Cut Elimination for Classical Proofs as Continuation Passing Style Computation

@inproceedings{Ogata1998CutEF,
  title={Cut Elimination for Classical Proofs as Continuation Passing Style Computation},
  author={Ichiro Ogata},
  booktitle={ASIAN},
  year={1998}
}
  • Ichiro Ogata
  • Published in ASIAN 8 December 1998
  • Computer Science
We show that the one can consider proof of the Gentzen's LK as the continuation passing style(CPS) programs; and the cut-elimination procedure for LK as computation. To be more precise, we observe that Strongly Normalizable(SN) and Church-Rosser(CR) cut-elimination procedure for (intuitionistic decoration of) LKT and LKQ, as presented in Danos et al.(1993), precisely corresponds to call-by-name(CBN) and call-by-value(CBV) CPS calculi, respectively. This can also be seen as an extension to… 
Gentzen-style Classical Proofs as -terms
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
A Proof Theoretical Account of Continuation Passing Style
TLDR
The CBV normalization for CND can be simulated by the cut-elimination procedure for LKQ (Danos-Joinet-Schellinx 93), namely the q-protocol, and a proof-term assignment system is used to prove this fact.
A CPS-Transform of Constructive Classical Logic
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Correspondence between Normalization of CND and Cut-Elimination of LKT
TLDR
It is argued that the translation from CND to LKT can be considered as a general form of call-by-name CPS-translation and the simulation theorem is shown; the normalization of CND can be simulated by cut-elimination of LKT.
A Curry-Howard Isomorphism for Compilation and Program Execution
TLDR
A Curry-Howard isomorphism for compilation and program execution is established by showing the set of A-normal forms corresponds to a subsystem of Kleene's contraction-free variant of Gentzen's intuitionistic sequent calculus.
From λ to π; or, Rediscovering continuations
TLDR
This work factorise the π-calculus encodings of (untyped as well as simply-typed) call-by-name and call- by-value λ-calculations into three steps: a CPS transform, the inclusion of CPS terms into HOπ and the compilation from HOπ to π -calculus.
Intuitionistic Dual-intuitionistic Nets
TLDR
This work defines a generic syntax of nets which can be used for any of these logics, and explains how the duality between these two systems exactly corresponds to the intensively studiedDuality between call-by-value systems and call- by-name systems for classical logic.
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