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- Johannes Hölzl, Armin Heller
- ITP
- 2011

(Most of the first three chapters)

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)

- Johannes Hölzl, Fabian Immler, Brian Huffman
- ITP
- 2013

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)

- Fabian Immler, Johannes Hölzl
- ITP
- 2012

- Andreas Lochbihler, Johannes Hölzl
- ITP
- 2014

- Jeremy Avigad, Johannes Hölzl, Luke Serafin
- Journal of Automated Reasoning
- 2017

We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle’s libraries for analysis and measure-theoretic probability. The proof of the theorem uses characteristic functions, which are a kind of Fourier transform, to demonstrate that, under suitable… (More)

- Johannes Hölzl
- 2013

- Andrei Popescu, Johannes Hölzl, Tobias Nipkow
- CPP
- 2012

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)

- Andrei Popescu, Johannes Hölzl, Tobias Nipkow
- CPP
- 2013

We present an Isabelle formalization of probabilistic noninterference for a multi-threaded language with uniform scheduling. Unlike in previous settings from the literature, here probabilistic behavior comes from both the sched-uler and the individual threads, making the language more realistic and the mathematics more challenging. We study resumption-based… (More)

- Manuel Eberl, Johannes Hölzl, Tobias Nipkow
- ESOP
- 2014

Bhat et al. [1] developed an inductive compiler that computes density functions for probability spaces described by programs in a prob-abilistic functional language. In this work, we implement such a compiler for a modified version of this language within the theorem prover Isabelle and give a formal proof of its soundness w.r.t. the semantics of the source… (More)