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Reducibility and ⊤⊤lifting for computation types
 In Proc. 7th International Conference on Typed Lambda Calculi and Applications (TLCA), volume 3461 of Lecture Notes in Computer Science
, 2005
"... Abstract. We propose ⊤⊤lifting as a technique for extending operational predicates to Moggi’s monadic computation types, independent of the choice of monad. We demonstrate the method with an application to GirardTait reducibility, using this to prove strong normalisation for the computational meta ..."
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Cited by 15 (2 self)
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Abstract. We propose ⊤⊤lifting as a technique for extending operational predicates to Moggi’s monadic computation types, independent of the choice of monad. We demonstrate the method with an application to GirardTait reducibility, using this to prove strong normalisation for the computational metalanguage λml. The particular challenge with reducibility is to apply this semantic notion at computation types when the exact meaning of “computation ” (stateful, sideeffecting, nondeterministic, etc.) is left unspecified. Our solution is to define reducibility for continuations and use that to support the jump from value types to computation types. The method appears robust: we apply it to show strong normalisation for the computational metalanguage extended with sums, and with exceptions. Based on these results, as well as previous work with local state, we suggest that this “leapfrog ” approach offers a general method for raising concepts defined at value types up to observable properties of computations. 1
Relational parametricity and control
 Logical Methods in Computer Science
"... www.lmcsonline.org ..."
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.
The differential λµcalculus
 Theor. Comput. Sci
, 2007
"... We define a differential λµcalculus which is an extension of both Parigot’s λµcalculus and EhrhardRégnier’s differential λcalculus. We prove some basic properties of the system: reduction enjoys ChurchRosser and simply typed terms are strongly normalizing. Contents 1 ..."
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Cited by 6 (2 self)
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We define a differential λµcalculus which is an extension of both Parigot’s λµcalculus and EhrhardRégnier’s differential λcalculus. We prove some basic properties of the system: reduction enjoys ChurchRosser and simply typed terms are strongly normalizing. Contents 1
NonStrictly Positive FixedPoints for Classical Natural Deduction, accepted for publication in APAL
, 2004
"... Termination for classical natural deduction is difficult in the presence of commuting/permutative conversions for disjunction. An approach based on reducibility candidates is presented that uses nonstrictly positive inductive definitions. It covers secondorder universal quantification and also the ..."
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Cited by 4 (0 self)
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Termination for classical natural deduction is difficult in the presence of commuting/permutative conversions for disjunction. An approach based on reducibility candidates is presented that uses nonstrictly positive inductive definitions. It covers secondorder universal quantification and also the extension of the logic by fixedpoints of nonstrictly positive operators, which appears to be a new result. Finally, the relation to Parigot’s strictlypositive inductive definition of his set of reducibility candidates and to his notion of generalized reducibility candidates is explained. Key words: PACS:
Relational parametricity for control considered as a computational effect
 Electr. Notes Theor. Comput. Sci
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 3 (2 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
ContinuationPassing Style and Strong Normalisation for Intuitionistic Sequent Calculi
"... Abstract. The intuitionistic fragment of the callbyname version of Curien and Herbelin’s λµ˜µcalculus is isolated and proved strongly normalising by means of an embedding into the simplytyped λcalculus. Our embedding is a continuationandgarbagepassing style translation, the inspiring idea co ..."
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Cited by 3 (2 self)
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Abstract. The intuitionistic fragment of the callbyname version of Curien and Herbelin’s λµ˜µcalculus is isolated and proved strongly normalising by means of an embedding into the simplytyped λcalculus. Our embedding is a continuationandgarbagepassing style translation, the inspiring idea coming from Ikeda and Nakazawa’s translation of Parigot’s λµcalculus. The embedding simulates reductions while usual continuationpassingstyle transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need “units of garbage ” to be passed. We apply the same method to other calculi, namely successive extensions of the simplytyped λcalculus leading to our intuitionistic system, and already for the simplest extension we consider (λcalculus with generalised application), this yields the first proof of strong normalisation through a reductionpreserving embedding. 1
A constructive restriction of the λµcalculus
, 1999
"... We define a very natural restriction of the λµcalculus which is stable under reduction and whose type system is a restriction of the Classical Natural Deduction to intuitionistic logic. However, we show that this system is in some sense degenerated unless we provide a native disjunction. We prove t ..."
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Cited by 2 (0 self)
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We define a very natural restriction of the λµcalculus which is stable under reduction and whose type system is a restriction of the Classical Natural Deduction to intuitionistic logic. However, we show that this system is in some sense degenerated unless we provide a native disjunction. We prove that the system with native disjunction is conservative over DISlogic and also that DISlogic is constructive. From a computational standpoint, this restriction on λµterms prevents a coroutine from accessing the local environment of another coroutine.
Poetic effects
 Lingua
, 1992
"... Abstract. This paper revisits the results of Barendregt and Ghilezan [3] and generalizes them for classical logic. Instead of λcalculus, we use here λµcalculus as the basic term calculus. We consider two extensionally equivalent type assignment systems for λµcalculus, one corresponding to classic ..."
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Cited by 1 (1 self)
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Abstract. This paper revisits the results of Barendregt and Ghilezan [3] and generalizes them for classical logic. Instead of λcalculus, we use here λµcalculus as the basic term calculus. We consider two extensionally equivalent type assignment systems for λµcalculus, one corresponding to classical natural deduction, and the other to classical sequent calculus. Their relations and normalisation properties are investigated. As a consequence a short proof of Cut elimination theorem is obtained.
Parigot's Second Order λμCalculus and Inductive Types
, 2001
"... . A new proof of strong normalization of Parigot's (second order) calculus is given by a reductionpreserving embedding into system F (second order polymorphic calculus). The main idea is to use the least stable supertype for any type. These nonstrictly positive inductive types and their associat ..."
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. A new proof of strong normalization of Parigot's (second order) calculus is given by a reductionpreserving embedding into system F (second order polymorphic calculus). The main idea is to use the least stable supertype for any type. These nonstrictly positive inductive types and their associated iteration principle are available in system F, and allow to give a translation vaguely related to CPS translations (corresponding to the Kolmogorov embedding of classical logic into intuitionistic logic). However, they simulate Parigot's reductions whereas CPS translations hide them. As a major advantage, this embedding does not use the idea of reducing stability (:: ! ) to that for atomic formulae. Therefore, it even extends to noninterleaving positive xedpoint types. As a nontrivial application, strong normalization of calculus, extended by primitive recursion on monotone inductive types, is established. 1 Introduction calculus [12] essentially is the extension of nat...