We develop a polarised variant of Curien and Herbelin's λµµ calculus suitable for sequent calculi that admit a focalising cut elimination (i.e. whose proofs are focalised when cut-free), such as Girard's classical logic LC or linear logic.Expand

We consider the Curry-Howard-Lambek correspondence for effectful computation and resource management, specifically proposing polarised calculi together with presheaf-enriched adjunction models as a comprehensive semantic theory relating logical systems, typed calculi, and categorical models in this context.Expand

We review the relationship between abstract machines for (call- by-name or call-by-value) λ-calculi (extended with Felleisen’s \(\mathcal C\)) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit of the duality of computation.Expand

The thesis is a contribution to the understanding of the nature, role, and mechanisms of polarisation in programming languages, proof theory and categorical models.Expand

We propose an untyped representation-an intermediate calculus-for the λ-calculus with sums, based on the following principles: 1) Computation is described as the reduction of pairs of an expression and a context; the context must be represented inside-out, 2) operations are represented abstractly by their transition rule, 3) Positive and negative expressions are respectively eager and lazy; this polarity is an approximation of the type.Expand

We show that there is a formulae-as-types correspondence between the involutive negation in proof theory and a notion of high-level access to the stacks studied by Felleisen and Clements.Expand

The understanding of continuation-passing style (CPS) translations, an historical source of denotational semantics for programming languages, benefits from notions brought by linear logic, such as… Expand

We present a resource-management model for ML-style programming languages, designed to be compatible with the OCaml philosophy and runtime model.Expand