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Complexity of strongly normalising λterms via nonidempotent intersection types
"... We present a typing system for the λcalculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a λterm is typable if and only if it is strongly normalising. Nonidempotency brings some further information into typing trees, such as a bound o ..."
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We present a typing system for the λcalculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a λterm is typable if and only if it is strongly normalising. Nonidempotency brings some further information into typing trees, such as a bound on the longest βreduction sequence reducing a term to its normal form. We actually present these results in Klop’s extension of λcalculus, where the bound that is read in the typing tree of a term is refined into an exact measure of the longest reduction sequence. This complexity result is, for longest reduction sequences, the counterpart of de Carvalho’s result for linear headreduction sequences.
Strong Normalisation of CutElimination that Simulates βReduction
"... This paper is concerned with strong normalisation of cutelimination for a standard intuitionistic sequent calculus. The cutelimination procedure is based on a rewrite system for proofterms with cutpermutation rules allowing the simulation of βreduction. Strong normalisation of the typed terms i ..."
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This paper is concerned with strong normalisation of cutelimination for a standard intuitionistic sequent calculus. The cutelimination procedure is based on a rewrite system for proofterms with cutpermutation rules allowing the simulation of βreduction. Strong normalisation of the typed terms is inferred from that of the simplytyped λcalculus, using the notions of safe and minimal reductions as well as a simulation in NederpeltKlop’s λIcalculus. It is also shown that the typefree terms enjoy the preservation of strong normalisation (PSN) property with respect to βreduction in an isomorphic image of the typefree λcalculus.
Addenda to “Delayed substitutions”
, 2008
"... A proposition in the author’s “Delayed substitutions”, RTA’07, concerned with preservation, by certain permutative reductions, of the length of the longest βreduction sequence from a λterm, has an incomplete proof in that paper. The purpose of this note is to fix that proof. This is achieved throu ..."
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A proposition in the author’s “Delayed substitutions”, RTA’07, concerned with preservation, by certain permutative reductions, of the length of the longest βreduction sequence from a λterm, has an incomplete proof in that paper. The purpose of this note is to fix that proof. This is achieved through a new, general result, from which one can prove preservation of the length of the longest βreduction by other notions of reduction.