Results 1  10
of
678
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 ..."
Abstract

Cited by 24 (6 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 438 (15 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
, 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
A Uniform Substitution Calculus for Differential Dynamic Logic?
"... Abstract. This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible to rely on axioms rather than axiom schemata, su ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible to rely on axioms rather than axiom schemata
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 ..."
Abstract
 Add to MetaCart
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 ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
. 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
Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the ChurchRosser Theorem
 INDAG. MATH
, 1972
"... In ordinary lambda calculus the occurrences of a bound variable are made recognizable by the use of one and the same (otherwise irrelevant) name at all occurrences. This convention is known to cause considerable trouble in cases of substitution. In the present paper a different notational system is ..."
Abstract

Cited by 369 (1 self)
 Add to MetaCart
In ordinary lambda calculus the occurrences of a bound variable are made recognizable by the use of one and the same (otherwise irrelevant) name at all occurrences. This convention is known to cause considerable trouble in cases of substitution. In the present paper a different notational system
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 ..."
Abstract
 Add to MetaCart
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 ..."
Abstract
 Add to MetaCart
. 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
Results 1  10
of
678