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Currently published HOL formalizations of measure theory concentrate on the Lebesgue integral and they are restricted to real-valued measures. We lift this restriction by introducing the extended real numbers. We define the Borel σ-algebra for an arbitrary type forming a topological space. Then, we introduce measure spaces with extended real numbers as… (More)

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)

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)

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)

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)

- 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)

We develop a framework for expressing and analyzing the behavior of probabilistic schedulers. There, we define noninterfering schedulers by a proba-bilistic interpretation of Goguen and Meseguer's seminal notion of noninterfer-ence. Noninterfering schedulers are proved to be safe in the following sense: if a multi-threaded program is possibilistically… (More)

The usual definition facilities in theorem provers cannot handle all recursive functions on lazy lists; the filter function is a prime counterexample. We present two new ways of directly defining functions like filter by exploiting their dual nature as producers and consumers. Borrowing from domain theory and topology, we define them as a least fixpoint… (More)