Schwichtenberg, Helmut Termination of permutative conversions in intuitionistic Gentzen calculi. (English) Zbl 0913.68135 Theor. Comput. Sci. 212, No. 1-2, 247-260 (1999). Summary: It is shown that permutative conversions terminate for the cut-free intuitionistic Gentzen (i.e. sequent) calculus; this proves a conjecture by Dyckhoff and Pinto. The main technical tool is a term notation for derivations in Gentzen calculi. These terms may be seen as \(\lambda\)-terms with explicit substitution, where the latter corresponds to the left introduction rules. Cited in 1 ReviewCited in 5 Documents MSC: 68Q60 Specification and verification (program logics, model checking, etc.) Keywords:termination of permutative conversions; explicit substitution; sequenterm; natural deduction; Gentzen calculus × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Dyckhoff, R.; Pinto, L., Permutability of proofs in intuitionistic sequent calculi, Theoret. Comput. Sci., 212, 141-155 (1999), (this Vol.) · Zbl 0913.68110 [2] Herbelin, H., A λ-calculus structure isomorphic to Gentzen-style sequent calculus structure, (Pacholski, L.; Tiuryn, J., Computer Science Logic. 8th Workshop, CSL’94. Computer Science Logic. 8th Workshop, CSL’94, Kazimierz, Poland, September 1994. Computer Science Logic. 8th Workshop, CSL’94. Computer Science Logic. 8th Workshop, CSL’94, Kazimierz, Poland, September 1994, Lecture Notes in Computer Science, vol. 933 (1995), Springer: Springer Berlin), 61-75 · Zbl 1044.03509 [3] Howard, W. A., The formulae-as-types notion of construction, (Seldin, J. P.; Hindley, J. R., Essays on Combinatory Logic, Lambda Calculus and Formalism (1980), Academic Press: Academic Press New York), 479-490, To H.B. Curry · Zbl 0469.03006 [4] Kleene, S. C., Permutability of inferences in Gentzen’s calculi LK and LJ, Memoirs of the American Mathematical Society No. 10, 1-26 (1952), Providence, RI · Zbl 0047.25002 [5] Mints, G., Normal forms for sequent derivations, (Odifreddi, P., Kreiseliana. About and Around Georg Kreisel (1996), A.K. Peters: A.K. Peters Wellesley, MA), 469-492 · Zbl 0897.03053 [6] Pottinger, G., Normalization as a homomorphic image of cut-elimination, Ann. Math. Logic, 12, 323-357 (1977) · Zbl 0378.02017 [7] Prawitz, D., Natural deduction, (Acta Universitatis Stockholmiensis, Stockholm Studies in Philosophy, vol. 3 (1965), Almqvist & Wiksell: Almqvist & Wiksell Stockholm) · Zbl 0173.00205 [8] A.S. Troelstra, Marginalia on sequent calculi, in Studia Logica, to appear.; A.S. Troelstra, Marginalia on sequent calculi, in Studia Logica, to appear. · Zbl 0924.03104 [9] Zucker, J. I., The correspondence between cut-elimination and normalization I, II, Ann. Math. Logic, 7, 1-156 (1974) · Zbl 0298.02023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.