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Arithmetical proofs of strong normalization results for symmetric λcalculi
"... symmetric λµcalculus ..."
2005, ‘A ProofTheoretic Foundation of Abortive Continuations (Extended version
"... Abstract. We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce’s law without enforcing Ex Falso Quodlibet. We show that a “natural ” implementation of this logic is Parigot’s classical natural deduction. We then move on to the comp ..."
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Cited by 9 (5 self)
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Abstract. We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce’s law without enforcing Ex Falso Quodlibet. We show that a “natural ” implementation of this logic is Parigot’s classical natural deduction. We then move on to the computational side and emphasize that Parigot’s λµ corresponds to minimal classical logic. A continuation constant must be added to λµ to get full classical logic. The extended calculus is isomorphic to a syntactical restriction of Felleisen’s theory of control that offers a more expressive reduction semantics. This isomorphic calculus is in correspondence with a refined version of Prawitz’s natural deduction.
Confluency property of the callbyvalue λµ ∧∨  calculus
 Computational Logic and Applications CLA’05. Discrete Mathematics and Theoretical Computer Science proc
, 2006
"... LAMA Équipe de logique, Université de Savoie, F73376 Le Bourget du Lac, France In this paper, we introduce the λµ ∧ ∨ callbyvalue calculus and we give a proof of the ChurchRosser property of this system. This proof is an adaptation of that of Andou (2003) which uses an extended parallel reduct ..."
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Cited by 3 (0 self)
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LAMA Équipe de logique, Université de Savoie, F73376 Le Bourget du Lac, France In this paper, we introduce the λµ ∧ ∨ callbyvalue calculus and we give a proof of the ChurchRosser property of this system. This proof is an adaptation of that of Andou (2003) which uses an extended parallel reduction method and complete development. Keywords: Callbyvalue, ChurchRosser, Propositional classical logic, Parallel reduction, Complete development 1
An OutputBased Semantics of Λµ with Explicit Substitution
 in the πcalculus. IFIPTCS’12, LNCS 7604
, 2012
"... We study the Λµcalculus, extended with explicit substitution, and define a compositional outputbased translation into a variant of the πcalculus with pairing. We show that this translation preserves singlestep explicit head reduction with respect to contextual equivalence. We use this result to ..."
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Cited by 1 (1 self)
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We study the Λµcalculus, extended with explicit substitution, and define a compositional outputbased translation into a variant of the πcalculus with pairing. We show that this translation preserves singlestep explicit head reduction with respect to contextual equivalence. We use this result to show operational soundness for head reduction, adequacy, and operational completeness. Using a notion of implicative typecontext assignment for the πcalculus, we also show that assignable types are preserved by the translation. We finish by showing that termination is preserved.
λµPRL – A Proof Refinement Calculus for Classical Reasoning
 in Computational Type Theory Diploma thesis, Institut für Informatik, Universität Potsdam
, 2009
"... Abstract. We present a hybrid proof calculus λµPRL that combines the propositional fragment of computational type theory with classical reasoning rules from the λµcalculi. The calculus supports the topdown development of proofs as well as the extraction of proof terms in a functional programming l ..."
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Abstract. We present a hybrid proof calculus λµPRL that combines the propositional fragment of computational type theory with classical reasoning rules from the λµcalculi. The calculus supports the topdown development of proofs as well as the extraction of proof terms in a functional programming language extended by a nonconstructive binding operator. It enables a user to employ a mix of constructive and classical reasoning techniques and to extract algorithms from proofs of specification theorems that are fully executable if classical arguments occur only in proof parts related to the validation of the algorithm. We prove the calculus sound and complete for classical propositional logic, introduce the concept of µsafe terms to identify proof terms corresponding to constructive proofs and show that the restriction of λµPRL to µsafe proof terms is sound and complete for intuitionistic propositional logic. We also show that an extension of λµPRL to arithmetical and firstorder expressions is isomorphic to Murthy’s calculus P ROGK.
Strong normalization results by translation
"... We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed λµcalculus. We also extend Mendler’s result on recursive equations to this system. 1 ..."
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We prove the strong normalization of full classical natural deduction (i.e. with conjunction, disjunction and permutative conversions) by using a translation into the simply typed λµcalculus. We also extend Mendler’s result on recursive equations to this system. 1
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, 905
"... Arithmetical proofs of strong normalization results for the symmetric λµcalculus ..."
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Arithmetical proofs of strong normalization results for the symmetric λµcalculus