A Proof-Theoretic Foundation of Abortive Continuations

Zena Ariola 1 Hugo Herbelin 2 Amr Sabry 3
2 LOGICAL - Logic and computing
UP11 - Université Paris-Sud - Paris 11, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8623
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 lambda-mu corresponds to minimal classical logic. A continuation constant must be added to lambda-mu 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.
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Higher-Order and Symbolic Computation, Springer Verlag, 2007, 20 (4), 〈10.1007/s10990-007-9007-z〉
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Zena Ariola, Hugo Herbelin, Amr Sabry. A Proof-Theoretic Foundation of Abortive Continuations. Higher-Order and Symbolic Computation, Springer Verlag, 2007, 20 (4), 〈10.1007/s10990-007-9007-z〉. 〈hal-00697242〉

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