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16
Categorical models for simply typed resource calculi
 ENTCS
"... We introduce the notion of differential λcategory as an extension of BluteCockettSeely’s differential Cartesian categories. We prove that differential λcategories can be used to model the simply typed versions of: (i) the differential λcalculus, a λcalculus extended with a syntactic derivative ..."
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Cited by 7 (3 self)
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We introduce the notion of differential λcategory as an extension of BluteCockettSeely’s differential Cartesian categories. We prove that differential λcategories can be used to model the simply typed versions of: (i) the differential λcalculus, a λcalculus extended with a syntactic derivative operator; (ii) the resource calculus, a nonlazy axiomatisation of Boudol’s λcalculus with multiplicities. Finally, we provide two
The differential λµcalculus
 Theor. Comput. Sci
, 2007
"... We define a differential λµcalculus which is an extension of both Parigot’s λµcalculus and EhrhardRégnier’s differential λcalculus. We prove some basic properties of the system: reduction enjoys ChurchRosser and simply typed terms are strongly normalizing. Contents 1 ..."
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Cited by 6 (2 self)
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We define a differential λµcalculus which is an extension of both Parigot’s λµcalculus and EhrhardRégnier’s differential λcalculus. We prove some basic properties of the system: reduction enjoys ChurchRosser and simply typed terms are strongly normalizing. Contents 1
Execution time of lambdaterms via non uniform semantics and intersection types. Research report
, 2006
"... Abstract. The relational semantics for Linear Logic induces a semantics for the type free Lambda Calculus. This one is built on nonidempotent intersection types. We give a principal typing property for this type system. We then prove that the size of the derivations is closely related to the execut ..."
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Cited by 4 (2 self)
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Abstract. The relational semantics for Linear Logic induces a semantics for the type free Lambda Calculus. This one is built on nonidempotent intersection types. We give a principal typing property for this type system. We then prove that the size of the derivations is closely related to the execution time of lambdaterms in a particular environment machine, Krivine’s machine.
A finiteness structure on resource terms
 IN LICS
, 2010
"... We study the Taylor expansion of lambdaterms in a nondeterministic or algebraic setting, where terms can be added. The target language is a resource lambda calculus based on a differential lambdacalculus we introduced recently. This operation is not possible in the general untyped case where redu ..."
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Cited by 3 (1 self)
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We study the Taylor expansion of lambdaterms in a nondeterministic or algebraic setting, where terms can be added. The target language is a resource lambda calculus based on a differential lambdacalculus we introduced recently. This operation is not possible in the general untyped case where reduction can produce unbounded coefficients. We endow resource terms with a finiteness structure (in the sense of our earlier work on finiteness spaces) and show that the Taylor expansions of terms typeable in Girard’s system F are finitary by a reducibility method.
Full Abstraction for Resource Calculus with Tests
 In CSL, Lecture Notes in Computer Science
, 2011
"... We study the semantics of a resource sensitive extension of the λcalculus in a canonical reflexive object of a category of sets and relations, a relational version of the original Scott D ∞ model of the pure λcalculus. This calculus is related to Boudol’s resource calculus and is derived from Ehrh ..."
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Cited by 2 (1 self)
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We study the semantics of a resource sensitive extension of the λcalculus in a canonical reflexive object of a category of sets and relations, a relational version of the original Scott D ∞ model of the pure λcalculus. This calculus is related to Boudol’s resource calculus and is derived from Ehrhard and Regnier’s differential extension of Linear Logic and of the λcalculus. We extend it with new constructions, to be understood as implementing a very simple exception mechanism, and with a “must ” parallel composition. These new operations allow to associate a context of this calculus with any point of the model and to prove full abstraction for the finite subcalculus where ordinary λcalculus application is not allowed. The result is then extended to the full calculus by means of a Taylor Expansion formula. 1998 ACM Subject Classification F.4.1 Lambda calculus and related systems
Resource combinatory algebras
"... Abstract. We initiate a purely algebraic study of Ehrhard and Regnier’s resource λcalculus, by introducing three equational classes of algebras: resource combinatory algebras, resource lambdaalgebras and resource lambdaabstraction algebras. We establish the relations between them, laying down fou ..."
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Cited by 2 (0 self)
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Abstract. We initiate a purely algebraic study of Ehrhard and Regnier’s resource λcalculus, by introducing three equational classes of algebras: resource combinatory algebras, resource lambdaalgebras and resource lambdaabstraction algebras. We establish the relations between them, laying down foundations for a model theory of resource λcalculus. We also show that the ideal completion of a resource combinatory (resp. lambda, lambdaabstraction) algebra induces a “classical ” combinatory (resp. lambda, lambdaabstraction) algebra, and that any model of the classical λcalculus raising from a resource lambdaalgebra determines a λtheory which equates all terms having the same Böhm tree. 1
Transport of finiteness structures and applications
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... ..."
Differential Linear Logic and Polarization
"... We study an extension of EhrhardRegnier's differential linear logic along the lines of Laurent's polarization. We show that a particular object of the wellknown relational model of linear logic provides a denotational semantics for this new system, which canonically extends the semantics of both ..."
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We study an extension of EhrhardRegnier's differential linear logic along the lines of Laurent's polarization. We show that a particular object of the wellknown relational model of linear logic provides a denotational semantics for this new system, which canonically extends the semantics of both differential and polarized linear logics: this justifies our choice of cut elimination rules. Then we show this new system models the recently introduced convolution _*ucalculus, the same as linear logic decomposes calculus.
Di erential linear logic and polarization
 in Curien (2009
"... We extend Ehrhard Regnier's di erential linear logic along the lines of Laurent's polarization. We provide a denotational semantics of this new system in the wellknown relational model of linear logic, extending canonically the semantics of both di erential and polarized linear logics: this justi e ..."
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We extend Ehrhard Regnier's di erential linear logic along the lines of Laurent's polarization. We provide a denotational semantics of this new system in the wellknown relational model of linear logic, extending canonically the semantics of both di erential and polarized linear logics: this justi es our choice of cut elimination rules. Then we show this polarized di erential linear logic re nes the recently introduced convolution ¯λµcalculus, the same as linear logic decomposes λcalculus. 1
A NonUniform Finitary Relational Semantics of System T
, 2009
"... We study iteration and recursion operators in the denotational semantics of typed λcalculi derived from the multiset relational model of linear logic. Although these operators are defined as fixpoints of typed functionals, we prove them finitary in the sense of Ehrhard’s finiteness spaces. 1 ..."
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We study iteration and recursion operators in the denotational semantics of typed λcalculi derived from the multiset relational model of linear logic. Although these operators are defined as fixpoints of typed functionals, we prove them finitary in the sense of Ehrhard’s finiteness spaces. 1