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Title: Type systems for nominal terms
Author: Fairweather, Elliot Peter Marshall
ISNI:       0000 0004 5368 2260
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2014
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This thesis concerns types systems for nominal terms, a new syntax, close to informal practice, for representing and reasoning about formal languages that use binders. Nominal techniques allow a rst-order approach to binding in formal languages, providing direct access to both binders and bound variables and a formal axiomatisation of -equivalence. This approach is promising, not least because it has been shown that unication and matching of nominal representations is both decidable and tractable, giving rise to nominal models of computation and programming languages. Nominal terms, a nominal extension of rst-order terms, are now well studied, particularly in the context of equational reasoning. However, type systems for nominal terms have not yet been extensively researched. The development of type systems for nominal terms allows the application of the nominal approach to binding to the areas of specication and verication. Programming languages and environments based upon certifying type systems facilitate formal descriptions of operational semantics and the implementation of ecient compilers. Such features are increasingly important, particularly in critical domains where mathematical certainty is a necessity, such as medicine, telecommunications, transport and defence. This work rst denes three variations on a simple type system for nominal terms in the style of Church's simply typed lambda calculus. An ML-style polymorphic type system is then studied for which a type inference algorithm is provided and implemented. This type system is then applied to equational theories. Two formulations of typed rewriting are presented, one more expressive and one more ecient. Finally, a dependent type system is given for nominal terms extended with atom substitution, with a view to developing a nominal logical framework.
Supervisor: Fernandez, Maria Isabel Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available