26 research outputs found
ATP and Presentation Service for Mizar Formalizations
This paper describes the Automated Reasoning for Mizar (MizAR) service, which
integrates several automated reasoning, artificial intelligence, and
presentation tools with Mizar and its authoring environment. The service
provides ATP assistance to Mizar authors in finding and explaining proofs, and
offers generation of Mizar problems as challenges to ATP systems. The service
is based on a sound translation from the Mizar language to that of first-order
ATP systems, and relies on the recent progress in application of ATP systems in
large theories containing tens of thousands of available facts. We present the
main features of MizAR services, followed by an account of initial experiments
in finding proofs with the ATP assistance. Our initial experience indicates
that the tool offers substantial help in exploring the Mizar library and in
preparing new Mizar articles
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
Premise Selection and External Provers for HOL4
Learning-assisted automated reasoning has recently gained popularity among
the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an
add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system
that provides machine learning-based premise selection and automated reasoning
also for HOL4. We efficiently record the HOL4 dependencies and extract features
from the theorem statements, which form a basis for premise selection.
HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof
formats, which are then processed by the ATPs. We discuss the different
evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure
the performance of HOLyHammer on the HOL4 standard library. The results are
combined accordingly and compared with the HOL Light experiments, showing a
comparably high quality of predictions. The system directly benefits HOL4 users
by automatically finding proofs dependencies that can be reconstructed by
Metis
HOL(y)Hammer: Online ATP Service for HOL Light
HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable)
mathematics encoded in the HOL Light system. The service allows its users to
upload and automatically process an arbitrary formal development (project)
based on HOL Light, and to attack arbitrary conjectures that use the concepts
defined in some of the uploaded projects. For that, the service uses several
automated reasoning systems combined with several premise selection methods
trained on all the project proofs. The projects that are readily available on
the server for such query answering include the recent versions of the
Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service
runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP
combinations and 4 decision procedures that contribute to its overall
performance. The system is also available for local installation by interested
users, who can customize it for their own proof development. An Emacs interface
allowing parallel asynchronous queries to the service is also provided. The
overall structure of the service is outlined, problems that arise and their
solutions are discussed, and an initial account of using the system is given
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Smart premise selection is essential when using automated reasoning as a tool
for large-theory formal proof development. A good method for premise selection
in complex mathematical libraries is the application of machine learning to
large corpora of proofs. This work develops learning-based premise selection in
two ways. First, a newly available minimal dependency analysis of existing
high-level formal mathematical proofs is used to build a large knowledge base
of proof dependencies, providing precise data for ATP-based re-verification and
for training premise selection algorithms. Second, a new machine learning
algorithm for premise selection based on kernel methods is proposed and
implemented. To evaluate the impact of both techniques, a benchmark consisting
of 2078 large-theory mathematical problems is constructed,extending the older
MPTP Challenge benchmark. The combined effect of the techniques results in a
50% improvement on the benchmark over the Vampire/SInE state-of-the-art system
for automated reasoning in large theories.Comment: 26 page
A theorem proving framework for the formal verification of Web Services Composition
We present a rigorous framework for the composition of Web Services within a
higher order logic theorem prover. Our approach is based on the
proofs-as-processes paradigm that enables inference rules of Classical Linear
Logic (CLL) to be translated into pi-calculus processes. In this setting,
composition is achieved by representing available web services as CLL
sentences, proving the requested composite service as a conjecture, and then
extracting the constructed pi-calculus term from the proof. Our framework,
implemented in HOL Light, not only uses an expressive logic that allows us to
incorporate multiple Web Services properties in the composition process, but
also provides guarantees of soundness and correctness for the composition.Comment: In Proceedings WWV 2011, arXiv:1108.208
GRUNGE: A Grand Unified ATP Challenge
This paper describes a large set of related theorem proving problems obtained
by translating theorems from the HOL4 standard library into multiple logical
formalisms. The formalisms are in higher-order logic (with and without type
variables) and first-order logic (possibly with multiple types, and possibly
with type variables). The resultant problem sets allow us to run automated
theorem provers that support different logical formats on corresponding
problems, and compare their performances. This also results in a new "grand
unified" large theory benchmark that emulates the ITP/ATP hammer setting, where
systems and metasystems can use multiple ATP formalisms in complementary ways,
and jointly learn from the accumulated knowledge.Comment: CADE 27 -- 27th International Conference on Automated Deductio