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Modalités de ressource et contrôle en logique tensorielle

Abstract : This thesis presents tensorial logic, a primitive version of linear logic where involutive negation is replaced by tensorial negation. As an illustration, we reformulate coherent spaces and finiteness spaces as two different models of linear logic obtained from the same model of tensorial logic by changing the negation. Tensorial logic semantics is, from our point of view, categorical and built on the notions of dialogue category and resource modalities. We provide a mild extension of Conway games that models tensorial logic and where all connectors, and in particular resource modalities, are interpreted in non-degenerate fashion. In order to construct resource modalities more automatically, a framework for computing the free algebras of an enriched T-theory is developed. This construction, based on the notion of proarrow equipment, relies on two properties: a combinatorial one, operadicity; and an algebraic one, algebraic completeness. Next, a game model equipped with a trace operator and a notion of multibracketing is presented. The control obtained from multibracketing is seen as a resource policy. This model is used to interpret a language with higher order references. Finally, we consider lower level semantics. We begin with studying the multicategorical structure induced by a dialogue category; this leads us to define control multicategories. We then formalize a semantic type safety for a compiler (assembly code) in Coq. This formalization depends upon the definition of a relational semantics for memory states whose structure is inspired by dialogue categories.
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Contributor : Nicolas Tabareau Connect in order to contact the contributor
Submitted on : Thursday, December 4, 2008 - 5:00:10 PM
Last modification on : Friday, October 23, 2020 - 4:52:08 PM
Long-term archiving on: : Saturday, November 26, 2016 - 2:44:01 AM


  • HAL Id : tel-00339149, version 3



Nicolas Tabareau. Modalités de ressource et contrôle en logique tensorielle. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2008. Français. ⟨tel-00339149v3⟩



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