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Mizari¾?is one of the pioneering systems for mathematics formalization, which still has ani¾?active user community. The project has been in constant development since 1973, when Andrzej Trybulec designed the fundamentals of ai¾?language capable of rigorously encoding mathematical knowledge in ai¾?computerized environment which guarantees its full logical correctness. Since then, the system with its feature-rich language devised to approximate mathematics writing has influenced other formalization projects and has given rise to ai¾?number of Mizari¾?modes implemented on top of other systems. However, the information about the system as ai¾?whole is not readily available to developers of other systems. Various papers describing Mizari¾?features have been rather incremental and focused only on particular newly implemented Mizari¾?aspects. The objective of the current paper is to give ai¾?survey of the most important Mizari¾?features that distinguish it from other popular proof checkers. We also go ai¾?step further and describe most important current trends and lines of development that go beyond the state-of-the-art system.

In this paper, we report our first experiments in using learning-assisted automated reasoning for the formal analysis of physical systems. In particular, we investigate the performance of automated proofs as compared to interactive ones done in HOL for the verification of ray and electromagnetic optics. Apart from automation, we also provide brief initial exploration of more general issues in formalization of physics, such as its presentation and foundations.

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In recent years, large corpora of formally expressed knowledge have become available in the fields of formal mathematics, software verification, and real-world ontologies. The Learning2Reason project aims to develop novel machine learning methods for computer-assisted reasoning on such corpora. Our global research goals are to provide good methods for selecting relevant knowledge from large formal knowledge bases, and to combine them with automated reasoning methods.

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We recently started the Formalin project to create a formal version of the C99 standard for the C programming language. We are writing three matching formalizations for the interactive theorem provers HOL4, Isabelle/HOL and Coq, that all closely follow the existing C99 standard text. The project runs from 2011 to 2015, and involves a full time PhD student, a half time researcher and several scientific advisors. The project differs from existing work in that our aim is to formalize the full C99 standard. This means that we treat the C preprocessor, the C standard library, floating point arithmetic, and 'dirty' C features like signal handling and volatile variables. Importantly, this means we also treat embedded C programs without explicit input/output.

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. We provide an implementation of the exact real numbers in the Coq proof assistant. This improves on the earlier Coq-implementation by O'Connor in two ways: we use dyadic rationals built from the machine integers and we optimize computation of power series by using approximate division. Moreover, we use type classes for clean mathematical interfaces. This appears to be the first time that type classes are used in heavy computation. We obtain over a 100 times speed up of the basic operations and indications for improving the Coq system.

We present several steps towards large formal mathematical wikis. The Coq proof assistant together with the CoRN repository are added to the pool of systems handled by the general wiki system described in \cite{DBLP:conf/aisc/UrbanARG10}. A smart re-verification scheme for the large formal libraries in the wiki is suggested for Mizar/MML and Coq/CoRN, based on recently developed precise tracking of mathematical dependencies. We propose to use features of state-of-the-art filesystems to allow real-time cloning and sandboxing of the entire libraries, allowing also to extend the wiki to a true multi-user collaborative area. A number of related issues are discussed.

We mark up a corpus of LATEX lecture notes semantically and expose them as Linked Data in XHTML+MathML+RDFa. Our application makes the resulting documents interactively browsable for students. Our ontology helps to answer queries from students and lecturers, and paves the path towards an integration of our corpus with external sites. © 2010 Springer-Verlag.

A total of 13,732 animals were allotted to 64 pens (average 215 head per pen) in two commercial feedyards to compare the effects of growth-promoting implants with and without tylosin tartrate on performance, carcass merit and buller incidence in yearling steers. Implant formulations used in the study included 120 mg trenbolone acetate and 24 mg estradiol with 29 mg of tylosin tartrate (120/24 T) and 120 mg trenbolone acetate and 24 mg estradiol (120/24). Steers implanted without tylosin tartrate tended to have a lower incidence of bullers (1.17 vs 1.49%; P =0.08), and had a greater percentage of USDA quality grade Prime and Choice carcasses (42.51 vs. 40.26%; P =0.02) than steers given an implant with tylosin tartrate. No other differences in performance or carcass characteristics were noted ( P >0.10). Under the conditions of this study, there was no benefit to using tylosin tartrate in generically comparable growth-promoting implants., The Bovine Practitioner, Vol. 42, No. 2 (2008 Summer)