Related papers: Formalising the Double-Pushout Approach to Graph T…
Graph transformation is the rule-based modification of graphs, and is a discipline dating back to the 1970s. In general, to match the left-hand graph of a fixed rule within a host graph requires polynomial time, but to improve matching…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
We want to verify the correctness of optimization phases in the GraalVM compiler, which consist of many thousands of lines of complex Java code performing sophisticated graph transformations. We have built high-level models of the data…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
Graphs and graph transformation systems are a frequently used modelling technique for a wide range of different domains, cover- ing areas as diverse as refactorings, network topologies or reconfigurable software. Being a formal method,…
We present an ongoing effort to build a framework and a library in Isabelle/HOL for formalising primal-dual arguments for the analysis of algorithms. We discuss a number of example formalisations from the theory of matching algorithms,…
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…
Many problems in computer algebra and numerical analysis can be reduced to counting or approximating the real roots of a polynomial within an interval. Existing verified root-counting procedures in major proof assistants are mainly based on…
Many automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter when translating monomorphic to…
Bond graph is a unified graphical approach for describing the dynamics of complex engineering and physical systems and is widely adopted in a variety of domains, such as, electrical, mechanical, medical, thermal and fluid mechanics.…
In the present paper we introduce and study the push pull operators on the formal affine Demazure algebra and its dual. As an application we provide a non-degenerate pairing on the dual of the formal affine Demazure algebra which serves as…
Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL…
Our objective is to formally verify the correctness of the hundreds of expression optimization rules used within the GraalVM compiler. When defining the semantics of a programming language, expressions naturally form abstract syntax trees,…
This is an overview of a formalisation project in the proof assistant Isabelle/HOL of a number of research results in infinitary combinatorics and set theory (more specifically in ordinal partition relations) by Erd\H{o}s--Milner, Specker,…
We present an automated verification of the well-known modal logic cube in Isabelle/HOL, in which we prove the inclusion relations between the cube's logics using automated reasoning tools. Prior work addresses this problem but without…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in…
Simulation and formal verification are important complementary techniques necessary in high assurance model-based systems development. In order to support coherent results, it is necessary to provide unifying semantics and automation for…
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…
Special Relativity is a cornerstone of modern physical theory. While a standard coordinate model is well-known and widely taught today, several alternative systems of axioms exist. This paper reports on the formalisation of one such system…