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dc.contributor.advisorStokes, Tim E.
dc.contributor.authorSu, Roger Chi-Wei
dc.date.accessioned2018-05-13T22:45:45Z
dc.date.available2018-05-13T22:45:45Z
dc.date.issued2018
dc.identifier.citationSu, R. C.-W. (2018). The Algebraic Properties of if-then-else with Commutative Three-Valued Tests (Thesis, Master of Science (MSc)). The University of Waikato, Hamilton, New Zealand. Retrieved from https://hdl.handle.net/10289/11820en
dc.identifier.urihttps://hdl.handle.net/10289/11820
dc.description.abstractThis thesis studies an algebraic model of computable programs and the if-then-else operation. The programs here are considered deterministic, but not assumed to be always halting, so they are modelled by a semigroup of partial functions, with several extra operations in addition to the original binary operation of the semigroup. The if-then-else operation involves not only programs, but logical tests too. Hence, it calls for a separate algebra of tests. Evaluating a test often requires running another program, so the tests are also possibly non halting. When tests do not always halt, the results of conjunctions (logical ‘and’) and disjunctions (logical ‘or’) can differ, depending on whether sequential or parallel evaluation is applied. The parallel evaluation is what this thesis adopts. The overall ‘program algebra’ consists of two sorts, one of programs and the other of tests. Each sort has its own operations, and there are hybrid operations such as if-then-else which involve both sorts. This thesis establishes the axioms of all these operations by building an embedding from the abstract program algebra into a concrete one. At the end is a discussion on the algebra of tests without the programs, where the differences between the two evaluation paradigms are explored in detail.
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherThe University of Waikato
dc.rightsAll items in Research Commons are provided for private study and research purposes and are protected by copyright with all rights reserved unless otherwise indicated.
dc.subjectif-then-else
dc.subjectalgebra of programs
dc.subjectfunction semigroups
dc.titleThe Algebraic Properties of if-then-else with Commutative Three-Valued Tests
dc.typeThesis
thesis.degree.grantorThe University of Waikato
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (MSc)
dc.date.updated2018-02-19T00:00:35Z
pubs.place-of-publicationHamilton, New Zealanden_NZ


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