Algorithm and proof as Ω-invariance and transfer: a new model of computation in nonstandard analysis

We propose a new model of computation based on Nonstandard Analysis. Intuitively, the role of `algorithm' is played by a new notion of finite procedure, called $\Omega$-invariance and inspired by physics, from Nonstandard Analysis. Moreover, the role of `proof' is taken up by the Transfer Principle from Nonstandard Analysis. We obtain a number of results in Constructive Reverse Mathematics to illustrate the tight correspondence to Errett Bishop's \emph{Constructive Analysis} and the associated \emph{Constructive Reverse Mathematics}