@phdthesis{Boehne2019,
  author    = {B{\"o}hne, Sebastian},
  title     = {Different degrees of formality},
  doi       = {10.25932/publishup-42379},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-423795},
  school      = {Universit{\"a}t Potsdam},
  pages     = {VI, 167},
  year      = {2019},
  abstract  = {In this thesis we introduce the concept of the degree of formality. It is directed against a dualistic point of view, which only distinguishes between formal and informal proofs. This dualistic attitude does not respect the differences between the argumentations classified as informal and it is unproductive because the individual potential of the respective argumentation styles cannot be appreciated and remains untapped. This thesis has two parts. In the first of them we analyse the concept of the degree of formality (including a discussion about the respective benefits for each degree) while in the second we demonstrate its usefulness in three case studies. In the first case study we will repair Haskell B. Curry's view of mathematics, which incidentally is of great importance in the first part of this thesis, in light of the different degrees of formality. In the second case study we delineate how awareness of the different degrees of formality can be used to help students to learn how to prove. Third, we will show how the advantages of proofs of different degrees of formality can be combined by the development of so called tactics having a medium degree of formality. Together the three case studies show that the degrees of formality provide a convincing solution to the problem of untapped potential.},
  language  = {en}
}
@phdthesis{Frank2024,
  author    = {Frank, Mario},
  title     = {On synthesising Linux kernel module components from Coq formalisations},
  doi       = {10.25932/publishup-64255},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-642558},
  school      = {Universit{\"a}t Potsdam},
  pages     = {IX, 78},
  year      = {2024},
  abstract  = {This thesis presents an attempt to use source code synthesised from Coq formalisations of device drivers for existing (micro)kernel operating systems, with a particular focus on the Linux Kernel. In the first part, the technical background and related work are described. The focus is here on the possible approaches to synthesising certified software with Coq, namely the extraction to functional languages using the Coq extraction plugin and the extraction to Clight code using the CertiCoq plugin. It is noted that the implementation of CertiCoq is verified, whereas this is not the case for the Coq extraction plugin. Consequently, there is a correctness guarantee for the generated Clight code which does not hold for the code being generated by the Coq extraction plugin. Furthermore, the differences between user space and kernel space software are discussed in relation to Linux device drivers. It is elaborated that it is not possible to generate working Linux kernel module components using the Coq extraction plugin without significant modifications. In contrast, it is possible to produce working user space drivers both with the Coq extraction plugin and CertiCoq. The subsequent parts describe the main contributions of the thesis. In the second part, it is demonstrated how to extend the Coq extraction plugin to synthesise foreign function calls between the functional language OCaml and the imperative language C. This approach has the potential to improve the type-safety of user space drivers. Furthermore, it is shown that the code being synthesised by CertiCoq cannot be used in kernel space without modifications to the necessary runtime. Consequently, the necessary modifications to the runtimes of CertiCoq and VeriFFI are introduced, resulting in the runtimes becoming compatible components of a Linux kernel module. Furthermore, justifications for the transformations are provided and possible further extensions to both plugins and solutions to failing garbage collection calls in kernel space are discussed. The third part presents a proof of concept device driver for the Linux Kernel. To achieve this, the event handler of the original PC Speaker driver is partially formalised in Coq. Furthermore, some relevant formal properties of the formalised functionality are discussed. Subsequently, a kernel module is defined, utilising the modified variants of CertiCoq and VeriFFI to compile a working device driver. It is furthermore shown that it is possible to compile the synthesised code with CompCert, thereby extending the guarantee of correctness to the assembly layer. This is followed by a performance evaluation that compares a naive formalisation of the PC speaker functionality with the original PC Speaker driver pointing out the weaknesses in the formalisation and possible improvements. The part closes with a summary of the results, their implications and open questions being raised. The last part lists all used sources, separated into scientific literature, documentations or reference manuals and artifacts, i.e. source code.},
  language  = {en}
}