Gentzen-style Classical Proofs as -terms
نویسنده
چکیده
We show that the Gentzen-style 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 faithfully simulates cut-elimination procedure, namely tq-protocol. Then, we give a translation of Parigot's -calculus. This translation can be seen as the classical extension to the Plotkin's CPS translation. Using this translation, one can show that reductions of the -calculus can be simulated by the tq-protocol. Speci cally the Strongly Normalizable(SN) and Church-Rosser(CR) property of the -calculus is shown to be a consequence of that of the tq-protocol.
منابع مشابه
Classical Proofs as Programs, Cut Elimination as Computation
We show that the SN and CR cut-elimination procedure on Gentzen-style classical logic LKT/LKQ, as presented in Danos et al.(1994), is isomorphic to call-by-name (CBN) and call-by-value (CBV) reduction system respectively. Our method is simple. We assign typed -terms on intuitionistic decoration of LKT/LKQ so as to simulate the cut-elimination procedure by -contraction | i.e. we simulate cutelim...
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