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Sequent Calculus and Cut-Elimination  

Cheong, Kye-Seop (Duksung Women's University)
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Journal for History of Mathematics / v.23, no.3, 2010 , pp. 45-56 More about this Journal
Sequent Calculus is a symmetrical version of the Natural Deduction which Gentzen restructured in 1934, where he presents 'Hauptsatz'. In this thesis, we will examine why the Cut-Elimination Theorem has such an important status in Proof Theory despite of the efficiency of the Cut Rule. Subsequently, the dynamic side of Curry-Howard correspondence which interprets the system of Natural Deduction as 'Simply typed $\lambda$-calculus', so to speak the correspondence of Cut-Elimination and $\beta$-reduction in $\lambda$-calculus, will also be studied. The importance of this correspondence lies in matching the world of program and the world of mathematical proof. Also it guarantees the accuracy of program.
Sequent calculus; Cut Rule; Cut-Elimination; $\lambda$-Calculus; Curry-Howard Correspondence;
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