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This thesis describes the results of a collaborative effort to formalize the proof of the central limit theorem of probability theory. That project was carried out in the Isabelle proof assistant, and builds upon and extends the libraries for mathematical analysis, in particular measure-theoretic probability theory. The formalization introduces the notion… (More)

(Most of the first three chapters)

- M. Feuerecker, D. Hauer, R. Toth, F. Demetz, J. Hölzl, M. Thiel +3 others
- European Journal of Applied Physiology
- 2011

The effects of physical exercise stress on the endocannabinoid system in humans are almost unexplored. In this prospective study, we investigated in a crossover design and under field conditions at different altitudes the effects of physical exercise on the endocannabinoid system (ECS) in 12 trained healthy volunteers. For determination of alterations on… (More)

The theory of analysis in Isabelle/HOL derives from earlier formalizations that were limited to specific concrete types: R, C and R n. Isabelle's new analysis theory unifies and generalizes these earlier efforts. The improvements are centered on two primary contributions: a generic theory of limits based on filters, and a new hierarchy of type classes that… (More)

We extended Isabelle/HOL with a pair of definitional commands for datatypes and codatatypes. They support mutual and nested (co)recursion through well-behaved type constructors, including mixed recursion–corecursion, and are complemented by syntaxes for introducing primitive (co)recursive functions and by a general proof method for reasoning coinductively.… (More)

Sparse matrix formats are typically implemented with low-level imperative programs. The optimized nature of these implementations hides the structural organization of the sparse format and complicates its verification. We define a variable-free functional language (LL) in which even advanced formats can be expressed naturally, as a pipeline-style… (More)

- Fabian Immler, Johannes Hölzl
- 2013

Since many ordinary differential equations (ODEs) do not have a closed solution, approximating them is an important problem in numerical analysis. This work formalizes a method to approximate solutions of ODEs in Isabelle/HOL. We formalize initial value problems (IVPs) of ODEs and prove the existence of a unique solution, i.e. the Picard-Lindelöf theorem.… (More)

- Johannes Hölzl
- 2013

We perform a formal analysis of compositionality techniques for proving possibilistic noninterference for a while language with parallel composition. We develop a uniform framework where we express a wide range of noninter-ference variants from the literature and compare them w.r.t. their contracts: the strength of the security properties they ensure… (More)