• Journal for History of Mathematics
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• v.23 no.3
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• pp.45-56
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• 2010

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.