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Focalisation and Classical Realisability
TLDR
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
A theory of effects and resources: adjunction models and polarised calculi
TLDR
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
Models of a Non-associative Composition
TLDR
We characterise the polarised evaluation order through a categorical structure where the hypothesis that composition is associative is relaxed. Expand
The Duality of Computation under Focus
TLDR
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
Syntax and Models of a non-Associative Composition of Programs and Proofs. (Syntaxe et modèles d'une composition non-associative des programmes et des preuves)
TLDR
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
Polarised Intermediate Representation of Lambda Calculus with Sums
TLDR
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
Formulae-as-types for an involutive negation
TLDR
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
From delimited CPS to polarisation
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 asExpand
Resource Polymorphism
TLDR
We present a resource-management model for ML-style programming languages, designed to be compatible with the OCaml philosophy and runtime model. Expand
Efficient Deconstruction with Typed Pointer Reversal (abstract)
TLDR
The resource-management model of C++ and Rust relies on compiler-generated destructors called predictably and reliably. Expand
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