Titlebook: Interactive Theorem Proving; 9th International Co Jeremy Avigad,Assia Mahboubi Conference proceedings 2018 Springer Nature Switzerland AG 2

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,A Coq Formalisation of SQL’s Execution Engines,level Coq specification for data-centric operators intended to capture their essence. We, then, provide two Coq implementations of our specification. The first one, the physical algebra, consists in the low level operators found in systems such as Postgresql or Oracle. The second, SQL algebra, is an

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A , Tactic for Equality Learning in Linear Arithmetic,mprove this behavior: when the goal is not provable in linear arithmetic, we strengthen the hypotheses with new equalities discovered from the linear inequalities. These equalities may help other . tactics to discharge the goal. In other words, we apply – in interactive proofs – a seminal idea of SM

煤渣

The Coinductive Formulation of Common Knowledge,ics, similar in form to the epistemic system S5, but at the level of events on possible worlds rather than as a logical derivation system. We have two major new results. Firstly, the operator semantics is equivalent to the relational semantics: we discovered that this requires a new hypothesis of .

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A Formal Proof of the Minor-Exclusion Property for Treewidth-Two Graphs,s a minor. This result is a milestone towards a formal proof of the recent result that isomorphism of treewidth-two graphs can be finitely axiomatized. The proof is based on a function extracting terms from K4-free graphs in such a way that the interpretation of an extracted term yields a treewidth-

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Verified Analysis of Random Binary Tree Structures,assistant Isabelle/HOL. In particular, we consider the expected number of comparisons in randomised quicksort, the relationship between randomised quicksort and average-case deterministic quicksort, the expected shape of an unbalanced random Binary Search Tree, and the expected shape of a Treap. The

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HOL Light QE, do not allow one to discuss syntax. . is a version of Church’s type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the . logic is also a version of Church’s type theory, we decided to add quotation and evaluation to . to demon

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