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This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be
isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's λμ-calculus with the idea
of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms.
This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction
system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of
the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics
of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned
isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third
problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format,
that affects mainly the recent proof-theoretic efforts of derivation of λ-calculi for call-by-value. An isomorphic counterpart
to the Q-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new
λ-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT
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