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**1 - 5**of**5**### Checking Proofs from Linked Tools

, 1996

"... We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, verified proof checkers for the HOL theorem proving system. We then briefly overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commenc ..."

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We describe a Cambridge project (now completed) which demonstrated the feasibility of producing independent, verified proof checkers for the HOL theorem proving system. We then briefly overview a joint Cambridge University/Hong Kong Baptist University proof checking project which is about to commence. It aims to extend the HOL work to other logics and proof tools. We discuss how this relates to the formal linking of tools and theories.

### A Generic Proof Checker

, 2001

"... The use of formal methods in software development seeks to increase our confidence in the resultant system. Their use often requires tool support, so the integrity of a development using formal methods is dependent on the integrity of the tool-set used. Specifically its integrity depends on the theo ..."

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The use of formal methods in software development seeks to increase our confidence in the resultant system. Their use often requires tool support, so the integrity of a development using formal methods is dependent on the integrity of the tool-set used. Specifically its integrity depends on the theorem prover, since in a typical formal development system the theorem prover is used to establish the validity of the proof obligations incurred by all the steps in the design and refinement process. In this

### unknown title

, 1999

"... this document I will lay out a possible PhD project in Automated Reasoning, discussing the principle objectives, some implementation ideas, and alternative lines of research if unexpected obstacles arise. The aim is that this plan will be suciently detailed to serve as proof of concept for the proje ..."

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this document I will lay out a possible PhD project in Automated Reasoning, discussing the principle objectives, some implementation ideas, and alternative lines of research if unexpected obstacles arise. The aim is that this plan will be suciently detailed to serve as proof of concept for the project.

### zur Erlangung des Doktorgrades

"... Tag der mündlichen Prüfung: This thesis deals with Baker domains and approximation of Julia sets, so it belongs to the area of ”Holomorphic Dynamical Systems”. Dynamical systems belong to the all-day life of scientists and engineers and are closely related to the term of iteration. Processes of iter ..."

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Tag der mündlichen Prüfung: This thesis deals with Baker domains and approximation of Julia sets, so it belongs to the area of ”Holomorphic Dynamical Systems”. Dynamical systems belong to the all-day life of scientists and engineers and are closely related to the term of iteration. Processes of iteration occur if the state of a system is changed by external influences at discrete points of time. Examples are the weather, turbulent flows in liquids or the development of populations. Moreover, iteration can be a tool to solve other mathematical problems or to approximate their solutions. Among various numerical methods we only mention Newton’s method to approximate roots of differentiable functions. All these dynamical systems have in common that they may develop in different directions. The boundary between different initial states of different developments is just the Julia set of the corresponding function. Julia sets were systematically analyzed for the first time around 1920 by the French matematicians P. Fatou and G. Julia, who concentrated on rational functions and observed that Julia sets are either very simple objects or extremly complicated. The development of powerful computers and new mathematical methods gave a boost to the research in this area in the 80’s, and since then also a theory of iteration of entire transcendental functions has been founded. The aim of this work is to describe what can happen to the Julia sets if an entire transcendental function satisfying a certain condition (having so-called Baker domains or wandering domains) is approximated by a sequence of polynomials or is perturbed holomorphically in a class of entire transcendental functions. 4 Organization of the paper This paper comes in four chapters: the Introduction, Preliminaries and Notation, the Results and the Proofs. All the results will be stated in chapter 3, and, for example, a result in section 3.1.1 will have its proof located in section 4.1.1.