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The monitoring power of forcing transformations

Abstract : In this thesis, we are interested in semantical proof of correctness results for complex programming languages. We advocate the need for a theoretical framework that allows one to build realizability semantics using basic blocks and use algebraic constructions to combine those blocks. We propose a framexork based on the composition of Linear variants of Krivine realizability and Cohen forcing. The first ingredient of environment that prossesses special memory cells used to monitor the execution of programs, in the style of Miquel's KFAM. It is shown how this new machine emerges from a Linear forcing program transformation. We then introduce the central notionof Monitoring Algebra and the associated realizability interpretation. Different monitoring algebras induce sound semantics of different programing languages. We then present an algebraic construction to combine different Monitoring Algebras based on the techniuqe of forcing iteration. We show that the forcing structure can be used to represent the consumption or resources, in particular time, but also step-indexing or the use of higher-order references. We finally apply our results to retrieve three complex soundness results : - We give the first semantical proof of the consistency of a contraction-free nave set theory, originally introduced by Grishin. - Wuse our framework to obtain a polynomial time terminationresult for a light-logic based programming language featuring recursive types. - We reprove to soundness of a language with references that supports strong updates, based on a Linear type system inspired by a workof Ahmed et al.
Keywords : Realizability
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Aloïs Brunel. The monitoring power of forcing transformations. Logic in Computer Science [cs.LO]. Université Paris-Nord - Paris XIII, 2014. English. ⟨NNT : 2014PA132069⟩. ⟨tel-02335554⟩

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