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Categorical Models for Simply Typed Resource Calculi
TLDR
We introduce the notion of differential @l-category as an extension of Blute-Cockett-Seely's differential Cartesian categories. Expand
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The Bang Calculus and the Two Girard's Translations
TLDR
We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call- by-name and call-by-value lambda-calculi to be encoded in. Expand
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Not Enough Points Is Enough
TLDR
Models of the untyped λ-calculus may be defined either as applicative structures satisfying a bunch of first-order axioms (λ-models), or as reflexive objects in cartesian closed categories (categorical models). Expand
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Weighted Relational Models of Typed Lambda-Calculi
TLDR
The category Rel of sets and relations yields one of the simplest denotational semantics of Linear Logic, and its (co)Kleisli category is an adequate model of an extension of PCF, parametrized by R. Expand
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A relational semantics for parallelism and non-determinism in a functional setting
TLDR
We introduce a λ -calculus extended with non-deterministic choice and parallel composition, and we define its operational semantics (based on the may and must intuitions underlying our two additional operations). Expand
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What is a categorical model of the differential and the resource λ-calculi?
  • Giulio Manzonetto
  • Computer Science
  • Mathematical Structures in Computer Science
  • 27 February 2012
TLDR
The differential λ-calculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator. Expand
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Applying Universal Algebra to Lambda Calculus
The aim of this article is double. From one side we survey the knowledge we have acquired these last ten years about the lattice of all λ-theories (equational extensions of untyped λ-calculus) andExpand
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A General Class of Models of H*
TLDR
We provide sufficient conditions for categorical models living in arbitrary cpo-enriched cartesian closed categories to have H∗, the maximal consistent sensible λ-theory, as their equational theory, and prove that our relational model fulfils these conditions. Expand
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Boolean Algebras for Lambda Calculus
TLDR
In this paper we show that the Stone representation theorem for Boolean algebras can be generalized to combinatory alagbras. Expand
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Full Abstraction for Resource Calculus with Tests
TLDR
We study the semantics of a resource sensitive extension of the lambda-calculus in a canonical reflexive object of a category of sets and relations, a relational version of the original Scott D infinity model of the pure lambda-Calculus. Expand
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