Exploring Formalisation : A Primer in Human-Readable Mathematics in Lean 3 with Examples from Simplicial Topology (Surveys and Tutorials in the Applied Mathematical Sciences)

Löh, Clara

Springer International Publishing AG（2022/09発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 147 p.
• 商品コード 9783031146480

Full Description

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 elementarycategory theory and algebraic topology is recommended.

Contents

Introduction.- 1 The Lean Proof Assistant.- 2 Basic Examples.- 3 Design Choices.- 4 Abstraction and Prototyping.