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Computer-Supported Modeling and Reasoning - Lectures
| Date | Topic |
|---|---|
| 22.10.2007 | Organizational matters, Introduction, Propositional logic |
| 29.10.2007 | First-order logic |
| 05.11.2007 | Equality, Theories, Sets |
| 12.11.2007 | The lambda-calculus |
| 19.11.2007 | The lambda-calculus, Metatheory: Representing syntax in the typed lambda-calculus |
| Metatheory: Representing syntax in the typed lambda-calculus | |
| 26.11.2007 | Resolution, Proof Search, Rewriting |
| 03.12.2007 | Rewriting, Isabelle's Metalogic |
| Isabelle's Metalogic | |
| 10.12.2007 | Isabelle's Metalogic, HOL: Introduction |
| HOL: Introduction | |
| 17.12.2007 | HOL: Derived Rules, Some Isabelle and HOL Applications |
| 07.01.2008 | Conservative extensions |
| Conservative extensions, HOL Library, Orders, Sets | |
| 14.01.2008 | Functions, Background: Recursion, Induction, and Fixpoints, Least Fixpoints |
| 21.01.2008 | Well-Founded Recursion |
| 28.01.2008 | Arithmetic |
| Datatypes | |
| 04.02.2008 | Imperative Languages |
| 11.02.2008 | Imperative Languages |
Lecture Notes for printout
Screen Notes for online study
Literature
Books and articles
- D. van Dalen: Logic and Structure. Springer-Verlag, 1980. An introductory textbook on logic
- Michael Huth and Mark Ryan: Logic in Computer Science. Modelling and Reasoning about Systems. Cambridge University Press, 2004. This book covers many of the topics of the lecture. It is interesting because it uses a style of doing natural deduction proofs that is different from the one we use in the lecture.
- Simon Thompson: Type Theory and Functional Programming. Addison-Wesley, 1991. Chapter 1 is an introduction to propositional and first-order logic. Chapter 2 is an introduction to the lambda-calculus.
- David Basin and Seán Matthews: Logical Frameworks. In Dov Gabbay and Franz Guenthner, editors, Handbook of Philosophical Logic, second edition. Reidel, 2002.
- N.G. de Bruijn: A Survey of the Project AUTOMATH. In Essays in Combinatory Logic, Lambda Calculus, and Formalism. Academic Press, 1980.
- Robert Harper, Furio Honsell, and Gordon D. Plotkin: A Framework for Defining Logics. Journal of the ACM, 40(1):143-184, 1993.
- Arnon Avron, Furio Honsell, Ian A. Mason, and Robert Pollack: Using Typed Lambda Calculus to Implement Formal Systems on a Machine. Journal of Automated Reasoning 9(3):309-354, 1992
- Henk Barendregt: Introduction to Generalized Type Systems. Journal of Functional Programming 1(2):125-154, 1991.
- Lawrence C. Paulson: Isabelle: A Generic Theorem Prover. Springer LNCS 828, 1994.
- Tobias Nipkow: Hoare Logics in Isabelle/HOL. In H. Schwichtenberg and R. Steinbrüggen, editors, Proceedings of Proof and System-Reliability, pages 341-367, Kluwer, 2002.
Manuals and Tutorials
- Proof General
- Isabelle (Cambridge) (München). You will find lots of documentation there, including the
- Sara Kalvala: A gentle introduction to Isabelle.
Projects
- Angelika Kimmig: Red-black Trees of slmnj. A Studienarbeit by a former student of this course.
- Larry Paulson: Overview of Isabelle Projects.
Related Lectures
- Larry Paulson: Logic and Proof. An introductory lecture on logic, mainly on syntax and semantics of propositional and first-order logic, and proof systems for those logics.
- Frank Pfenning: Automated Theorem Proving.