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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)

NEW Screen Notes for online study (work in progress) NEW

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

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.