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Computer-Supported Modeling and Reasoning - Lectures

Date Topic
20.10.2008 Organizational matters, Introduction, Propositional logic
27.10.2008 First-order logic
03.11.2008 Equality, Theories, Sets
10.11.2008 The lambda-calculus
17.11.2008 The lambda-calculus, Metatheory: Representing syntax in the typed lambda-calculus
24.11.2008 Metatheory: Representing syntax in the typed lambda-calculus, Resolution
26.11.2008 Proof Search, Rewriting
01.12.2008 Rewriting, Isabelle's Metalogic
03.12.2008 Isabelle's Metalogic
08.12.2008 Isabelle's Metalogic, HOL: Introduction
10.12.2008 HOL: Introduction
15.12.2008 HOL: Derived Rules, Conservative extensions
17.12.2008 Conservative extensions, HOL Library, Some Isabelle and HOL Applications
22.12.2008 Orders, Sets, Functions Background: Recursion, Induction, and Fixpoints, Least Fixpoints
12.01.2009 Least Fixpoints, Well-Founded Recursion
19.01.2009 Well-Founded Recursion
21.01.2009 Arithmetic
26.01.2009 Datatypes, Imperative Languages
02.02.2009 Imperative Languages
09.02.2009 Imperative Languages

Lecture Notes for printout

Screen Notes for online study

The course is now finished.


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


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.