297 research outputs found
Initial Experiments with TPTP-style Automated Theorem Provers on ACL2 Problems
This paper reports our initial experiments with using external ATP on some
corpora built with the ACL2 system. This is intended to provide the first
estimate about the usefulness of such external reasoning and AI systems for
solving ACL2 problems.Comment: In Proceedings ACL2 2014, arXiv:1406.123
Learning-Assisted Automated Reasoning with Flyspeck
The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers
MaLeS is an automatic tuning framework for automated theorem provers. It
provides solutions for both the strategy finding as well as the strategy
scheduling problem. This paper describes the tool and the methods used in it,
and evaluates its performance on three automated theorem provers: E, LEO-II and
Satallax. An evaluation on a subset of the TPTP library problems shows that on
average a MaLeS-tuned prover solves 8.67% more problems than the prover with
its default settings
CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates
Termination is an important property of programs; notably required for
programs formulated in proof assistants. It is a very active subject of
research in the Turing-complete formalism of term rewriting systems, where many
methods and tools have been developed over the years to address this problem.
Ensuring reliability of those tools is therefore an important issue. In this
paper we present a library formalizing important results of the theory of
well-founded (rewrite) relations in the proof assistant Coq. We also present
its application to the automated verification of termination certificates, as
produced by termination tools
- …