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combinatory algebra for sequential computation
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To: types@cs.indiana.edu
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Subject: combinatory algebra for sequential computation
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From: Jaap van Oosten <jvoosten@math.ruu.nl>
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Date: Thu, 13 Feb 1997 14:57:03 +0100
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Delivery-Date: Thu, 13 Feb 1997 08:57:09 -0500
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''.