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Abstract: We show that one can consider the Gentzenstyle classical logic LKT, as presented in Danos et al.(1993), can be considered as the classical call-by-name (CBN) calculus. First, we present a new term calculus for LKT which is isomorphic to cut-elimination procedure(tq-protocol) for LKT. Then, we present a translation of Parigot's ¯- calculus into our term calculus. This translation is essentially identical with so-called Continuation Passing Style. Using this translation, one can show that LKT... (Update)
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BibTeX entry: (Update)
@misc{ ogata-gentzenstyle,
author = "Ichiro Ogata",
title = "Gentzen-Style Classical Proofs asλμ-Terms",
url = "citeseer.ist.psu.edu/article/ogata99gentzenstyle.html" }
Citations (may not include all citations):283 Theoretical Computer Science (context) - Plotkin, call-by-value et al. - 1975
215 Theoretical Computer Science (context) - Girard - 1987
110 A formulae-as-types notion of control - Griffin - 1990
58 Untersuchungen uber das logische schließen (context) - Gentzen - 1935
57 A new deconstructive logic: linear logic - Danos, Joinet et al. - 1997
40 Strong normalization for second order classical natural dedu.. (context) - Parigot - 1993
40 A curryhoward foundation for functional computation with con.. - Ong, Stewart - 1997
32 Normalization as a homomorphic image of cut-elimination (context) - Pottinger - 1977
32 Classical proofs as programs (context) - Parigot - 1993
24 A computational analysis of Girard's translation and LC (context) - Murthy - 1992
24 A semantics view of classical proofs: type-theoretic (context) - Ong - 1996
24 Normal forms for sequent derivations (context) - Mints - 1996
24 Almquist and Wiksell (context) - Prawitz, Study - 1965
21 A new constructive logic: Classical logic (context) - Girard - 1991
20 Annals of Pure and Applied Logic (context) - Girard, unity - 1993
18 Lambda-mu-calculus: An algorithmic interpretation of classic.. (context) - Parigot - 1992
16 A cps-translation of the ¯-calculus (context) - de Groote - 1994
12 La Logique Lin'eaire Appliqu 'ee `a l (context) - Danos - 1990
9 calculus structure ismorphic to gentzen-style sequent calcul.. (context) - Herbelin - 1994
7 Cut elimination for classical proofs as continuation passing.. - Ogata - 1998
4 Annals of Mathematical Logic (context) - Zucker, cutelimination et al.
Documents on the same site (http://www.etl.go.jp/~ogata/): More
Classical Proofs as Programs, Cut Elimination as Computation - Ogata (Correct)
Gentzen-style classical logic as CPS calculus - Ogata (Correct)
Classical Proofs as Programs, Cut Elimination as Computation - Ogata (Correct)
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