Lehmann, Daniel (1976) Categories for fixpoint semantics. PhD thesis, University of Warwick.

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Abstract

A precise meaning is given to general recursive definitions
of functionals of arbitrarily high type, including non-deterministic
definitions. Domain equations involving products, sums, powers and
functor domains are solved.
The use of categories with ω-colimits as semantic domains is
investigated and it is shown that such categories provide a general
construction for power-domains and that no such construction can be
obtained with partial orders.
Initial fixpoints of continuous functors on such categories are
defined and studied. They provide a meaning for recursive definitions
of the type x:=f(x).
The category of domains is defined and shown to possess ω-colimits.
Initial fixpoints of continuous functors on the category of domains
provide the solution to domain equations.
The product, sum, power and functor domain of domains are defined and
studied. Product, sum, power and functor domain are proved to be
continuous functors in the category of domains.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Computer programs -- Mathematical models, Partially ordered sets
Official Date:	1976
Dates:	Date Event 1976 Submitted
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Shamir, Eliahu
Sponsors:	Science Research Council (Great Britain) (SRC)
Extent:	75 pages
Language:	eng
Related URLs:	Related item in WRAP

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