28,881 research outputs found
The Common HOL Platform
The Common HOL project aims to facilitate porting source code and proofs
between members of the HOL family of theorem provers. At the heart of the
project is the Common HOL Platform, which defines a standard HOL theory and API
that aims to be compatible with all HOL systems. So far, HOL Light and hol90
have been adapted for conformance, and HOL Zero was originally developed to
conform. In this paper we provide motivation for a platform, give an overview
of the Common HOL Platform's theory and API components, and show how to adapt
legacy systems. We also report on the platform's successful application in the
hand-translation of a few thousand lines of source code from HOL Light to HOL
Zero.Comment: In Proceedings PxTP 2015, arXiv:1507.0837
Sharing a Library between Proof Assistants: Reaching out to the HOL Family
We observe today a large diversity of proof systems. This diversity has the
negative consequence that a lot of theorems are proved many times. Unlike
programming languages, it is difficult for these systems to co-operate because
they do not implement the same logic. Logical frameworks are a class of theorem
provers that overcome this issue by their capacity of implementing various
logics. In this work, we study the STTforall logic, an extension of Simple Type
Theory that has been encoded in the logical framework Dedukti. We present a
translation from this logic to OpenTheory, a proof system and interoperability
tool between provers of the HOL family. We have used this translation to export
an arithmetic library containing Fermat's little theorem to OpenTheory and to
two other proof systems that are Coq and Matita.Comment: In Proceedings LFMTP 2018, arXiv:1807.0135
Translating HOL to Dedukti
Dedukti is a logical framework based on the lambda-Pi-calculus modulo
rewriting, which extends the lambda-Pi-calculus with rewrite rules. In this
paper, we show how to translate the proofs of a family of HOL proof assistants
to Dedukti. The translation preserves binding, typing, and reduction. We
implemented this translation in an automated tool and used it to successfully
translate the OpenTheory standard library.Comment: In Proceedings PxTP 2015, arXiv:1507.0837
On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants
We study the Chern-Simons topological quantum field theory with an
inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple
one by taking its semi-direct product with its Lie algebra. We find that the
standard knot observables (i.e. traces of holonomies along knots) essentially
vanish, but yet, the non-semi-simplicity of our gauge group allows us to
consider a class of un-orthodox observables which breaks gauge invariance at
one point and which lead to a non-trivial theory on long knots in
. We have two main morals : 1. In the non-semi-simple case, there
is more to observe in Chern-Simons theory! There might be other interesting non
semi-simple gauge groups to study in this context beyond our example. 2. In our
case of an inhomogeneous gauge group, we find that Chern-Simons theory with the
un-orthodox observable is actually the same as 3D BF theory with the
Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a
simplification of their results and enables us to generalize and solve a
problem they posed regarding the relation between BF theory and the
Alexander-Conway polynomial. Our result is that the most general knot invariant
coming from pure BF topological quantum field theory is in the algebra
generated by the coefficients of the Alexander-Conway polynomial.Comment: To appear in Journal of Mathematical Physics vol.46 issue 12.
Available on http://link.aip.org/link/jmapaq/v46/i1
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