A theory of dependent record types with structural subtyping
نویسنده
چکیده
Type theory stemmed from the philosophical discussion on foundation of logic and set theory, and aroused interest from researchers in logic and formalism who gave it a clear format based on the λ-calculi. With the growth of the discipline of computing, various forms of type theory have brought in a common interest in developing computer-aided proof assistants. From this multi-disciplinary nature and development of type theory, it has clearly become a pluralistic subject of study that contains elements from philosophy, logic, foundation of mathematics, computing science, and even linguistics, etc. In this thesis, I present and study a type system of dependent record types. Dependent record types (DRTs) are types of records in which the type of a field may depend on the value of an earlier field. In this thesis, I prove several metatheoretic properties, such as structural properties, subject reduction, strong normalisation and Church-Rosser property of DRTs as defined with the logical framework LF, using the method of typed operational semantics first developed by Goguen. I also study how structural subtyping may be applied to DRTs, by extending the type theory LF and DRTs with coercive subtyping, and prove that the resulting set of coercions is coherent. This work makes dependent record types a possible theoretical basis for modelling module mechanisms in computer languages.
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