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

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

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

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

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) and… Expand

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

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