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| EPSRC Reference: |
GR/S46710/01 |
| Title: |
Topological Models for Computational Metalanguages |
| Principal Investigator: |
Dr AK Simpson |
| Other Investigators: |
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| Researcher Co-investigator: |
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| Project Partner: |
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| Department: |
Sch of Informatics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Standard Research |
| Starts: |
01 October 2003 |
Ends: |
30 September 2006 |
Value (£): |
215,308
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| EPSRC Research Topic Classifications: |
| Fundamentals of Computing |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Related Grants: |
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| Panel History: |
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Summary |
This basic research will establish a new notion of domain for use in the denotational semantics of programming languages. The new notion of domain has a simple definition using elementary concepts from topology. We shall demonstrate the ability of such "topological domains" to model an unprecedented variety of computational features in combination, thus resolving known problems arising in conventional domain theory.
Applications of denotational semantics are, in general, facilitated through the provision of "computational metalanguages": theoretically tractable idealized programming languages into which other more realistic languages can be translated. We shall exploit the flexibility of topological domains by using them to model powerful computational metalanguages exhibiting interesting and novel syntactic and operational features.
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| Final Report Summary |
This basic research established a new notion of "domain"
for use in providing mathematical models of computational
behaviour. The new notion of domain has a simple
definition using concepts from mathematical topology.
The project demonstrated the ability of such "topological domains" to model an unprecedented variety of computational features in combination, thus resolving
known problems arising in conventional approaches to
domain theory.
A particular success of the project was an in-depth
study of how to model the non-functional aspects
of computation (such as interactive, imperative and nondeterministic computation) using topological
domains. Collectively known as "computational effects",
we showed that such features can be modelled by
adapting tools from topological algebra.
We also discovered an alternative approach
to computational effects,
based on analysing the "observations" that can be
performed on computations, which led in particular
to a new model of probabilistic computation that simultaneosly generalises established approaches
to probability in domain theory and in mathematical
analysis.
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| Further Information: |
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| Organisation Website: |
http://www.ed.ac.uk |
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