Cut Elimination for Classical Proofs as Continuation Passing Style Computation

  title={Cut Elimination for Classical Proofs as Continuation Passing Style Computation},
  author={Ichiro Ogata},
  • 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
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
It is shown that the cut-elimination for LKT, as presented in Danos et al.(1993), simulates the normalization for classical natural deduction (CND), and can be considered as a classical extension to call-byname (CBN) CPS-transform.
Correspondence between Normalization of CND and Cut-Elimination of LKT
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
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
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
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.


Classical Proofs as Programs , Cut Elimination as Computation ( Draft )
It is shown 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 and the isomorphism between-calculus and CPS calculus is revealed.
A Curry-Howard foundation for functional computation with control
The goal is that ¿µv and µPCFv respectively should be to functional computation with first-class access to the flow of control what ¿-calculus and PCF respectively are to pure functional programming.
A computational analysis of Girard's translation and LC
  • Chetan R. Murthy
  • Computer Science
    [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science
  • 1992
An intuitionistic term-extraction procedure is provided for Girard's new classical logic LC, and using the syntactic properties of this language, it is possible to give simple proofs for the evidence properties of LC.
A formulae-as-type notion of control
It is proved that all evaluations of typed terms in Idealized Scheme are finite, and the existence of computationally interesting “classical programs” is illustrated by the definition of conjunctively, disjunctive, and existential types using standard classical definitions.
Classical Proofs as Programs
  • M. Parigot
  • Computer Science, Mathematics
    Kurt Gödel Colloquium
  • 1993
The solution to the problem of how to extract the intuitionistic representation of a data from a classical one using an “output” operator, while keeping a confluent computation mechanism is developed.
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This paper presents a way of extending the paradigm "proofs as programs" to classical proofs, which can be seen as a simple extension of intuitionistic natural deduction, whose algorithmic interpretation is very well known.
A CPS-Translation of the Lambda-µ-Calculus
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A New Deconstructive Logic: Linear Logic
A comparison of the design of a noetherian and confluent normalization for LK2 (that is, classical second order predicate logic presented as a sequent calculus) brings to the fore the latter's defects for these 'deconstructive purposes'.
A Lambda-Calculus Structure Isomorphic to Gentzen-Style Sequent Calculus Structure
A λ-calculus for which applicative terms have no longer the form (...((u u1) u2)... un) but the form [u [u1;...;un], for which [u 1;... ;un] is a list of terms is considered.
Lectures on linear logic
1. Introduction 2. Sequent calculus for linear logic 3. Some elementary syntactic results 4. The calculus of two implications: a digression 5. Embeddings and approximations 6. Natural deduction