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Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…
We present an Isabelle/HOL formalization of a characterization of confluence for quasi-reductive strongly deterministic conditional term rewrite systems, due to Avenhaus and Lor\'ia-S\'aenz.
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates,…
The current verification flow of complex systems uses different engines synergistically: virtual prototyping, formal verification, simulation, emulation and FPGA prototyping. However, none is able to verify a complete architecture.…
This paper presents the mechanization of a process algebra for Mobile Ad hoc Networks and Wireless Mesh Networks, and the development of a compositional framework for proving invariant properties. Mechanizing the core process algebra in…
We present a tool called HHLPar for verifying hybrid systems modelled in Hybrid Communicating Sequential Processes (HCSP). HHLPar is built upon a Hybrid Hoare Logic for HCSP, which is able to reason about continuous-time properties of…
A hybrid model involves the cooperation of an interpretable model and a complex black box. At inference, any input of the hybrid model is assigned to either its interpretable or complex component based on a gating mechanism. The advantages…
For the design and implementation of engineering systems, performing model-based analysis can disclose potential safety issues at an early stage. The analysis of hybrid system models is in general difficult due to the intrinsic complexity…
We present a framework for C code in C11 syntax deeply integrated into the Isabelle/PIDE development environment. Our framework provides an abstract interface for verification back-ends to be plugged-in independently. Thus, various…
For the formal verification of a network security policy, it is crucial to express the verification goals. These formal goals, called security invariants, should be easy to express for the end user. Focusing on access control and…
The model-checking problem for hybrid systems is a well known challenge in the scientific community. Most of the existing approaches and tools are limited to safety properties only, or operates by transforming the hybrid system to be…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
This paper presents a novel approach to including non-instantaneous discrete control transitions in the linear hybrid automaton approach to simulation and verification of hybrid control systems. In this paper we study the control of a…
We propose a novel approach for the formal verification of biological systems based on the use of a modal linear logic. We show how such a logic can be used, with worlds as instants of time, as an unified framework to encode both biological…
Formalised libraries of combinatorial mathematics have rapidly expanded over the last five years, but few use one of the most important tools: probability. How can often intuitive probabilistic arguments on the existence of combinatorial…
In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and…
Modular reasoning about class invariants is challenging in the presence of dependencies among collaborating objects that need to maintain global consistency. This paper presents semantic collaboration: a novel methodology to specify and…
DHOL is an extensional, classical logic that equips the well-known higher-order logic (HOL) with dependent types. This allows for concise encodings of important domains like size-bounded data structures, category theory, or proof theory.…