University of Illinois Urbana-Champaign

Dinatural transformations and polymorphic operators

Smith, Cameron C.

This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.

Permalink

https://hdl.handle.net/2142/20346

Description

Title
Dinatural transformations and polymorphic operators
Author(s)
Smith, Cameron C.
Issue Date
1989
Doctoral Committee Chair(s)
Muller, David E.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Mathematics
  • Computer Science
Language
eng
Abstract
A notion of dinatural transformation more restrictive than that in the literature is presented. Canonical dinatural transformations are defined, and shown to have desirable properties not shared by dinaturals in general. Connections between the notions of canonical dinatural transformation, context-free grammar, initial algebra, and polymorphic operator are elaborated. The theorem that the dinatural transformations between certain functors in the category of partial equivalence relations are exactly the canonical dinaturals is proved. Open questions are discussed, and directions for further study suggested.
Type of Resource
text
Permalink
http://hdl.handle.net/2142/20346
Copyright and License Information
Copyright 1989 Smith, Cameron C.

Owning Collections

Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Mathematics