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A Logical Investigation of Interaction Systems

Abstract : The topic of this thesis is the study of interaction systems, a notion modeling interactions between a program and its environment.

The first part develops the general theory of those interaction systems in Martin-Löf dependent type theory. It introduces several inductive and coinductive definitions of interest on those interaction systems. We study in particular the strong link between interaction systems and formal topology and give an application by formulating a completeness theorem (in terms of interaction systems) with respect to a topological semantics for (linear) geometric theories.

In all the thesis, a central notion is that of _simulations:_ it allows to define the notion of morphism between interaction systems. It is possible to prove an equivalence between this category and the simpler category of predicate transformers.

We can then translate the constructions from the first part in this new context and obtain a new denotational model for linear logic. This model is then extended to second-order.

Finally, specific properties of interaction systems / predicate transformers are used to give a model of the differential lambda-calculus. This presupposes the addition of non-determinism, which is fully supported by interaction systems / predicate transformers.
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Contributor : Pierre Hyvernat Connect in order to contact the contributor
Submitted on : Thursday, March 9, 2006 - 10:58:45 AM
Last modification on : Monday, March 29, 2021 - 3:24:02 PM
Long-term archiving on: : Monday, September 17, 2012 - 12:30:09 PM


  • HAL Id : tel-00011871, version 1



Pierre Hyvernat. A Logical Investigation of Interaction Systems. Mathematics [math]. Université de la Méditerranée - Aix-Marseille II, 2005. English. ⟨tel-00011871⟩



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