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Interactive theorem provers are complex systems that require sophisticated platform efforts - and hence systems programming environments - to manage effectively. The Isabelle platform exemplifies this with its Isabelle/Scala systems…
Finite Automata (FAs) are fundamental components in the domains of programming languages. For instance, regular expressions, which are pivotal in languages such as JavaScript and Python, are frequently implemented using FAs. Finite…
Formal verification of traditional algorithms are of great significance due to their wide application in state-of-the-art software. Timsort is a complicated and hybrid stable sorting algorithm, derived from merge sort and insertion sort.…
Signal temporal logic (STL) was introduced for monitoring temporal properties of continuous-time signals for continuous and hybrid systems. Differential dynamic logic (dL) was introduced to reason about the end states of a hybrid program.…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of…
We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the…
We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low…
In this Masters thesis we present an implementation of a fragment of "book HoTT" as an object logic for the interactive proof assistant Isabelle. We also give a mathematical description of the underlying theory of the Isabelle/Pure logical…
The spread of autonomous systems into safety-critical areas has increased the demand for their formal verification, not only due to stronger certification requirements but also to public uncertainty over these new technologies. However, the…
Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle. The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized…
In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to…
Separation logic is successful for software verification in both theory and practice. Decision procedure for symbolic heaps is one of the key issues. This paper proposes a cyclic proof system for symbolic heaps with general form of…
We describe an approach to the verified implementation of transformations on functional programs that exploits the higher-order representation of syntax. In this approach, transformations are specified using the logic of hereditary Harrop…
Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the…
We argue that the implementation and verification of compilers for functional programming languages are greatly simplified by employing a higher-order representation of syntax known as Higher-Order Abstract Syntax or HOAS. The underlying…
We combine quantified differential dynamic logic (QdL) for reasoning about the possible behavior of distributed hybrid systems with temporal logic for reasoning about the temporal behavior during their operation. Our logic supports…
We formalise the basics of the double-pushout approach to graph transformation in the proof assistant Isabelle/HOL and provide associated machine-checked proofs. Specifically, we formalise graphs, graph morphisms and rules, and a definition…
It is common to prove by reasoning over source code that programs do not leak sensitive data. But doing so leaves a gap between reasoning and reality that can only be filled by accounting for the behaviour of the compiler. This task is…
Definition packages in theorem provers provide users with means of defining and organizing concepts of interest. This system description presents a new definition package for the hybrid systems theorem prover KeYmaera X based on…