Abstract versus concrete computation on metric partial algebras
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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.
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