Show simple item record

dc.contributor.authorHu, Zhong Sheng
dc.date.accessioned2019-08-28 13:21:57 (GMT)
dc.date.available2019-08-28 13:21:57 (GMT)
dc.date.issued2019-08-28
dc.date.submitted2019-08-20
dc.identifier.urihttp://hdl.handle.net/10012/14964
dc.description.abstractDependent Object Types, or DOT, is a family of calculi developed to study the Scala programming language. These calculi have path dependent types as a feature, and potentially intersection types, union types and recursive types. So far, the study of DOT calculi mostly focuses on the soundness proof, which does not directly contribute to development of compilers. This thesis presents a detailed investigation of decidability and algorithmic properties of the family of DOT calculi. In decidability analysis, the undecidability of subtyping of several calculi is formally established, including the D <: and D ∧ calculi. Prior to this investigation, the undecidability of subtyping of all DOT calculi including D <: was open. Decidability analysis puts emphasis on a particular form of subtyping rules, called normal form. It turns out that a normal form definition is not only as expressive, but also more suggestive than the original definition. A conceptual device, called small-step analysis, is introduced to assist converting a usual definition of subtyping to its normal form definition. Moreover, decidability analysis gives direct contributions to the algorithmic analysis, by revealing two decidable fragments of D <: in declarative form, called the kernels. Decidability analysis also suggests a novel subtyping algorithm framework, stare-at subtyping. Stare-at subtyping and an existing algorithm are shown to be sound and complete w.r.t. their corresponding kernels. In algorithmic analysis, stare-at subtyping is extended to other calculi, with more features than D <:, including D ∧, μDART and jDOT. In μDART and jDOT, bi-directional type assignment algorithms are developed. The algorithms developed in this thesis are all shown to be sound with respect to their target calculi and terminating. During the development of the algorithms, analysis shows a number of ways in which the Wadlerfest DOT calculus does not directly correspond to the Scala language, while substantially increases the difficulties of algorithmic design. jDOT, therefore, is developed as an alternative formalization of Scala.en
dc.language.isoenen
dc.publisherUniversity of Waterlooen
dc.subjectdependent object typesen
dc.subjecttype systemen
dc.subjectalgorithmic typingen
dc.subjectundecidabilityen
dc.titleDecidability and Algorithmic Analysis of Dependent Object Types (DOT)en
dc.typeMaster Thesisen
dc.pendingfalse
uws-etd.degree.departmentDavid R. Cheriton School of Computer Scienceen
uws-etd.degree.disciplineComputer Scienceen
uws-etd.degree.grantorUniversity of Waterlooen
uws-etd.degreeMaster of Mathematicsen
uws.contributor.advisorLhoták, Ondřej
uws.contributor.affiliation1Faculty of Mathematicsen
uws.published.cityWaterlooen
uws.published.countryCanadaen
uws.published.provinceOntarioen
uws.typeOfResourceTexten
uws.peerReviewStatusUnrevieweden
uws.scholarLevelGraduateen


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record


UWSpace

University of Waterloo Library
200 University Avenue West
Waterloo, Ontario, Canada N2L 3G1
519 888 4883

All items in UWSpace are protected by copyright, with all rights reserved.

DSpace software

Service outages