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Theses

Concurrency, references and linear logic

Abstract : The topic of this thesis is the study of the encoding of references andconcurrency in Linear Logic. Our perspective is to demonstrate the capabilityof Linear Logic to encode side-effects to make it a viable, formalized and wellstudied compilation target for functional languages in the future. The keynotion we develop is that of routing areas: a family of proof nets whichcorrespond to a fragment of differential linear logic and which implementscommunication primitives. We develop routing areas as a parametrizable deviceand study their theory. We then illustrate their expressivity by translating aconcurrent λ-calculus featuring concurrency, references and replication to afragment of differential nets. To this purpose, we introduce a language akin toAmadio’s concurrent λ-calculus, but with explicit substitutions for bothvariables and references. We endow this language with a type and effect systemand we prove termination of well-typed terms by a mix of reducibility and anew interactive technique. This intermediate language allows us to prove asimulation and an adequacy theorem for the translation
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Yann Hamdaoui. Concurrency, references and linear logic. Logic in Computer Science [cs.LO]. Université Sorbonne Paris Cité, 2018. English. ⟨NNT : 2018USPCC190⟩. ⟨tel-02448116⟩

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