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Computer-Supported Modeling and Reasoning - Lectures
| Date | Topic |
|---|---|
| 26.10.2005 | Organizational matters, Introduction, Propositional logic |
| 02.11.2005 | First-order logic |
| 09.11.2005 | Equality, Theories |
| 16.11.2005 | Sets, The lambda-calculus |
| 23.11.2005 | The lambda-calculus, Metatheory: Representing syntax in the typed lambda-calculus |
| 30.11.2005 | Resolution, Proof Search |
| 07.12.2005 | Rewriting, Isabelle's Metalogic |
| 09.12.2005 | Isabelle's Metalogic |
| 14.12.2005 | HOL: Introduction |
| 21.12.2005 | HOL: Derived Rules, towards Using HOL, Conservative extensions |
| 23.12.2005 | Some Isabelle and HOL Applications |
| 11.01.2006 | Conservative extensions, HOL Library, Orders, Sets, Functions, Background: Recursion, Induction, and Fixpoints |
| 18.01.2006 | Background: Recursion, Induction, and Fixpoints, Least Fixpoints, Well-Founded Recursion |
| 25.01.2006 | Well-Founded Recursion |
| 27.01.2006 | Arithmetic |
| 01.02.2006 | Datatypes, Imperative Languages |
| 08.02.2006 | Imperative Languages |
| 15.02.2006 | Imperative Languages |
Lecture Notes for printout (work in progress)
Screen Notes for online study (work in progress)
The course is now finished.
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.