Jeffery Zucker
Department of Computing & Software
McMaster University
Canada

"Abstract versus Concrete Models of Computation on Partial Metric Algebras"

ABSTRACT

A model of computation is abstract if, when applied to any
algebra, the resulting programs for computable functions
and sets on that algebra are invariant under isomorphisms,
and hence do not depend on a representation for the algebra.
Otherwise it is concrete.  Intuitively, concrete models depend
on the implementation of the algebra.

The difference is particularly striking in the case of
topological partial algebras, and notably in algebras over
the reals.  We investigate the relationship between abstract and
concrete models of partial metric algebras.  In the course of this
investigation, interesting aspects of continuity, extensionality and
non-determinism are uncovered.

This is joint work with J.V. Tucker (Swansea, Wales).

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