Translating set theoretical proofs into type theoretical programs
We show how to translate proofs of II20-sentences in the fragment of set theory KPIU+, which is an extension of Kripke-Platek set theory, into proofs of Martin-Löf's Type Theory using a cut elimination argument. This procedure is effective. The method used is an implementation of techniques from traditional proof theoretic analysis in type theory. It follows that KPIU+ and ML1 W show the same II20-sentences and have therefore the same programs. As a side result we get that II20-sentences provable in intensional and extensional version of ML1W are the same, solving partly a problem posed by M. Hofmann.
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