The differential lambda-calculus: syntax and semantics for differential geometry

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dc.contributor.advisorCockett, J. Robin B.
dc.contributor.authorGallagher, Jonathan
dc.contributor.committeememberBauer, Kristine
dc.contributor.committeememberBates, Larry M.
dc.contributor.committeememberPronk, Dorette A.
dc.contributor.committeememberJacobson, Michael J.
dc.date2018-11
dc.date.accessioned2018-10-09T18:52:51Z
dc.date.available2018-10-09T18:52:51Z
dc.date.issued2018-09-21
dc.description.abstractThe differential λ-calculus was introduced to study the resource usage of programs. This thesis marks a change in that belief system; our thesis can be summarized by the analogy λ-calculus : functions ::∂λ-calculus : smooth functions. To accomplish this, we will describe a precise categorical semantics for the differential λ-calculus using categories with a differential operator. We will then describe explicit models that are relevant to differential geometry, using categories like Sikorski spaces and diffeological spaces.en_US
dc.identifier.citationGallagher, J. (2018). The differential lambda-calculus: syntax and semantics for differential geometry (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/33144en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/33144
dc.identifier.urihttp://hdl.handle.net/1880/108793
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.facultyScience
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectdifferential geometry
dc.subjectlinear logic
dc.subjecttype theory
dc.subjectcategorical logic
dc.subjectinfinite dimension
dc.subjectconvenient differential geometry
dc.subjectlogic for differential geometry
dc.subjectlogic-differential geometry correspondence
dc.subject.classificationEducation--Mathematicsen_US
dc.subject.classificationEducation--Sciencesen_US
dc.subject.classificationEducation--Technologyen_US
dc.subject.classificationPhysicsen_US
dc.subject.classificationPhysics--Theoryen_US
dc.subject.classificationApplied Sciencesen_US
dc.subject.classificationComputer Scienceen_US
dc.titleThe differential lambda-calculus: syntax and semantics for differential geometry
dc.typedoctoral thesis
thesis.degree.disciplineComputer Science
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
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