# The Lambda Calculus, 185.299

Type: VU, 2.0 Std. (WS 2005/2006)

Lecturer: Alexander Leitsch

The lambda-calculus was developed around 1934 as tool to formalize the concept
of computable functions and to provide a firm foundation to mathematical
logic. In more recent times the lambda-calculus proved crucial in the
development of functional programming languages (like LISP) and in semantics
of programming languages (denotational semantics). Generally the
lambda-calculus is a flexible and powerful formalism connecting problems
in * logic*, * metamathematics* and * computer science*.

In the course we concentrate mainly on the mathematical foundations of the
Lambda calculus. The topics in more detail: syntax, lambda-conversion,
*beta*-reduction, *eta*-reduction, normal form, confluence and
termination, extensionality, the Church-Rosser theorem, lambda-definability,
numeral systems, recursive functions, undecidability results. Finally we
focus on combinatory logic, and the semantics of the lambda-calculus
(combinatory algebras).

The course is based on the textbook *The Lambda Calculus* from H.P.
Barendregt, North Holland, 1985.

## First meeting:

Monday, October 9 2006, 13:15

Zemanek Hoersaal, Favoritenstrasse 9, ground floor

## Preconditions:

none, but some basic knowledge in mathematical logic and theoretical computer science is helpful.

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