@article{Frank2012,
  author    = {Frank, Mario},
  title     = {Axiom relevance decision engine : technical report},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72128},
  year      = {2012},
  abstract  = {This document presents an axiom selection technique for classic first order theorem proving based on the relevance of axioms for the proof of a conjecture. It is based on unifiability of predicates and does not need statistical information like symbol frequency. The scope of the technique is the reduction of the set of axioms and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the axiom set, it can be used as a preprocessor for automated theorem proving. This technical report describes the conception, implementation and evaluation of ARDE. The selection method, which is based on a breadth-first graph search by unifiability of predicates, is a weakened form of the connection calculus and uses specialised variants or unifiability to speed up the selection. The implementation of the concept is evaluated with comparison to the results of the world championship of theorem provers of the year 2012 (CASC J6). It is shown that both the theorem prover leanCoP which uses the connection calculus and E which uses equality reasoning, can benefit from the selection approach. Also, the evaluation shows that the concept is applyable for theorem proving problems with thousands of formulae and that the selection is independent from the calculus used by the theorem prover.},
  language  = {en}
}
@misc{Frank2013,
  type      = {Master Thesis},
  author    = {Frank, Mario},
  title     = {TEMPLAR : efficient determination of relevant axioms in big formula sets for theorem proving},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72112},
  school      = {Universit{\"a}t Potsdam},
  year      = {2013},
  abstract  = {This document presents a formula selection system for classical first order theorem proving based on the relevance of formulae for the proof of a conjecture. It is based on unifiability of predicates and is also able to use a linguistic approach for the selection. The scope of the technique is the reduction of the set of formulae and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the formula set, it can be used as a preprocessor for automated theorem proving. The document contains the conception, implementation and evaluation of both selection concepts. While the one concept generates a search graph over the negation normal forms or Skolem normal forms of the given formulae, the linguistic concept analyses the formulae and determines frequencies of lexemes and uses a tf-idf weighting algorithm to determine the relevance of the formulae. Though the concept is built for first order logic, it is not limited to it. The concept can be used for higher order and modal logik, too, with minimal adoptions. The system was also evaluated at the world championship of automated theorem provers (CADE ATP Systems Competition, CASC-24) in combination with the leanCoP theorem prover and the evaluation of the results of the CASC and the benchmarks with the problems of the CASC of the year 2012 (CASC-J6) show that the concept of the system has positive impact to the performance of automated theorem provers. Also, the benchmarks with two different theorem provers which use different calculi have shown that the selection is independent from the calculus. Moreover, the concept of TEMPLAR has shown to be competitive to some extent with the concept of SinE and even helped one of the theorem provers to solve problems that were not (or slower) solved with SinE selection in the CASC. Finally, the evaluation implies that the combination of the unification based and linguistic selection yields more improved results though no optimisation was done for the problems.},
  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}
}