Cut-elimination, substitution and normalisation
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We present a proof (of the main parts of which there is a formal version, checked with the Isabelle proof assistant) that, for a G3-style calculus covering all of intuitionistic zero-order logic, with an associated term calculus, and with a particular strongly normalising and confluent system of cut-reduction rules, every reduction step has, as its natural deduction translation, a sequence of zero or more reduction steps (detour reductions, permutation reductions or simplifications). This complements and (we believe) clarifies earlier work by (e.g.) Zucker and Pottinger on a question raised in 1971 by Kreisel.
Dyckhoff , R 2015 , Cut-elimination, substitution and normalisation . in H Wansing (ed.) , Dag Prawitz on Proofs and Meaning . Outstanding Contributions to Logic , vol. 7 , Springer , pp. 163-187 . https://doi.org/10.1007/978-3-319-11041-7_7
Dag Prawitz on Proofs and Meaning
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