Fall 2000, CSE 520: Lecture 1


The Lambda Calculus

Some history

The Type-Free Lambda Calculus

Sintax

The terms of the lambda calculus are constructed over variables and two basic operations:

Formal syntax

Variables: V ::= x | y | z | ...
Lambda-Terms: M ::= V | (\V M) | (M M)

Notational convention

M1M2 ... Mk stands for ( ... (M1M2) ... Mk)
\x1x2 ... xk.M stands for (\x1(\x2 ... (\xk M) ... ))