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combinatory algebra for sequential computation



The following paper is available at the address
   
  http://www.math.ruu.nl/publications/preprints/996.ps.gz

A COMBINATORY ALGEBRA FOR SEQUENTIAL FUNCTIONALS OF FINITE TYPE
  by Jaap van Oosten

Abstract:
It is shown that the type structure of finite-type functionals
associated to a combinatory algebra of partial functions from $\N$ to
$\N$ (in the same way as the type structure of the countable
functionals is associated to the partial combinatory algebra of total
functions from $\N$ to $\N$), is isomorphic to the type structure
generated by object $N$ (the flat domain on the natural numbers) in
Ehrhard's category of ``dI-domains with coherence'', or his
``hypercoherences''.