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Dependent Types and Explicit Substitutions
, 1999
"... We present a dependenttype system for a #calculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization. ..."
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We present a dependenttype system for a #calculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.
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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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.
A Proof of Weak Termination of Typed λσCalculi
"... . We show that reducing any simplytyped oeterm (resp. oe*) by applying the rules in oe (resp. oe *) eagerly always terminates, by a translation to the simplytyped calculus. This holds even with term and substitution metavariables. In fact, every reduction terminates provided that (fi)redexes ..."
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. We show that reducing any simplytyped oeterm (resp. oe*) by applying the rules in oe (resp. oe *) eagerly always terminates, by a translation to the simplytyped calculus. This holds even with term and substitution metavariables. In fact, every reduction terminates provided that (fi)redexes are only contracted under socalled safe contexts; and in oe, resp. oe *normal forms, all contexts around terms of sort T are safe. The result is then extended to secondorder type systems. 1 Introduction The simplytyped oecalculus does not terminate strongly [8, 9], but it terminates in the weak sense: every typed term has a normal form. We present a proof of this; in fact, we prove the widely believed claim that every reduction where oe steps are applied eagerly is finite, as a consequence of a more general theorem stating that every reduction where (fi)contraction only occurs under socalled safe contexts terminates. For the sake of generality, we prove this result even in the pres...
Dependent Types with Explicit Substitutions: A metatheoretical development
, 1997
"... We present a theory of dependent types with explicit substitutions. We follow a metatheoretical approach where open expressions expressions with metavariables are firstclass objects. The system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normal ..."
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We present a theory of dependent types with explicit substitutions. We follow a metatheoretical approach where open expressions expressions with metavariables are firstclass objects. The system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.
Operated by Universities Space Research Association
"... CÉSAR MUÑOZ∗ Abstract. We present a dependenttype system for a λcalculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak ..."
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CÉSAR MUÑOZ∗ Abstract. We present a dependenttype system for a λcalculus with explicit substitutions. In this system, metavariables, as well as substitutions, are firstclass objects. We show that the system enjoys properties like type uniqueness, subject reduction, soundness, confluence and weak normalization.
Ptime Completeness of Light Linear Logic and its Nondeterministic Extension
, 2004
"... In CSL’99 Roversi pointed out that the Turing machine encoding of Girard’s seminal paper ”Light Linear Logic ” has a flaw. Moreover he presented a working version of the encoding in Light Affine Logic, but not in Light Linear Logic. In this paper we present a working version of the encoding in Light ..."
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In CSL’99 Roversi pointed out that the Turing machine encoding of Girard’s seminal paper ”Light Linear Logic ” has a flaw. Moreover he presented a working version of the encoding in Light Affine Logic, but not in Light Linear Logic. In this paper we present a working version of the encoding in Light Linear Logic. The idea of the encoding is based on a remark of Girard’s tutorial paper on Linear Logic. The encoding is also an example which shows usefulness of additive connectives. Moreover we also consider a nondeterministic extension of Light Linear Logic. We show that the extended system is NPcomplete in the same meaning as Pcompleteness of Light Linear Logic.