### Before we begin: Thank you, thank you, thank you,... Walter.WassollmanzudiesemMannnochsagen?

"... Doctor rerum naturalium ..."

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"... The Darwinian principle of adaptation through replication, heritable variation, and selection is not limited to a population of biological entities. It is applicable to any object that can be copied and varied, and for which at least some of the variants are distinguishable (by an arbitrary criterio ..."

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The Darwinian principle of adaptation through replication, heritable variation, and selection is not limited to a population of biological entities. It is applicable to any object that can be copied and varied, and for which at least some of the variants are distinguishable (by an arbitrary criterion called “fitness”). Genetic

### Theoretical Chemistry

"... The barrier of objects: From dynamical systems to bounded organizations ..."

### This document in subdirectoryRS/06/3/ A Concrete Framework for Environment Machines ∗

, 2006

"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."

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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS

### This document in subdirectoryRS/03/13/ A Functional Correspondence between Evaluators and Abstract Machines

, 2003

"... Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."

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Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS

### Implementing χ

, 2004

"... Calculi are used to reason about functional languages from a theoretical perspective. They allows us to make bold statements about programs based on sound and correct deductive methods. Methods of visualization allow us to gain a better understanding of the communication and interaction involved bet ..."

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Calculi are used to reason about functional languages from a theoretical perspective. They allows us to make bold statements about programs based on sound and correct deductive methods. Methods of visualization allow us to gain a better understanding of the communication and interaction involved between processes. Often, graphs are used because of the level of intuition they can bring to a system. A specific type of graph, called a ‘Term-Graph ’ is one method of implementing functional programming languages. It has the added benefit of increasing the efficiency of computations through a concept known as sharing. In this report we present the design and implementation of a term-graph rewriting system that implements a higher-order calculus. We evaluate the tool and present the main conclusions of the project. Acknowledgements I would like to thank the following people who have helped throughout the project. First and foremost, Dr. Steffen van Bakel, my supervisor, who not only gave great help and excellent guidance throughout the course of the project, but also kept me motivated through continued enthusiasm and positive feedback on my progress. Professor Chris Hankin, for taking the time to explain concepts I was unsure of, and giving guidance on where to research certain aspects of the project. Alex Summers, for testing the many implementations of the project (and giving insightful feedback).

### Functional Organization in Molecular Systems

"... and the *-calculus Dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium ..."

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and the *-calculus Dissertation zur Erlangung des akademischen Grades Doctor rerum naturalium

### General

"... I describe the mechanisation in HOL of some basic λ-calculus the-ory, using the axioms proposed by Gordon and Melham [4]. Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt [2 ..."

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I describe the mechanisation in HOL of some basic λ-calculus the-ory, using the axioms proposed by Gordon and Melham [4]. Using these as a foundation, I mechanised the proofs from Chapters 2 and 3 of Hankin [5] (equational theory and reduction theory), followed by most of Chapter 11 of Barendregt [2] (residuals, finiteness of developments, and the standardisation theorem). I discuss the ease of use of the Gordon-Melham axioms, as well as the mechanical support I implemented to make some basic tasks more straightfor-ward.