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Upper Bounds for Standardizations and an Application
 The Journal of Symbolic Logic
, 1996
"... We first present a new proof for the standardization theorem, a fundamental theorem in calculus. Since our proof is largely built upon structural induction on lambda terms, we can extract some bounds for the number of fireduction steps in the standard fireduction sequences obtained from transfor ..."
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Cited by 7 (1 self)
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We first present a new proof for the standardization theorem, a fundamental theorem in calculus. Since our proof is largely built upon structural induction on lambda terms, we can extract some bounds for the number of fireduction steps in the standard fireduction sequences obtained from transforming any given fireduction sequences. This result sharpens the standardization theorem and establishes a link between lazy and eager evaluation orders in the context of computational complexity. As an application, we establish a superexponential bound for the number of fireduction steps in fireduction sequences from any given simply typed terms. 1 Introduction The standardization theorem of Curry and Feys [CF58] is a very useful result, stating that if u reduces to v for terms u and v, then there is a standard fireduction from u to v. Using this theorem, we can readily prove the normalization theorem, i.e., a term has a normal form if and only if the leftmost fireduction sequence f...
Resource operators for λcalculus
 INFORM. AND COMPUT
, 2007
"... We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s proofnets. We show the operational behaviour of the calculus and some of its fundamental properties ..."
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Cited by 3 (2 self)
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We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic’s proofnets. We show the operational behaviour of the calculus and some of its fundamental properties such as confluence, preservation of strong normalisation, strong normalisation of simplytyped terms, step by step simulation of βreduction and full composition.
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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Cited by 2 (0 self)
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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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Cited by 2 (1 self)
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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.