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Lehmann, Daniel (1976) Categories for fixpoint semantics. University of Warwick. Department of Computer Science. (Theory of Computation Report). (Unpublished)
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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: | Report | ||||
|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Computer Science | ||||
| Library of Congress Subject Headings (LCSH): | Partially ordered sets, Computer programs -- Mathematical models | ||||
| Series Name: | Theory of Computation Report | ||||
| Publisher: | University of Warwick. Department of Computer Science | ||||
| Official Date: | June 1976 | ||||
| Dates: |
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| Number: | Number 15 | ||||
| Number of Pages: | 75 | ||||
| DOI: | CS-RR-015 | ||||
| Institution: | University of Warwick | ||||
| Theses Department: | Department of Computer Science | ||||
| Status: | Not Peer Reviewed | ||||
| Publication Status: | Unpublished | ||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||
| Description: | See Related URL for option to download full text |
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| Funder: | Science Research Council (Great Britain) (SRC) | ||||
| Version or Related Resource: | Lehmann, D.J. (1976). Categories for fixpoint semantics. Ph.D. thesis. University of Warwick | ||||
| Related URLs: |
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