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Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
, 1996
"... Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. In that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. The oe calculus of explicit s ..."
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Cited by 24 (6 self)
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Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. In that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. The oe calculus of explicit
Confluence and Preservation of Strong Normalisation in an Explicit Substitutions Calculus
, 1995
"... Explicit substitutions calculi are formal systems that implement fireduction by means of an internal substitution operator. Thus, in that calculi it is possible to delay the application of a substitution to a term or to consider terms with partially applied substitutions. This feature is useful, f ..."
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Cited by 10 (0 self)
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, for instance, to represent incomplete proofs in type based proof systems. The oe calculus of explicit substitutions proposed by Abadi, Cardelli, Curien and L'evy gives an elegant way to deal with management of variable names and substitutions of calculus. However, oe does not preserve strong
Formalizing a Named Explicit Substitutions Calculus in Coq
"... Abstract. Explicit Substitutions (ES) calculi are extensions of the λcalculus that internalize the substitution operation, which is a metaoperation, by taking it as an ordinary operation belonging to the grammar of the ES calculus. As a formal system, ES are closer to implementations of function ..."
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Abstract. Explicit Substitutions (ES) calculi are extensions of the λcalculus that internalize the substitution operation, which is a metaoperation, by taking it as an ordinary operation belonging to the grammar of the ES calculus. As a formal system, ES are closer to imple
Strong normalisation of Herbelin's explicit substitution calculus with substitution propagation
"... . Herbelin presented (at CSL'94) a simple sequent calculus for minimal implicational logic, extensible to full rstorder intuitionistic logic, with a complete system of cutreduction rules which is both conuent and strongly normalising. Some of the cut rules may be regarded as rules to construc ..."
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Cited by 6 (0 self)
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to construct explicit substitutions. He observed that the addition of a cut permutation rule, for propagation of such substitutions, breaks the proof of strong normalisation; the implicit conjecture is that the rule may be added without breaking strong normalisation. We prove this conjecture, thus showing how
Explicit substitutions
, 1996
"... The λσcalculus is a refinement of the λcalculus where substitutions are manipulated explicitly. The λσcalculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λcalculus and concrete implementatio ..."
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Cited by 438 (15 self)
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The λσcalculus is a refinement of the λcalculus where substitutions are manipulated explicitly. The λσcalculus provides a setting for studying the theory of substitutions, with pleasant mathematical properties. It is also a useful bridge between the classical λcalculus and concrete
Explicit substitutions for the calculus
"... Abstract. The calculus is a calculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong normalisa ..."
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Abstract. The calculus is a calculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce exp, an explicit substitution calculus for , and study its properties. In particular, we show that exp preserves strong
Explicit substitutions for the lambda Deltacalculus
"... . The \Deltacalculus is a calculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce \Deltaexp, an explicit substitution calculus for \Delta, and study its properties. In particular, we show that \Deltaexp preserves ..."
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. The \Deltacalculus is a calculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce \Deltaexp, an explicit substitution calculus for \Delta, and study its properties. In particular, we show that \Deltaexp preserves
Explicit Substitutions for the λΔcalculus
"... The λΔcalculus is a λcalculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce λΔexp, an explicit substitution calculus for λΔ, and study its properties. In particular, we show that λΔexp preserves strong normalisa ..."
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The λΔcalculus is a λcalculus with a controllike operator whose reduction rules are closely related to normalisation procedures in classical logic. We introduce λΔexp, an explicit substitution calculus for λΔ, and study its properties. In particular, we show that λΔexp preserves strong
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"... Strong normalisation of Herbelin's explicit substitution calculus with substitution propagation ..."
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Strong normalisation of Herbelin's explicit substitution calculus with substitution propagation
Results 1  10
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