Supporting formal reasoning about functional programs

Collins, Graham Richard McFarlane (2001) Supporting formal reasoning about functional programs. PhD thesis, University of Glasgow.

Abstract

It is often claimed that functional programming languages, and in particular pure functional languages are suitable for formal reasoning. This claim is supported by the fact that many people in the functional programming community do reason about languages and programs in a formal or semi-formal way. Different reasoning principles such as equational reasoning, induction and co-induction, are used, depending on the nature of the problem.

Using a computer program to check the application of rules and to mechanise the tedious bookkeeping involved can simplify proofs and provide more confidence in their correctness. When reasoning about programs, this can also allow experiments with new rules and reasoning styles, where a user may not be confident about structuring a proof on paper. Checking the applicability of a rule can eliminate the risk of mistakes caused by misunderstanding the theory being used. Just as there are different ways in which formal or informal reasoning can be applied in functional programming, there are different ways in which tools can be provided to support this reasoning.

This thesis describes an investigation of how to develop a mechanised reasoning system to allow reasoning about algorithms as a functional programmer would write them, not an encoding of the algorithm into a significantly different form. In addition, this work aims to develop a system to support a user who is not a theorem proving expert or an expert in the theoretical foundations of functional programming. The work is aimed towards a system that could be used by a functional programmer developing real programs and wishing to prove some or all of the programs correct or to prove that two programs are equivalent.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by funding from the Engineering and Physical Sciences Research Council.
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Supervisor's Name: Melham, Prof. Tom
• Date of Award: 2001
• Depositing User: Mrs Marie Cairney
• Unique ID: glathesis:2001-4609
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 02 Oct 2013 07:53
• Last Modified: 29 Apr 2024 09:42
• Thesis DOI: 10.5525/gla.thesis.4609
• URI: https://theses.gla.ac.uk/id/eprint/4609