3 research outputs found
Integrating multiple sources to answer questions in Algebraic Topology
We present in this paper an evolution of a tool from a user interface for a
concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to
a front-end allowing the interoperability among different sources for
computation and deduction. The architecture allows the system not only to
interface several systems, but also to make them cooperate in shared
calculations.Comment: To appear in The 9th International Conference on Mathematical
Knowledge Management: MKM 201
A Universal Machine for Biform Theory Graphs
Broadly speaking, there are two kinds of semantics-aware assistant systems
for mathematics: proof assistants express the semantic in logic and emphasize
deduction, and computer algebra systems express the semantics in programming
languages and emphasize computation. Combining the complementary strengths of
both approaches while mending their complementary weaknesses has been an
important goal of the mechanized mathematics community for some time. We pick
up on the idea of biform theories and interpret it in the MMTt/OMDoc framework
which introduced the foundations-as-theories approach, and can thus represent
both logics and programming languages as theories. This yields a formal,
modular framework of biform theory graphs which mixes specifications and
implementations sharing the module system and typing information. We present
automated knowledge management work flows that interface to existing
specification/programming tools and enable an OpenMath Machine, that
operationalizes biform theories, evaluating expressions by exhaustively
applying the implementations of the respective operators. We evaluate the new
biform framework by adding implementations to the OpenMath standard content
dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final
publication is available at http://link.springer.com