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Exploring Formalisation: A Primer in Human-Readable Mathematics in Lean 3 with Examples from Simplicial Topology
This primer on mathematics formalisation provides a rapid, hands-on introduction to proof verification in Lean.
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 elementary category theory and algebraic topology is recommended.
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 elementary category theory and algebraic topology is recommended.
153 pages, Paperback
Published September 25, 2022
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March 9, 2025
A fascinating overview of the why and how of proof assistants. Goes through topology, algebra, and graph-theoretic examples of proof by hand and in the Lean software. Clearly written with readable code, worth a look for anyone interested in the subject of mathematical proof and applications of computing in the formal sciences.
Displaying 1 of 1 review