Dialectica Interpretation of Intuitionistic Logic
The interpretation has two components: a formula translation and a proof translation. The formula translation describes how each formula of Heyting arithmetic is mapped to a quantifier-free formula of the system T, where and are tuples of fresh variables (not appearing free in ). Intuitively, is interpreted as . The proof translation shows how a proof of has enough information to witness the interpretation of, i.e. the proof of can be converted into a closed term and a proof of in the system T.
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