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TRUNCATION AND SEMI-DECIDABILITY NOTIONS IN APPLICATIVE THEORIES

  • GERHARD JÄGER (a1), TIMOTEJ ROSEBROCK (a2) and SATO KENTARO (a3)

Abstract

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.

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