High-Level Theories

Authors:
Jacques Carette;William M. Farmer
Affiliations:
Department of Computing and Software, McMaster University, Hamilton, Canada;Department of Computing and Software, McMaster University, Hamilton, Canada
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

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Abstract

We introduce high-level theories in analogy with high-level programming languages. The basic point is that even though one can define many theories via simple, low-level axiomatizations, that is neither an effective nor a comfortable way to work with such theories. We present an approach which is closer to what users of mathematics employ, while still being based on formal structures.