Sequent Calculus and Cut-Elimination

순차식 연산 (Sequent calculus)과 절단제거 (Cut elimination)

  • Received : 2010.07.13
  • Accepted : 2010.08.19
  • Published : 2010.08.31

Abstract

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.

순차식 연산은 겐첸이 자연연역을 1934년 대칭적 버전으로 재구성한 것으로서, 여기에서 그는 '주정리' 를 소개한다. 이 논문에서 우리는 절단의 유용성에도 불구하고 증명이론에서 왜 절단정리가 이토록 중요한 위상을 차지하는지 검토할 것이다. 이어서 커리-하우어드 대응의 역동적 측면, 즉 절단 제거와 단순히 유형화된 람다-연산에서 ${\beta}$-환원의 대응이 연구될 것이다. 이러한 대응의 중요성은 프로그램의 세계와 수학 증명의 세계를 마주보게 함으로써 프로그램의 정확성을 보증해준다는 데에 있다.

Keywords

References

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