  The aim of this paper is to highlight a hitherto unknown computational aspect
of Nonstandard Analysis. Recently, a number of nonstandard versions of Goedel's
system T have been introduced ([2,9,12]), and it was shown in [26] that the
systems from [2] play a pivotal role in extracting computational information
from proofs in Nonstandard Analysis. It is a natural question if similar
techniques may be used to extract computational information from proofs not
involving Nonstandard Analysis. In this paper, we provide a positive answer to
this question using the nonstandard system from [9]. This system validates
so-called non-standard uniform boundedness principles which are central to
Kohlenbach's approach to proof mining ([14]). In particular, we show that from
classical and ineffective existence proofs (not involving Nonstandard Analysis
but using weak Koenig's lemma), one can `automatically' extract approximations
to the objects claimed to exist.
