Type Theory and Formal Proof

Rob Nederpelt was Lecturer in Logic for Computer Science until his retirement. Currently he is a guest researcher in the Faculty of Mathematics and Computer Science at Eindhoven University of Technology, The Netherlands. Herman Geuvers is Professor in Theoretical Informatics at the Radboud University Nijmegen, and Professor in Proving with Computer Assistance at Eindhoven University of Technology, both in The Netherlands.

• Foreword; Preface; Acknowledgements; Greek alphabet; 1. Untyped lambda calculus; 2. Simply typed lambda calculus; 3. Second order typed lambda calculus; 4. Types dependent on types; 5. Types dependent on terms; 6. The Calculus of Constructions; 7. The encoding of logical notions in λC; 8. Definitions; 9. Extension of λC with definitions; 10. Rules and properties of λD; 11. Flag-style natural deduction in λD; 12. Mathematics in λD: a first attempt; 13. Sets and subsets; 14. Numbers and arithmetic in λD; 15. An elaborated example; 16. Further perspectives; Appendix A. Logic in λD; Appendix B. Arithmetical axioms, definitions and lemmas; Appendix C. Two complete example proofs in λD; Appendix D. Derivation rules for λD; References; Index of names; Index of technical notions; Index of defined constants; Index of subjects.