Computer-Supported Modeling and Reasoning - Lectures

Date Topic
19.10.2009 Organizational matters, Introduction, Propositional logic
26.10.2009 Propositional logic, First-order logic
02.11.2009 First-order logic, Equality, Theories
09.11.2009 Sets, The lambda-calculus
11.11.2009 The lambda-calculus
16.11.2009 The lambda-calculus, Metatheory: Representing syntax in the typed lambda-calculus
23.11.2009 Metatheory: Representing syntax in the typed lambda-calculus, Resolution, Proof Search
25.11.2009 Proof Search, Rewriting
30.11.2009 Isabelle's Metalogic
02.12.2009 Isabelle's Metalogic
07.12.2009 Isabelle's Metalogic
09.12.2009 HOL: Introduction
14.12.2009 HOL: Introduction, HOL: Derived Rules
18.12.2009 Conservative extensions, HOL Library, Orders, Sets
21.12.2009 Functions, Background: Recursion, Induction, and Fixpoints, A Taste of some Isabelle and HOL Applications
11.01.2010 Least Fixpoints, Well-Founded Recursion
18.01.2010 Well-Founded Recursion
20.01.2010 Arithmetic
25.01.2010 Datatypes, Imperative Languages
01.02.2010 Imperative Languages
08.02.2010 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.