Type classes and filters for mathematical analysis in Isabelle/HOL

Authors:
Johannes Hölzl;Fabian Immler;Brian Huffman
Affiliations:
Institut für Informatik, Technische Universität München, Germany;Institut für Informatik, Technische Universität München, Germany;Galois, Inc.
Venue:
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Year:
2013

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Abstract

The theory of analysis in Isabelle/HOL derives from earlier formalizations that were limited to specific concrete types: ℝ, ℂ and ℝn. Isabelle's new analysis theory unifies and generalizes these earlier efforts. The improvements are centered on two primary contributions: a generic theory of limits based on filters, and a new hierarchy of type classes that includes various topological, metric, vector, and algebraic spaces. These let us apply many results in multivariate analysis to types which are not Euclidean spaces, such as the extended real numbers, bounded continuous functions, or finite maps.