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The aim of this paper is to highlight a hitherto unknown computational aspectof Nonstandard Analysis pertaining to Reverse Mathematics (RM). In particular,we shall establish RM-equivalences between theorems from Nonstandard Analysisin a fragment of Nelson's internal set theory. We then extract primitiverecursive terms from Goedel's system T (not involving Nonstandard Analysis)from the proofs of the aforementioned nonstandard equivalences. The resultingterms turn out to be witnesses for effective1 equivalences in Kohlenbach'shigher-order RM. In other words, from an RM-equivalence in NonstandardAnalysis, we can extract the associated effective higher-order RM-equivalencewhich does not involve Nonstandard Analysis anymore. Finally, we show thatcertain effective equivalences in turn give rise to the original nonstandardtheorems from which they were derived.

The effective content of Reverse Nonstandard Mathematics and the nonstandard content of effective Reverse Mathematics