128 research outputs found
Matching concepts across HOL libraries
Many proof assistant libraries contain formalizations of the same
mathematical concepts. The concepts are often introduced (defined) in different
ways, but the properties that they have, and are in turn formalized, are the
same. For the basic concepts, like natural numbers, matching them between
libraries is often straightforward, because of mathematical naming conventions.
However, for more advanced concepts, finding similar formalizations in
different libraries is a non-trivial task even for an expert.
In this paper we investigate automatic discovery of similar concepts across
libraries of proof assistants. We propose an approach for normalizing
properties of concepts in formal libraries and a number of similarity measures.
We evaluate the approach on HOL based proof assistants HOL4, HOL Light and
Isabelle/HOL, discovering 398 pairs of isomorphic constants and types
Sharing HOL4 and HOL Light proof knowledge
New proof assistant developments often involve concepts similar to already
formalized ones. When proving their properties, a human can often take
inspiration from the existing formalized proofs available in other provers or
libraries. In this paper we propose and evaluate a number of methods, which
strengthen proof automation by learning from proof libraries of different
provers. Certain conjectures can be proved directly from the dependencies
induced by similar proofs in the other library. Even if exact correspondences
are not found, learning-reasoning systems can make use of the association
between proved theorems and their characteristics to predict the relevant
premises. Such external help can be further combined with internal advice. We
evaluate the proposed knowledge-sharing methods by reproving the HOL Light and
HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose
single best strategy could automatically find proofs for 30% of the HOL Light
problems, can prove 40% with the knowledge from HOL4
Graft versus host inhibition, fetal liver and thymus cells to minimize secondary disease.
Graft-versus-host inhibition. Iii. Fetal thymic factor and fetal liver cells to minimize secondary disease.
Graft-versus-host inhibition. Iii. Fetal thymic factor and fetal liver cells to minimize secondary disease. Abstr.
Практическое пособие направлено на закрепление теоретического материала курса «Экономика предприятия промышленности». Содержит задачи, тестовые задания и вопросы для обсуждения. Призвано оказать методическую помощь при подготовке курсовых, дипломных работ, сдаче экзамена. Материал, представленный в наглядной и доступной форме, позволит слушателям быстро освоить основные положения дисциплины.
Издание предназначено для слушателей вечерней и заочной форм обучения института повышения квалификации и переподготовки кадров
Immunologic incompetence of mouse perinatal liver hematopoietic cells against transplantation antigens.
Graft versus host inhibition ii. Fetal liver and thymus cells to minimize secondary disease. Abstr.
A modified technique for collection and processing of mouse fetal hematopoietic tissue for production of radiation chimeras. Abstr.
- …