TY - JOUR
T1 - Truncation and Semi-Decidability Notions in Applicative Theories
Y1 - Submitted
A1 - Gerhard Jäger
A1 - Timtej Rosebrock
A1 - Kentaro Sato
AB - BON+ is an applicative theory and closely related to the first order parts of the standard systems of explicit mathematics. As such it is also a natural framework for abstract computations. In this article we analyze this aspect of BON+ more closely. First a point is made for introducing a new operation τN , called truncation, to obtain a natural formalization of partial recursive functions in our applicative framework. Then we introduce the operational versions of a series of notions that are all equivalent to semi- decidability in ordinary recursion theory on the natural numbers, and study their mutual relationships over BON+ with τN .
UR - http://www.iam.unibe.ch/ltgpub/2016/jarosa16.pdf
ER -