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Enriched concurrent games : witnesses for proofs and resource analysis

Aurore Alcolei 1, 2
2 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This thesis presents a general framework for enriching causal concurrent games model with annotations. These annotations can be viewed as meta-data on strategies: they are modified throughout interactions but do not affect their general flow of control. These data can be of various nature, in particular our enrichment is parametrised over any multi-sorted equational theory and can also reflect structure upon these data such as a partial order. From a semantics point of view, this construction is motivated by problems from both logic and programming languages: On the logic side, the annotated games model specialised to first-order terms enables us to give a novel interpretation of first-order classical proofs as concurrent strategies carrying first-order witnesses. In particular this answer the question of giving a compositional version to Herbrand’s theorem while avoiding the usual proof sequentialization of other denotational approaches. On the programming language side, annotations on games offer intrinsic quantitative models. We show that those can be used to provide denotational semantics for resource consumption analysis of concurrent higher order programming language with shared memory.These enrichments, strongly connected to the causal structure of concurrent games, give an argument in favor of a causal meaning of computations.
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Submitted on : Wednesday, January 22, 2020 - 3:48:08 PM
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Aurore Alcolei. Enriched concurrent games : witnesses for proofs and resource analysis. Logic in Computer Science [cs.LO]. Université de Lyon; University of Cambridge, 2019. English. ⟨NNT : 2019LYSEN054⟩. ⟨tel-02448974⟩



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