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.

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

Autorentext

Clara Löh is Professor of Mathematics at the University of Regensburg, Germany. Her research focuses on simplicial volume and the interaction between geometric topology, geometric group theory, and measured group theory. This includes cohomological, geometric, and combinatorial methods. She is also interested in the foundations of mathematics and the formalisation/verification of mathematics in proof assistants.

Klappentext

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

Inhalt

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