In mathematics, constructive nonstandard analysis is a version of Abraham Robinson's nonstandard analysis, developed by Moerdijk (1995), Palmgren (1998), Ruokolainen (2004). Ruokolainen wrote:
The possibility of constructivization of nonstandard analysis was studied by Palmgren (1997, 1998, 2001). The model of constructive nonstandard analysis studied there is an extension of Moerdijk’s (1995) model for constructive nonstandard arithmetic.
"Abstract: This paper provides an explicit description of a model for intuitionistic nonstandard arithmetic, which can be formalized in a constructive metatheory without the axiom of choice."http://www.sciencedirect.com/science/journal/01680072
"Abstract: We develop a constructive version of nonstandard analysis, extending Bishop's constructive analysis with infinitesimal methods. ..."http://projecteuclid.org/euclid.bsl/1182353577