Alternative Aggregates in Mizar

Authors:
Gilbert Lee;Piotr Rudnicki
Affiliations:
Dept. of Computer Science, University of Victoria,;Dept. of Computing Science, University of Alberta,
Venue:
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Year:
2007

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Abstract

Mizarprovides built-in support for defining structures (aggregates) like the familiar algebraic systems of groups or vector spaces. When trying to employ these structures for formalizing graph algorithms we ran into substantial problems stemming from the fact that fields in Mizarstructures are not first class objects. We decided that a different approach would be more suitable for the task at hand. Starting from scratch, we modeled structures as functions. In our approach, fields in structures are first class objects and just this one factor made working with graph algorithms much more convenient. We report on our experience and argue that our approach to aggregates is more suitable for a proof assistant like Mizar.