Proof Engineering and Theory at LICS'26
The paper The Algebra of Iterative Constructions by Kevin Batz, Benjamin Lucien Kaminski, Lucas Kehrer, Gerwin Klein, Henning Urbat, and Todd Schmid was presented at the 41st Annual Symposium on Logic in Computer Science (LICS) in Lisbon this week. This paper in theoretical computer science is about an algebraic abstraction and reasoning principles for the iterative construction of fixed points. Fixed points are a recurring theme in computer science with many famous results such as the Kleene fixed point theorem. The algebra shown in this paper allows expressing such theorems concisely and enables reasoning about them in an abstract and streamlined way that can be implemented efficiently in proof assistants such as Isabelle/HOL, which Proofcraft is using for the verification of the seL4 microkernel.
The highly automated Isabelle/HOL implementation of iteration algebra in this paper resulted from a spontaneous collaboration between Proofcraft’s Chief Scientist Gerwin Klein and Benjamin Kaminski that started at the IFIP Working Group 2.3 (Programming Methodology) meeting in Athens in 2025. It shows that proof engineering ranges from practical application all the way to deep theory.
