Overview
- Example driven: each topic is first presented in pen-and-paper style and then formalised in Lean
- Starts at a very elementary level and ends with examples from current research
- Aims for human-readable code and includes a variety of exercises
Part of the book series: Surveys and Tutorials in the Applied Mathematical Sciences (STAMS, volume 11)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
After a quick introduction to Lean, the basic techniques of human-readable formalisation are introduced, illustrated by simple examples on maps, induction and real numbers. Subsequently, typical design options are discussed and brought to life through worked examples in the setting of simplicial complexes (a higher-dimensional generalisation of graph theory). Finally, the book demonstrates how current research in algebraic and geometric topology can be formalised by means of suitable abstraction layers.
Informed by the author's recent teaching and research experience, this book allows students and researchers to quickly get started with formalising and checking their proofs. The core material of the book is accessible to mathematics students with basic programming skills. For the final chapter, familiarity with elementarycategory theory and algebraic topology is recommended.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Exploring Formalisation
Book Subtitle: A Primer in Human-Readable Mathematics in Lean 3 with Examples from Simplicial Topology
Authors: Clara Löh
Series Title: Surveys and Tutorials in the Applied Mathematical Sciences
DOI: https://doi.org/10.1007/978-3-031-14649-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-14648-0Published: 25 September 2022
eBook ISBN: 978-3-031-14649-7Published: 24 September 2022
Series ISSN: 2199-4765
Series E-ISSN: 2199-4773
Edition Number: 1
Number of Pages: VI, 147
Number of Illustrations: 1 b/w illustrations
Topics: Mathematical Logic and Foundations, Algebraic Topology, Mathematical Logic and Formal Languages, Symbolic and Algebraic Manipulation, Topology