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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
21.11.2007 Metatheory: Representing syntax in the typed lambda-calculus
26.11.2007 Resolution, Proof Search, Rewriting
03.12.2007 Rewriting, Isabelle's Metalogic
05.12.2007 Isabelle's Metalogic
10.12.2007 Isabelle's Metalogic, HOL: Introduction
12.12.2007 HOL: Introduction
17.12.2007 HOL: Derived Rules, Some Isabelle and HOL Applications
07.01.2008 Conservative extensions
09.01.2008 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
30.01.2008 Datatypes
04.02.2008 Imperative Languages
11.02.2008 Imperative Languages

Lecture Notes for printout

Screen Notes for online study


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.