive proofs. However, it still requires human ingenuity to decide what arguments to pass to those induction tactics. To automate this process, we present smart_induct for Isabelle/HOL. Given…
The Students' Proof Assistant (SPA) aims to both teach how to use a proof assistant like Isabelle and also to teach how reliable proof assistants are built. Technically it is a miniature proof assistant inside the Isabelle proof assistant.…
How difficult are interactive theorem provers to use? We respond by reviewing the formalization of Hilbert's tenth problem in Isabelle/HOL carried out by an undergraduate research group at Jacobs University Bremen. We argue that, as…
Interpretable explanations for recommender systems and other machine learning models are crucial to gain user trust. Prior works that have focused on paths connecting users and items in a heterogeneous network have several limitations, such…
Network administration is an inherently complex task, in particular with regard to security. Using the Isabelle interactive proof assistant, we develop two automated, formally verified tools which help uncovering and preventing bugs in…
We present a formalization of higher-order logic in the Isabelle proof assistant, building directly on the foundational framework Isabelle/Pure and developed to be as small and readable as possible. It should therefore serve as a good…
We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof…
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…
Execution of concurrent programs implies frequent switching between different thread contexts. This property perplexes analyzing and reasoning about concurrent programs. Trace simplification is a technique that aims at alleviating this…
In interactive theorem proving, formalization quality is a key factor for maintainability and re-usability of developments and can also impact proof-checking performance. Commonly, anti-patterns that cause quality issues are known to…
This paper describes the initial progress towards integrating the Coq proof assistant with the PIDE architecture initially developed for Isabelle. The architecture is aimed at asynchronous, parallel interaction with proof assistants, and is…
We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…
In recent years the effectiveness of interactive theorem provers has increased to an extent that the bottleneck in the interactive process shifted to efficiency: while in principle large and complex theorems are provable (effectiveness), it…
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…
Information Retrieval (IR) evaluation involves far more complexity than merely presenting performance measures in a table. Researchers often need to compare multiple models across various dimensions, such as the Precision-Recall trade-off…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
The heterogeneous nature of the logical foundations used in different interactive proof assistant libraries has rendered discovery of similar mathematical concepts among them difficult. In this paper, we compare a previously proposed…
Requirements traceability can in principle support stakeholders coping with rising development complexity. However, studies showed that practitioners rarely use available traceability information after its initial creation. In the position…
In this paper, we argue that database systems be augmented with an automated data exploration service that methodically steers users through the data in a meaningful way. Such an automated system is crucial for deriving insights from…