181 research outputs found
Eliciting implicit assumptions of proofs in the MIZAR Mathematical Library by property omission
When formalizing proofs with interactive theorem provers, it often happens
that extra background knowledge (declarative or procedural) about mathematical
concepts is employed without the formalizer explicitly invoking it, to help the
formalizer focus on the relevant details of the proof. In the contexts of
producing and studying a formalized mathematical argument, such mechanisms are
clearly valuable. But we may not always wish to suppress background knowledge.
For certain purposes, it is important to know, as far as possible, precisely
what background knowledge was implicitly employed in a formal proof. In this
note we describe an experiment conducted on the MIZAR Mathematical Library of
formal mathematical proofs to elicit one such class of implicitly employed
background knowledge: properties of functions and relations (e.g.,
commutativity, asymmetry, etc.).Comment: 11 pages, 3 tables. Preliminary version presented at the 3rd Workshop
on Modules and Libraries for Proof Assistants (MLPA-11), affiliated with the
2nd Conference on Interactive Theorem Proving (ITP-2011), Nijmegen, the
Netherland
SEPIA: Search for Proofs Using Inferred Automata
This paper describes SEPIA, a tool for automated proof generation in Coq.
SEPIA combines model inference with interactive theorem proving. Existing proof
corpora are modelled using state-based models inferred from tactic sequences.
These can then be traversed automatically to identify proofs. The SEPIA system
is described and its performance evaluated on three Coq datasets. Our results
show that SEPIA provides a useful complement to existing automated tactics in
Coq.Comment: To appear at 25th International Conference on Automated Deductio
Vortex density models for superconductivity and superfluidity
We study some functionals that describe the density of vortex lines in
superconductors subject to an applied magnetic field, and in Bose-Einstein
condensates subject to rotational forcing, in quite general domains in 3
dimensions. These functionals are derived from more basic models via
Gamma-convergence, here and in a companion paper. In our main results, we use
these functionals to obtain descriptions of the critical applied magnetic field
(for superconductors) and forcing (for Bose-Einstein), above which ground
states exhibit nontrivial vorticity, as well as a characterization of the
vortex density in terms of a non local vector-valued generalization of the
classical obstacle problem.Comment: 34 page
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