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Title: Using proof-planning to investigate the structure of proof in non-standard analysis
Author: Maclean, Ewen
ISNI:       0000 0004 2724 9674
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2004
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This thesis presents an investigation into the structure of proof in non-standard analysis using proof-planning. The theory of non-standard analysis, developed by Robinson in the 1960s, offers a more algebraic way of looking at proof in analysis. Proof-planning is a technique for reasoning about proof at the meta-level. In this thesis, we use it to encapsulate the patterns of reasoning that occur in non-standard analysis proofs. We first introduce in detail the mathematical theory and the proof-planning architecture. We then present our research methodology, describe the formal framework, which includes an axiomatisation, and develop suitable evaluation criteria. We then present our development of proof-plans for theorems involving limits, continuity and differentiation. We then explain how proof-planning applies to theorems which combine induction and non-standard analysis. Finally we give a detailed evaluation of the results obtained by combining the two attractive approaches of proof-planning and non-standard analysis, and draw conclusions from the work.
Supervisor: Fleuriot, Jacques. ; Smaill, Alan. Sponsor: Engineering and Physical Sciences Research Council (EPSRC)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Informatics ; Computer Science ; non-standard analysis ; proof-planning