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Computer-Supported Modeling and Reasoning - Lectures

Date Topic
20.10.2004 Organizational matters, Introduction, Propositional logic
27.10.2004 First-order logic
03.11.2004 Equality, Theories
10.11.2004 Sets, The lambda-calculus
17.11.2004 The lambda-calculus, Metatheory: Representing syntax in the typed lambda-calculus
24.11.2004 Resolution, Proof Search
01.12.2004 Rewriting, Isabelle's Metalogic
03.12.2004 (52-00-016) Isabelle's Metalogic
08.12.2004 Isabelle's Metalogic, HOL: Introduction
10.12.2004 (52-00-016) HOL: Introduction
15.12.2004 HOL: Derived rules, towards using HOL
22.12.2004 Conservative extensions, HOL Library, Orders, Sets, Functions
12.01.2005 Background: Recursion, Induction, and Fixpoints, Least Fixpoints
19.01.2005 Well-Founded Recursion
26.01.2005 Arithmetic, Datatypes
02.02.2005 Datatypes, Imperative Languages
09.02.2005 Imperative Languages
16.02.2005 Imperative Languages,Some Isabelle and HOL Applications

Lecture Notes for printout (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
  • 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.